@article {3461, title = {Quantum One-Wayness of the Single-Round Sponge with Invertible Permutations}, year = {2024}, month = {3/7/2024}, abstract = {

Sponge hashing is a novel class of cryptographic hash algorithms which underlies the current international hash function standard SHA-3. In a nutshell, a sponge function takes as input a bit-stream of any length and processes it via a simple iterative procedure: it repeatedly feeds each block of the input into a so-called block function, and then produces a short digest which consists of a subset of the final output bits. While much is known about the post-quantum security of the sponge construction in the case when the block function is modeled as a random function or permutation, the case of invertible permutations, which more accurately models the construction underlying SHA-3, has so far remained a fundamental open problem.
In this work, we make new progress towards overcoming this barrier and show several results. First, we prove the \"double-sided zero-search\" conjecture proposed by Unruh (eprint\&$\#$39; 2021) and show that finding zero-pairs in a random 2n-bit permutation requires at least Ω(2n/2) many queries -- and this is tight due to Grover\&$\#$39;s algorithm. At the core of our proof lies a novel \"symmetrization argument\" which uses insights from the theory of Young subgroups. Second, we consider more general variants of the double-sided search problem and show similar query lower bounds for them. As an application, we prove the quantum one-wayness of the single-round sponge with invertible permutations in the quantum random oracle model.

}, url = {https://arxiv.org/abs/2403.04740}, author = {Joseph Carolan and Alexander Poremba} } @article {3257, title = {Accelerating Progress Towards Practical Quantum Advantage: The Quantum Technology Demonstration Project Roadmap}, year = {2023}, month = {3/20/2023}, abstract = {

Quantum information science and technology (QIST) is a critical and emerging technology with the potential for enormous world impact and is currently invested in by over 40 nations. To bring these large-scale investments to fruition and bridge the lower technology readiness levels (TRLs) of fundamental research at universities to the high TRLs necessary to realize the promise of practical quantum advantage accessible to industry and the public, we present a roadmap for Quantum Technology Demonstration Projects (QTDPs). Such QTDPs, focused on intermediate TRLs, are large-scale public-private partnerships with a high probability of translation from laboratory to practice. They create technology demonstrating a clear \&$\#$39;quantum advantage\&$\#$39; for science breakthroughs that are user-motivated and will provide access to a broad and diverse community of scientific users. Successful implementation of a program of QTDPs will have large positive economic impacts.

}, url = {https://arxiv.org/abs/2210.14757}, author = {Paul Alsing and Phil Battle and Joshua C. Bienfang and Tammie Borders and Tina Brower-Thomas and Lincoln D. Carr and Fred Chong and Siamak Dadras and Brian DeMarco and Ivan Deutsch and Eden Figueroa and Danna Freedman and Henry Everitt and Daniel Gauthier and Ezekiel Johnston-Halperin and Jungsang Kim and Mackillo Kira and Prem Kumar and Paul Kwiat and John Lekki and Anjul Loiacono and Marko Lon{\v c}ar and John R. Lowell and Mikhail Lukin and Celia Merzbacher and Aaron Miller and Christopher Monroe and Johannes Pollanen and David Pappas and Michael Raymer and Ronald Reano and Brandon Rodenburg and Martin Savage and Thomas Searles and Jun Ye} } @article {3056, title = {Advantages and limitations of quantum routing}, journal = {PRX Quantum}, volume = {4}, year = {2023}, month = {2/1/2023}, abstract = {

The Swap gate is a ubiquitous tool for moving information on quantum hardware, yet it can be considered a classical operation because it does not entangle product states. Genuinely quantum operations could outperform Swap for the task of permuting qubits within an architecture, which we call routing. We consider quantum routing in two models: (1) allowing arbitrary two-qubit unitaries, or (2) allowing Hamiltonians with norm-bounded interactions. We lower bound the circuit depth or time of quantum routing in terms of spectral properties of graphs representing the architecture interaction constraints, and give a generalized upper bound for all simple connected n-vertex graphs. In particular, we give conditions for a superpolynomial classical-quantum routing separation, which exclude graphs with a small spectral gap and graphs of bounded degree. Finally, we provide examples of a quadratic separation between gate-based and Hamiltonian routing models with a constant number of local ancillas per qubit and of an Ω(n) speedup if we also allow fast local interactions.

}, keywords = {Data Structures and Algorithms (cs.DS), FOS: Computer and information sciences, FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {https://doi.org/10.1103/PRXQuantum.4.010313}, url = {https://arxiv.org/abs/2206.01766}, author = {Bapat, Aniruddha and Andrew M. Childs and Alexey V. Gorshkov and Schoute, Eddie} } @article {3246, title = {Analyzing Convergence in Quantum Neural Networks: Deviations from Neural Tangent Kernels}, year = {2023}, month = {3/26/2023}, abstract = {

A quantum neural network (QNN) is a parameterized mapping efficiently implementable on near-term Noisy Intermediate-Scale Quantum (NISQ) computers. It can be used for supervised learning when combined with classical gradient-based optimizers. Despite the existing empirical and theoretical investigations, the convergence of QNN training is not fully understood. Inspired by the success of the neural tangent kernels (NTKs) in probing into the dynamics of classical neural networks, a recent line of works proposes to study over-parameterized QNNs by examining a quantum version of tangent kernels. In this work, we study the dynamics of QNNs and show that contrary to popular belief it is qualitatively different from that of any kernel regression: due to the unitarity of quantum operations, there is a non-negligible deviation from the tangent kernel regression derived at the random initialization. As a result of the deviation, we prove the at-most sublinear convergence for QNNs with Pauli measurements, which is beyond the explanatory power of any kernel regression dynamics. We then present the actual dynamics of QNNs in the limit of over-parameterization. The new dynamics capture the change of convergence rate during training and implies that the range of measurements is crucial to the fast QNN convergence.

}, url = {https://arxiv.org/abs/2303.14844}, author = {Xuchen You and Shouvanik Chakrabarti and Boyang Chen and Xiaodi Wu} } @article {3248, title = {Collision-resolved pressure sensing}, year = {2023}, month = {3/17/2023}, abstract = {

Heat and pressure are ultimately transmitted via quantized degrees of freedom, like gas particles and phonons. While a continuous Brownian description of these noise sources is adequate to model measurements with relatively long integration times, sufficiently precise measurements can resolve the detailed time dependence coming from individual bath-system interactions. We propose the use of nanomechanical devices operated with impulse readout sensitivity around the {\textquoteleft}{\textquoteleft}standard quantum limit\&$\#$39;\&$\#$39; to sense ultra-low gas pressures by directly counting the individual collisions of gas particles on a sensor. We illustrate this in two paradigmatic model systems: an optically levitated nanobead and a tethered membrane system in a phononic bandgap shield.

}, url = {https://arxiv.org/abs/2303.09922}, author = {Daniel S. Barker and Daniel Carney and Thomas W. LeBrun and David C. Moore and Jacob M. Taylor} } @article {3415, title = {Compressed gate characterization for quantum devices with time-correlated noise}, year = {2023}, month = {12/22/2023}, abstract = {

As quantum devices make steady progress towards intermediate scale and fault-tolerant quantum computing, it is essential to develop rigorous and efficient measurement protocols that account for known sources of noise. Most existing quantum characterization protocols such as gate set tomography and randomized benchmarking assume the noise acting on the qubits is Markovian. However, this assumption is often not valid, as for the case of 1/f charge noise or hyperfine nuclear spin noise. Here, we present a general framework for quantum process tomography (QPT) in the presence of time-correlated noise. We further introduce fidelity benchmarks that quantify the relative strength of different sources of Markovian and non-Markovian noise. As an application of our method, we perform a comparative theoretical and experimental analysis of silicon spin qubits. We first develop a detailed noise model that accounts for the dominant sources of noise and validate the model against experimental data. Applying our framework for time-correlated QPT, we find that the number of independent parameters needed to characterize one and two-qubit gates can be compressed by 10x and 100x, respectively, when compared to the fully generic case. These compressions reduce the amount of tomographic measurements needed in experiment, while also significantly speeding up numerical simulations of noisy quantum circuit dynamics compared to time-dependent Hamiltonian simulation. Using this compressed noise model, we find good agreement between our theoretically predicted process fidelities and two qubit interleaved randomized benchmarking fidelities of 99.8\% measured in recent experiments on silicon spin qubits. More broadly, our formalism can be directly extended to develop efficient and scalable tuning protocols for high-fidelity control of large-arrays of quantum devices with non-Markovian noise.

}, url = {https://arxiv.org/abs/2307.14432}, author = {M. J. Gullans and M. Caranti and A. R. Mills and J. R. Petta} } @article {3396, title = {Data Needs and Challenges of Quantum Dot Devices Automation: Workshop Report}, year = {2023}, month = {12/21/2023}, abstract = {

Gate-defined quantum dots are a promising candidate system to realize scalable, coupled qubit systems and serve as a fundamental building block for quantum computers. However, present-day quantum dot devices suffer from imperfections that must be accounted for, which hinders the characterization, tuning, and operation process. Moreover, with an increasing number of quantum dot qubits, the relevant parameter space grows sufficiently to make heuristic control infeasible. Thus, it is imperative that reliable and scalable autonomous tuning approaches are developed. In this report, we outline current challenges in automating quantum dot device tuning and operation with a particular focus on datasets, benchmarking, and standardization. We also present ideas put forward by the quantum dot community on how to overcome them.

}, doi = {https://doi.org/10.48550/arXiv.2312.14322}, url = {https://arxiv.org/abs/2312.14322}, author = {Justyna P. Zwolak and Jacob M. Taylor and Reed Andrews and Jared Benson and Garnett Bryant and Donovan Buterakos and Anasua Chatterjee and Sankar Das Sarma and Mark A. Eriksson and Eli{\v s}ka Greplov{\'a} and Michael J. Gullans and Fabian Hader and Tyler J. Kovach and Pranav S. Mundada and Mick Ramsey and Torbjoern Rasmussen and Brandon Severin and Anthony Sigillito and Brennan Undseth and Brian Weber} } @article {3074, title = {Decoherence from Long-Range Forces in Atom Interferometry}, journal = {Phys. Rev. A }, volume = {107}, year = {2023}, month = {3/17/2023}, doi = {https://doi.org/10.1103/PhysRevA.107.033319}, url = {https://arxiv.org/abs/2205.03006}, author = {Jonathan Kunjummen and Daniel Carney and Jacob M. Taylor} } @article {3421, title = {Digital quantum simulation of NMR experiments}, journal = {Science Advances}, volume = {9}, year = {2023}, month = {11/29/2023}, abstract = {

Simulations of nuclear magnetic resonance (NMR) experiments can be an important tool for extracting information about molecular structure and optimizing experimental protocols but are often intractable on classical computers for large molecules such as proteins and for protocols such as zero-field NMR. We demonstrate the first quantum simulation of an NMR spectrum, computing the zero-field spectrum of the methyl group of acetonitrile using four qubits of a trapped-ion quantum computer. We reduce the sampling cost of the quantum simulation by an order of magnitude using compressed sensing techniques. We show how the intrinsic decoherence of NMR systems may enable the zero-field simulation of classically hard molecules on relatively near-term quantum hardware and discuss how the experimentally demonstrated quantum algorithm can be used to efficiently simulate scientifically and technologically relevant solid-state NMR experiments on more mature devices. Our work opens a practical application for quantum computation.

}, issn = {2375-2548}, doi = {10.1126/sciadv.adh2594}, url = {https://arxiv.org/abs/2109.13298}, author = {Seetharam, Kushal and Biswas, Debopriyo and Noel, Crystal and Risinger, Andrew and Zhu, Daiwei and Katz, Or and Chattopadhyay, Sambuddha and Cetina, Marko and Monroe, Christopher and Demler, Eugene and Sels, Dries} } @article {3426, title = {The discrete adiabatic quantum linear system solver has lower constant factors than the randomized adiabatic solver}, year = {2023}, month = {12/12/2023}, abstract = {

The solution of linear systems of equations is the basis of many other quantum algorithms, and recent results provided an algorithm with optimal scaling in both the condition number κ and the allowable error ϵ [PRX Quantum \textbf{3}, 0403003 (2022)]. That work was based on the discrete adiabatic theorem, and worked out an explicit constant factor for an upper bound on the complexity. Here we show via numerical testing on random matrices that the constant factor is in practice about 1,500 times smaller than the upper bound found numerically in the previous results. That means that this approach is far more efficient than might naively be expected from the upper bound. In particular, it is over an order of magnitude more efficient than using a randomised approach from [arXiv:2305.11352] that claimed to be more efficient.

}, url = {https://arxiv.org/abs/2312.07690}, author = {Pedro C. S. Costa and Dong An and Ryan Babbush and Dominic Berry} } @article {3261, title = {Ever more optimized simulations of fermionic systems on a quantum computer}, year = {2023}, month = {3/6/2023}, abstract = {

Despite using a novel model of computation, quantum computers break down programs into elementary gates. Among such gates, entangling gates are the most expensive. In the context of fermionic simulations, we develop a suite of compilation and optimization techniques that massively reduce the entangling-gate counts. We exploit the well-studied non-quantum optimization algorithms to achieve up to 24\% savings over the state of the art for several small-molecule simulations, with no loss of accuracy or hidden costs. Our methodologies straightforwardly generalize to wider classes of near-term simulations of the ground state of a fermionic system or real-time simulations probing dynamical properties of a fermionic system.\ 

}, url = {https://arxiv.org/abs/2303.03460}, author = {Qingfeng Wang and Ze-Pei Cian and Ming Li and Igor L. Markov and Yunseong Nam} } @article {3126, title = {Fat Pointers for Temporal Memory Safety of C}, journal = {Proceedings of the ACM on Programming Languages}, volume = {7}, year = {2023}, month = {3/20/2023}, pages = {316-347}, abstract = {

Temporal memory safety bugs, especially use-after-free and double free bugs, pose a major security threat to C programs. Real-world exploits utilizing these bugs enable attackers to read and write arbitrary memory locations, causing disastrous violations of confidentiality, integrity, and availability. Many previous solutions retrofit temporal memory safety to C, but they all either incur high performance overhead and/or miss detecting certain types of temporal memory safety bugs.
In this paper, we propose a temporal memory safety solution that is both efficient and comprehensive. Specifically, we extend Checked C, a spatially-safe extension to C, with temporally-safe pointers. These are implemented by combining two techniques: fat pointers and dynamic key-lock checks. We show that the fat-pointer solution significantly improves running time and memory overhead compared to the disjoint-metadata approach that provides the same level of protection. With empirical program data and hands-on experience porting real-world applications, we also show that our solution is practical in terms of backward compatibility -- one of the major complaints about fat pointers.

}, keywords = {Cryptography and Security (cs.CR), FOS: Computer and information sciences}, doi = {10.1145/3586038}, url = {https://arxiv.org/abs/2208.12900}, author = {Zhou, Jie and Criswell, John and Hicks, Michael} } @article {3408, title = {A general approach to backaction-evading receivers with magnetomechanical and electromechanical sensors}, year = {2023}, month = {11/16/2023}, abstract = {

Today\&$\#$39;s mechanical sensors are capable of detecting extremely weak perturbations while operating near the standard quantum limit. However, further improvements can be made in both sensitivity and bandwidth when we reduce the noise originating from the process of measurement itself -- the quantum-mechanical backaction of measurement -- and go below this \&$\#$39;standard\&$\#$39; limit, possibly approaching the Heisenberg limit. One of the ways to eliminate this noise is by measuring a quantum nondemolition variable such as the momentum in a free-particle system. Here, we propose and characterize theoretical models for direct velocity measurement that utilize traditional electric and magnetic transducer designs to generate a signal while enabling this backaction evasion. We consider the general readout of this signal via electric or magnetic field sensing by creating toy models analogous to the standard optomechanical position-sensing problem, thereby facilitating the assessment of measurement-added noise. Using simple models that characterize a wide range of transducers, we find that the choice of readout scheme -- voltage or current -- for each mechanical detector configuration implies access to either the position or velocity of the mechanical sub-system. This in turn suggests a path forward for key fundamental physics experiments such as the direct detection of dark matter particles.

}, url = {https://arxiv.org/abs/2311.09587}, author = {Brittany Richman and Sohitri Ghosh and Daniel Carney and Gerard Higgins and Peter Shawhan and C. J. Lobb and Jacob M. Taylor} } @article {3428, title = {Generalized Hybrid Search and Applications to Blockchain and Hash Function Security}, year = {2023}, month = {11/7/2023}, abstract = {

In this work we first examine the hardness of solving various search problems by hybrid quantum-classical strategies, namely, by algorithms that have both quantum and classical capabilities. We then construct a hybrid quantum-classical search algorithm and analyze its success probability. Regarding the former, for search problems that are allowed to have multiple solutions and in which the input is sampled according to arbitrary distributions we establish their hybrid quantum-classical query complexities -- i.e., given a fixed number of classical and quantum queries, determine what is the probability of solving the search task. At a technical level, our results generalize the framework for hybrid quantum-classical search algorithms proposed by Rosmanis. Namely, for an arbitrary distribution D on Boolean functions, the probability an algorithm equipped with τc classical and τq quantum queries succeeds in finding a preimage of 1 for a function sampled from D is at most νD\⋅(2τc\−\−\√+2τq+1)2, where νD captures the average (over D) fraction of preimages of 1. As applications of our hardness results, we first revisit and generalize the security of the Bitcoin protocol called the Bitcoin backbone, to a setting where the adversary has both quantum and classical capabilities, presenting a new hybrid honest majority condition necessary for the protocol to properly operate. Secondly, we examine the generic security of hash functions against hybrid adversaries. Regarding our second contribution, we design a hybrid algorithm which first spends all of its classical queries and in the second stage runs a {\textquoteleft}{\textquoteleft}modified Grover\&$\#$39;\&$\#$39; where the initial state depends on the distribution D. We show how to analyze its success probability for arbitrary target distributions and, importantly, its optimality for the uniform and the Bernoulli distribution cases.

}, url = {arXiv:2311.03723}, author = {Alexandru Cojocaru and Juan Garay and Fang Song} } @article {3356, title = {Hamiltonians whose low-energy states require $\Omega(n)$ T gates}, year = {2023}, month = {10/2/2023}, abstract = {

The recent resolution of the NLTS Conjecture [ABN22] establishes a prerequisite to the Quantum PCP (QPCP) Conjecture through a novel use of newly-constructed QLDPC codes [LZ22]. Even with NLTS now solved, there remain many independent and unresolved prerequisites to the QPCP Conjecture, such as the NLSS Conjecture of [GL22]. In this work we focus on a specific and natural prerequisite to both NLSS and the QPCP Conjecture, namely, the existence of local Hamiltonians whose low-energy states all require ω(logn) T gates to prepare. In fact, we prove a stronger result which is not necessarily implied by either conjecture: we construct local Hamiltonians whose low-energy states require Ω(n) T gates. Following a previous work [CCNN23], we further show that our procedure can be applied to the NLTS Hamiltonians of [ABN22] to yield local Hamiltonians whose low-energy states require both Ω(logn)-depth and Ω(n) T gates to prepare. Our results utilize a connection between T-count and stabilizer groups, which was recently applied in the context of learning low T-count states [GIKL23a, GIKL23b, GIKL23c].

}, url = {https://arxiv.org/abs/2310.01347}, author = {Nolan J. Coble and Matthew Coudron and Jon Nelson and Seyed Sajjad Nezhadi} } @article {3352, title = {Ion Trap with In-Vacuum High Numerical Aperture Imaging for a Dual-Species Modular Quantum Computer}, year = {2023}, month = {10/10/2023}, abstract = {

Photonic interconnects between quantum systems will play a central role in both scalable quantum computing and quantum networking. Entanglement of remote qubits via photons has been demonstrated in many platforms; however, improving the rate of entanglement generation will be instrumental for integrating photonic links into modular quantum computers. We present an ion trap system that has the highest reported free-space photon collection efficiency for quantum networking. We use a pair of in-vacuum aspheric lenses, each with a numerical aperture of 0.8, to couple 10\% of the 493 nm photons emitted from a 138Ba+ ion into single-mode fibers. We also demonstrate that proximal effects of the lenses on the ion position and motion can be mitigated.

}, url = {https://arxiv.org/abs/2310.07058}, author = {Allison L. Carter and Jameson O{\textquoteright}Reilly and George Toh and Sagnik Saha and Mikhail Shalaev and Isabella Goetting and Christopher Monroe} } @article {3252, title = {Local Hamiltonians with no low-energy stabilizer states}, year = {2023}, month = {2/28/2023}, abstract = {

The recently-defined No Low-energy Sampleable States (NLSS) conjecture of Gharibian and Le Gall [GL22] posits the existence of a family of local Hamiltonians where all states of low-enough constant energy do not have succinct representations allowing perfect sampling access. States that can be prepared using only Clifford gates (i.e. stabilizer states) are an example of sampleable states, so the NLSS conjecture implies the existence of local Hamiltonians whose low-energy space contains no stabilizer states. We describe families that exhibit this requisite property via a simple alteration to local Hamiltonians corresponding to CSS codes. Our method can also be applied to the recent NLTS Hamiltonians of Anshu, Breuckmann, and Nirkhe [ABN22], resulting in a family of local Hamiltonians whose low-energy space contains neither stabilizer states nor trivial states. We hope that our techniques will eventually be helpful for constructing Hamiltonians which simultaneously satisfy NLSS and NLTS.

}, url = {https://arxiv.org/abs/2302.14755}, author = {Nolan J. Coble and Matthew Coudron and Jon Nelson and Seyed Sajjad Nezhadi} } @article {3401, title = {Logical quantum processor based on reconfigurable atom arrays}, journal = {Nature}, year = {2023}, month = {12/7/2023}, issn = {1476-4687}, doi = {10.1038/s41586-023-06927-3}, url = {https://arxiv.org/abs/2312.03982}, author = {Bluvstein, Dolev and Evered, Simon J. and Geim, Alexandra A. and Li, Sophie H. and Zhou, Hengyun and Manovitz, Tom and Ebadi, Sepehr and Cain, Madelyn and Kalinowski, Marcin and Hangleiter, Dominik and Ataides, J. Pablo Bonilla and Maskara, Nishad and Cong, Iris and Gao, Xun and Rodriguez, Pedro Sales and Karolyshyn, Thomas and Semeghini, Giulia and Gullans, Michael J. and Greiner, Markus and Vuletic, Vladan and Lukin, Mikhail D.} } @article {3247, title = {The maximum refractive index of an atomic crystal - from quantum optics to quantum chemistry}, year = {2023}, month = {3/20/2023}, abstract = {

All known optical materials have an index of refraction of order unity. Despite the tremendous implications that an ultrahigh index could have for optical technologies, little research has been done on why the refractive index of materials is universally small, and whether this observation is fundamental. Here, we investigate the index of an ordered arrangement of atoms, as a function of atomic density. At dilute densities, this problem falls into the realm of quantum optics, where atoms do not interact with one another except via the scattering of light. On the other hand, when the lattice constant becomes comparable to the Bohr radius, the electronic orbitals begin to overlap, giving rise to quantum chemistry. We present a minimal model that allows for a unifying theory of index spanning these two regimes. A key aspect is the treatment of multiple light scattering, which can be highly non-perturbative over a large density range, and which is the reason that conventional theories of the index break down. In the quantum optics regime, we show that ideal light-matter interactions can have a single-mode nature, allowing for a purely real refractive index that grows with density as (N/V)1/3. At the onset of quantum chemistry, we show how two physical mechanisms (excited electron tunneling dynamics and the buildup of electronic density-density correlations) can open up inelastic or spatial multi-mode light scattering processes, which ultimately reduce the index back to order unity while introducing absorption. Around the onset of chemistry, our theory predicts that ultrahigh index (n\∼30), low-loss materials could in principle be allowed by the laws of nature.\ 

}, url = {https://arxiv.org/abs/2303.10998}, author = {Francesco Andreoli and Bennet Windt and Stefano Grava and Gian Marcello Andolina and Michael J. Gullans and Alexander A. High and Darrick E. Chang} } @article {3395, title = {Microwave signal processing using an analog quantum reservoir computer}, year = {2023}, month = {12/26/2023}, abstract = {

Quantum reservoir computing (QRC) has been proposed as a paradigm for performing machine learning with quantum processors where the training is efficient in the number of required runs of the quantum processor and takes place in the classical domain, avoiding the issue of barren plateaus in parameterized-circuit quantum neural networks. It is natural to consider using a quantum processor based on superconducting circuits to classify microwave signals that are analog -- continuous in time. However, while theoretical proposals of analog QRC exist, to date QRC has been implemented using circuit-model quantum systems -- imposing a discretization of the incoming signal in time, with each time point input by executing a gate operation. In this paper we show how a quantum superconducting circuit comprising an oscillator coupled to a qubit can be used as an analog quantum reservoir for a variety of classification tasks, achieving high accuracy on all of them. Our quantum system was operated without artificially discretizing the input data, directly taking in microwave signals. Our work does not attempt to address the question of whether QRCs could provide a quantum computational advantage in classifying pre-recorded classical signals. However, beyond illustrating that sophisticated tasks can be performed with a modest-size quantum system and inexpensive training, our work opens up the possibility of achieving a different kind of advantage than a purely computational advantage: superconducting circuits can act as extremely sensitive detectors of microwave photons; our work demonstrates processing of ultra-low-power microwave signals in our superconducting circuit, and by combining sensitive detection with QRC processing within the same system, one could achieve a quantum sensing-computational advantage, i.e., an advantage in the overall analysis of microwave signals comprising just a few photons.

}, url = {https://arxiv.org/abs/2312.16166}, author = {Alen Senanian and Sridhar Prabhu and Vladimir Kremenetski and Saswata Roy and Yingkang Cao and Jeremy Kline and Tatsuhiro Onodera and Logan G. Wright and Xiaodi Wu and Valla Fatemi and Peter L. McMahon} } @article {3358, title = {Non-equilibrium critical scaling and universality in a quantum simulator}, year = {2023}, month = {9/19/2023}, abstract = {

Universality and scaling laws are hallmarks of equilibrium phase transitions and critical phenomena. However, extending these concepts to non-equilibrium systems is an outstanding challenge. Despite recent progress in the study of dynamical phases, the universality classes and scaling laws for non-equilibrium phenomena are far less understood than those in equilibrium. In this work, using a trapped-ion quantum simulator with single-ion resolution, we investigate the non-equilibrium nature of critical fluctuations following a quantum quench to the critical point. We probe the scaling of spin fluctuations after a series of quenches to the critical Hamiltonian of a long-range Ising model. With systems of up to 50 spins, we show that the amplitude and timescale of the post-quench fluctuations scale with system size with distinct universal critical exponents. While a generic quench can lead to thermal critical behaviour, we find that a second quench from one critical state to another (i.e. a double quench) results in critical behaviour that does not have an equilibrium counterpart. Our results demonstrate the ability of quantum simulators to explore universal scaling beyond the equilibrium paradigm.

}, url = {https://arxiv.org/abs/2309.10856}, author = {A. De and P. Cook and K. Collins and W. Morong and D. Paz and P. Titum and G. Pagano and A. V. Gorshkov and M. Maghrebi and C. Monroe} } @article {3413, title = {Observation of a finite-energy phase transition in a one-dimensional quantum simulator}, year = {2023}, month = {10/30/2023}, abstract = {

One of the most striking many-body phenomena in nature is the sudden change of macroscopic properties as the temperature or energy reaches a critical value. Such equilibrium transitions have been predicted and observed in two and three spatial dimensions, but have long been thought not to exist in one-dimensional (1D) systems. Fifty years ago, Dyson and Thouless pointed out that a phase transition in 1D can occur in the presence of long-range interactions, but an experimental realization has so far not been achieved due to the requirement to both prepare equilibrium states and realize sufficiently long-range interactions. Here we report on the first experimental demonstration of a finite-energy phase transition in 1D. We use the simple observation that finite-energy states can be prepared by time-evolving product initial states and letting them thermalize under the dynamics of a many-body Hamiltonian. By preparing initial states with different energies in a 1D trapped-ion quantum simulator, we study the finite-energy phase diagram of a long-range interacting quantum system. We observe a ferromagnetic equilibrium phase transition as well as a crossover from a low-energy polarized paramagnet to a high-energy unpolarized paramagnet in a system of up to 23 spins, in excellent agreement with numerical simulations. Our work demonstrates the ability of quantum simulators to realize and study previously inaccessible phases at finite energy density.

}, url = {https://arxiv.org/abs/2310.19869}, author = {Alexander Schuckert and Or Katz and Lei Feng and Eleanor Crane and Arinjoy De and Mohammad Hafezi and Alexey V. Gorshkov and Christopher Monroe} } @article {3314, title = {Qafny: Quantum Program Verification Through Type-guided Classical Separation Logic}, year = {2023}, month = {7/12/2023}, abstract = {

Formal verification has been proven instrumental to ensure that quantum programs implement their specifications but often requires a significant investment of time and labor. To address this challenge, we present Qafny, an automated proof system designed for verifying quantum programs. At its core, Qafny uses a type-guided quantum proof system that translates quantum operations to classical array operations. By modeling these operations as proof rules within a classical separation logic framework, Qafny provides automated support for the reasoning process that would otherwise be tedious and time-consuming. We prove the soundness and completeness of our proof system and implement a prototype compiler that transforms Qafny programs both into the Dafny programming language and into executable quantum circuits. Using Qafny, we demonstrate how to efficiently verify prominent quantum algorithms, including quantum-walk algorithms, Grover\&$\#$39;s search algorithm, and Shor\&$\#$39;s factoring algorithm, with significantly reduced human efforts.

}, url = {https://arxiv.org/abs/2211.06411}, author = {Liyi Li and Mingwei Zhu and Rance Cleaveland and Yi Lee and Le Chang and Xiaodi Wu} } @article {2448, title = {Quantum algorithm for estimating volumes of convex bodies}, journal = {ACM Transactions on Quantum Computing}, volume = {4}, year = {2023}, month = {4/2023}, chapter = {20}, abstract = {

Estimating the volume of a convex body is a central problem in convex geometry and can be viewed as a continuous version of counting. We present a quantum algorithm that estimates the volume of an n-dimensional convex body within multiplicative error ε using O~(n3.5+n2.5/ε) queries to a membership oracle and O~(n5.5+n4.5/ε) additional arithmetic operations. For comparison, the best known classical algorithm uses O~(n4+n3/ε2) queries and O~(n6+n5/ε2) additional arithmetic operations. To the best of our knowledge, this is the first quantum speedup for volume estimation. Our algorithm is based on a refined framework for speeding up simulated annealing algorithms that might be of independent interest. This framework applies in the setting of \"Chebyshev cooling\", where the solution is expressed as a telescoping product of ratios, each having bounded variance. We develop several novel techniques when implementing our framework, including a theory of continuous-space quantum walks with rigorous bounds on discretization error.

}, url = {https://arxiv.org/abs/1908.03903}, author = {Shouvanik Chakrabarti and Andrew M. Childs and Shih-Han Hung and Tongyang Li and Chunhao Wang and Xiaodi Wu} } @article {3402, title = {Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters}, year = {2023}, month = {12/6/2023}, abstract = {

We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially enhance the accuracy of the recently introduced linear combination of Hamiltonian simulation (LCHS) method [An, Liu, and Lin, Physical Review Letters, 2023]. For the first time, this approach enables quantum algorithms to solve linear differential equations with both optimal state preparation cost and near-optimal scaling in matrix queries on all parameters.

}, url = {https://arxiv.org/abs/2312.03916}, author = {Dong An and Andrew M. Childs and Lin Lin} } @article {3269, title = {Quantum Algorithms and the Power of Forgetting}, journal = {14th Innovations in Theoretical Computer Science Conference (ITCS 2023)}, volume = {251}, year = {2023}, pages = {37:1--37:22}, abstract = {

The so-called welded tree problem provides an example of a black-box problem that can be solved exponentially faster by a quantum walk than by any classical algorithm [Andrew M. Childs et al., 2003]. Given the name of a special entrance vertex, a quantum walk can find another distinguished exit vertex using polynomially many queries, though without finding any particular path from entrance to exit. It has been an open problem for twenty years whether there is an efficient quantum algorithm for finding such a path, or if the path-finding problem is hard even for quantum computers. We show that a natural class of efficient quantum algorithms provably cannot find a path from entrance to exit. Specifically, we consider algorithms that, within each branch of their superposition, always store a set of vertex labels that form a connected subgraph including the entrance, and that only provide these vertex labels as inputs to the oracle. While this does not rule out the possibility of a quantum algorithm that efficiently finds a path, it is unclear how an algorithm could benefit by deviating from this behavior. Our no-go result suggests that, for some problems, quantum algorithms must necessarily forget the path they take to reach a solution in order to outperform classical computation.

}, isbn = {978-3-95977-263-1}, doi = {10.4230/LIPIcs.ITCS.2023.37}, url = {https://drops.dagstuhl.de/opus/volltexte/2023/17540}, author = {Andrew M. Childs and Coudron, Matthew and Gilani, Amin Shiraz}, editor = {Tauman Kalai, Yael} } @article {3400, title = {Quantum Algorithms for Simulating Nuclear Effective Field Theories}, year = {2023}, month = {12/8/2023}, abstract = {

Quantum computers offer the potential to simulate nuclear processes that are classically intractable. With the goal of understanding the necessary quantum resources, we employ state-of-the-art Hamiltonian-simulation methods, and conduct a thorough algorithmic analysis, to estimate the qubit and gate costs to simulate low-energy effective field theories (EFTs) of nuclear physics. In particular, within the framework of nuclear lattice EFT, we obtain simulation costs for the leading-order pionless and pionful EFTs. We consider both static pions represented by a one-pion-exchange potential between the nucleons, and dynamical pions represented by relativistic bosonic fields coupled to non-relativistic nucleons. We examine the resource costs for the tasks of time evolution and energy estimation for physically relevant scales. We account for model errors associated with truncating either long-range interactions in the one-pion-exchange EFT or the pionic Hilbert space in the dynamical-pion EFT, and for algorithmic errors associated with product-formula approximations and quantum phase estimation. Our results show that the pionless EFT is the least costly to simulate and the dynamical-pion theory is the costliest. We demonstrate how symmetries of the low-energy nuclear Hamiltonians can be utilized to obtain tighter error bounds on the simulation algorithm. By retaining the locality of nucleonic interactions when mapped to qubits, we achieve reduced circuit depth and substantial parallelization. We further develop new methods to bound the algorithmic error for classes of fermionic Hamiltonians that preserve the number of fermions, and demonstrate that reasonably tight Trotter error bounds can be achieved by explicitly computing nested commutators of Hamiltonian terms. This work highlights the importance of combining physics insights and algorithmic advancement in reducing quantum-simulation costs.

}, url = {https://arxiv.org/abs/2312.05344}, author = {James D. Watson and Jacob Bringewatt and Alexander F. Shaw and Andrew M. Childs and Alexey V. Gorshkov and Zohreh Davoudi} } @article {3368, title = {Quantum computation of dynamical quantum phase transitions and entanglement tomography in a lattice gauge theory}, year = {2023}, month = {10/6/2023}, abstract = {

Strongly-coupled gauge theories far from equilibrium may exhibit unique features that could illuminate the physics of the early universe and of hadron and ion colliders. Studying real-time phenomena has proven challenging with classical-simulation methods, but is a natural application of quantum simulation. To demonstrate this prospect, we quantum compute non-equal time correlation functions and perform entanglement tomography of non-equilibrium states of a simple lattice gauge theory, the Schwinger model, using a trapped-ion quantum computer by IonQ Inc. As an ideal target for near-term devices, a recently-predicted [Zache et al., Phys. Rev. Lett. 122, 050403 (2019)] dynamical quantum phase transition in this model is studied by preparing, quenching, and tracking the subsequent non-equilibrium dynamics in three ways: i) overlap echos signaling dynamical transitions, ii) non-equal time correlation functions with an underlying topological nature, and iii) the entanglement structure of non-equilibrium states, including entanglement Hamiltonians. These results constitute the first observation of a dynamical quantum phase transition in a lattice gauge theory on a quantum computer, and are a first step toward investigating topological phenomena in nuclear and high-energy physics using quantum technologies.

}, url = {https://arxiv.org/abs/2210.03089}, author = {Niklas Mueller and Joseph A. Carolan and Andrew Connelly and Zohreh Davoudi and Eugene F. Dumitrescu and K{\"u}bra Yeter-Aydeniz} } @article {3362, title = {Quantum Lego Expansion Pack: Enumerators from Tensor Networks}, year = {2023}, month = {8/9/2023}, abstract = {

We provide the first tensor network method for computing quantum weight enumerator polynomials in the most general form. As a corollary, if a quantum code has a known tensor network construction of its encoding map, our method produces an algorithm that computes its distance. For non-(Pauli)-stabilizer codes, this constitutes the current best algorithm for computing the code distance. For degenerate stabilizer codes, it can provide up to an exponential speed up compared to the current methods. We also introduce a few novel applications of different weight enumerators. In particular, for any code built from the quantum lego method, we use enumerators to construct its (optimal) decoders under any i.i.d. single qubit or qudit error channels and discuss their applications for computing logical error rates. As a proof of principle, we perform exact analyses of the deformed surface codes, the holographic pentagon code, and the 2d Bacon-Shor code under (biased) Pauli noise and limited instances of coherent error at sizes that are inaccessible by brute force.

}, url = {https://arxiv.org/abs/2308.05152}, author = {ChunJun Cao and Michael J. Gullans and Brad Lackey and Zitao Wang} } @article {3355, title = {Quantum Sensing with Erasure Qubits}, year = {2023}, month = {10/2/2023}, abstract = {

The dominant noise in an \"erasure qubit\" is an erasure -- a type of error whose occurrence and location can be detected. Erasure qubits have potential to reduce the overhead associated with fault tolerance. To date, research on erasure qubits has primarily focused on quantum computing and quantum networking applications. Here, we consider the applicability of erasure qubits to quantum sensing and metrology. We show theoretically that, for the same level of noise, an erasure qubit acts as a more precise sensor or clock compared to its non-erasure counterpart. We experimentally demonstrate this by artificially injecting either erasure errors (in the form of atom loss) or dephasing errors into a differential optical lattice clock comparison, and observe enhanced precision in the case of erasure errors for the same injected error rate. Similar benefits of erasure qubits to sensing can be realized in other quantum platforms like Rydberg atoms and superconducting qubits

}, url = {https://arxiv.org/abs/2310.01512}, author = {Pradeep Niroula and Jack Dolde and Xin Zheng and Jacob Bringewatt and Adam Ehrenberg and Kevin C. Cox and Jeff Thompson and Michael J. Gullans and Shimon Kolkowitz and Alexey V. Gorshkov} } @article {3397, title = {Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions}, year = {2023}, month = {12/14/2023}, abstract = {

Computational models are an essential tool for the design, characterization, and discovery of novel materials. Hard computational tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming much of their simulation, analysis, and data resources. Quantum computing, on the other hand, is an emerging technology with the potential to accelerate many of the computational tasks needed for materials science. In order to do that, the quantum technology must interact with conventional high-performance computing in several ways: approximate results validation, identification of hard problems, and synergies in quantum-centric supercomputing. In this paper, we provide a perspective on how quantum-centric supercomputing can help address critical computational problems in materials science, the challenges to face in order to solve representative use cases, and new suggested directions.

}, url = {https://arxiv.org/abs/2312.09733}, author = {Yuri Alexeev and Maximilian Amsler and Paul Baity and Marco Antonio Barroca and Sanzio Bassini and Torey Battelle and Daan Camps and David Casanova and Young jai Choi and Frederic T. Chong and Charles Chung and Chris Codella and Antonio D. Corcoles and James Cruise and Alberto Di Meglio and Jonathan Dubois and Ivan Duran and Thomas Eckl and Sophia Economou and Stephan Eidenbenz and Bruce Elmegreen and Clyde Fare and Ismael Faro and Cristina Sanz Fern{\'a}ndez and Rodrigo Neumann Barros Ferreira and Keisuke Fuji and Bryce Fuller and Laura Gagliardi and Giulia Galli and Jennifer R. Glick and Isacco Gobbi and Pranav Gokhale and Salvador de la Puente Gonzalez and Johannes Greiner and Bill Gropp and Michele Grossi and Emmanuel Gull and Burns Healy and Benchen Huang and Travis S. Humble and Nobuyasu Ito and Artur F. Izmaylov and Ali Javadi-Abhari and Douglas Jennewein and Shantenu Jha and Liang Jiang and Barbara Jones and Wibe Albert de Jong and Petar Jurcevic and William Kirby and Stefan Kister and Masahiro Kitagawa and Joel Klassen and Katherine Klymko and Kwangwon Koh and Masaaki Kondo and Doga Murat Kurkcuoglu and Krzysztof Kurowski and Teodoro Laino and Ryan Landfield and Matt Leininger and Vicente Leyton-Ortega and Ang Li and Meifeng Lin and Junyu Liu and Nicolas Lorente and Andre Luckow and Simon Martiel and Francisco Martin-Fernandez and Margaret Martonosi and Claire Marvinney and Arcesio Castaneda Medina and Dirk Merten and Antonio Mezzacapo and Kristel Michielsen and Abhishek Mitra and Tushar Mittal and Kyungsun Moon and Joel Moore and Mario Motta and Young-Hye Na and Yunseong Nam and Prineha Narang and Yu-ya Ohnishi and Daniele Ottaviani and Matthew Otten and Scott Pakin and Vincent R. Pascuzzi and Ed Penault and Tomasz Piontek and Jed Pitera and Patrick Rall and Gokul Subramanian Ravi and Niall Robertson and Matteo Rossi and Piotr Rydlichowski and Hoon Ryu and Georgy Samsonidze and Mitsuhisa Sato and Nishant Saurabh and Vidushi Sharma and Kunal Sharma and Soyoung Shin and George Slessman and Mathias Steiner and Iskandar Sitdikov and In-Saeng Suh and Eric Switzer and Wei Tang and Joel Thompson and Synge Todo and Minh Tran and Dimitar Trenev and Christian Trott and Huan-Hsin Tseng and Esin Tureci and David Garc{\'\i}a Valinas and Sofia Vallecorsa and Christopher Wever and Konrad Wojciechowski and Xiaodi Wu and Shinjae Yoo and Nobuyuki Yoshioka and Victor Wen-zhe Yu and Seiji Yunoki and Sergiy Zhuk and Dmitry Zubarev} } @article {2859, title = {Shadow process tomography of quantum channels}, journal = {Phys. Rev. A}, volume = {107}, year = {2023}, month = {4/4/2023}, abstract = {

Quantum process tomography is a critical capability for building quantum computers, enabling quantum networks, and understanding quantum sensors. Like quantum state tomography, the process tomography of an arbitrary quantum channel requires a number of measurements that scale exponentially in the number of quantum bits affected. However, the recent field of shadow tomography, applied to quantum states, has demonstrated the ability to extract key information about a state with only polynomially many measurements. In this work, we apply the concepts of shadow state tomography to the challenge of characterizing quantum processes. We make use of the Choi isomorphism to directly apply rigorous bounds from shadow state tomography to shadow process tomography, and we find additional bounds on the number of measurements that are unique to process tomography. Our results, which include algorithms for implementing shadow process tomography enable new techniques including evaluation of channel concatenation and the application of channels to shadows of quantum states. This provides a dramatic improvement for understanding large-scale quantum systems.

}, doi = {https://doi.org/10.1103/PhysRevA.107.042403}, url = {https://arxiv.org/abs/2110.03629}, author = {Jonathan Kunjummen and Minh C. Tran and Daniel Carney and Jacob M. Taylor} } @article {3357, title = {Streaming quantum state purification}, year = {2023}, month = {9/28/2023}, abstract = {

Quantum state purification is the task of recovering a nearly pure copy of an unknown pure quantum state using multiple noisy copies of the state. This basic task has applications to quantum communication over noisy channels and quantum computation with imperfect devices, but has only been studied previously for the case of qubits. We derive an efficient purification procedure based on the swap test for qudits of any dimension, starting with any initial error parameter. Treating the initial error parameter and the dimension as constants, we show that our procedure has sample complexity asymptotically optimal in the final error parameter. Our protocol has a simple recursive structure that can be applied when the states are provided one at a time in a streaming fashion, requiring only a small quantum memory to implement.

}, url = {https://arxiv.org/abs/2309.16387}, author = {Andrew M. Childs and Honghao Fu and Debbie Leung and Zhi Li and Maris Ozols and Vedang Vyas} } @article {3266, title = {Strongly incoherent gravity}, year = {2023}, month = {1/20/2023}, abstract = {

While most fundamental interactions in nature are known to be mediated by quantized fields, the possibility has been raised that gravity may behave differently. Making this concept precise enough to test requires consistent models. Here we construct an explicit example of a theory where a non-entangling version of an arbitrary two-body potential V(r) arises from local measurements and feedback forces. While a variety of such theories exist, our construction causes particularly strong decoherence compared to more subtle approaches. Regardless, expectation values of observables obey the usual classical dynamics, while the interaction generates no entanglement. Applied to the Newtonian potential, this produces a non-relativistic model of gravity with fundamental loss of unitarity. The model contains a pair of free parameters, a substantial range of which is not excluded by observations to date. As an alternative to testing entanglement properties, we show that the entire remaining parameter space can be tested by looking for loss of quantum coherence in small systems like atom interferometers coupled to oscillating source masses.

}, url = {https://arxiv.org/abs/2301.08378}, author = {Daniel Carney and Jacob M. Taylor} } @article {3288, title = {Thermally driven quantum refrigerator autonomously resets superconducting qubit}, year = {2023}, month = {5/26/2023}, abstract = {

The first thermal machines steered the industrial revolution, but their quantum analogs have yet to prove useful. Here, we demonstrate a useful quantum absorption refrigerator formed from superconducting circuits. We use it to reset a transmon qubit to a temperature lower than that achievable with any one available bath. The process is driven by a thermal gradient and is autonomous -- requires no external control. The refrigerator exploits an engineered three-body interaction between the target qubit and two auxiliary qudits coupled to thermal environments. The environments consist of microwave waveguides populated with synthesized thermal photons. The target qubit, if initially fully excited, reaches a steady-state excited-level population of 5\×10\−4\±5\×10\−4 (an effective temperature of 23.5~mK) in about 1.6~μs. Our results epitomize how quantum thermal machines can be leveraged for quantum information-processing tasks. They also initiate a path toward experimental studies of quantum thermodynamics with superconducting circuits coupled to propagating thermal microwave fields.

}, url = {https://arxiv.org/abs/2305.16710}, author = {Mohammed Ali Aamir and Paul Jamet Suria and Jos{\'e} Antonio Mar{\'\i}n Guzm{\'a}n and Claudia Castillo-Moreno and Jeffrey M. Epstein and Nicole Yunger Halpern and Simone Gasparinetti} } @article {3406, title = {{\AE} codes}, year = {2023}, month = {11/21/2023}, abstract = {

Diatomic molecular codes [{arXiv:1911.00099}] are designed to encode quantum information in the orientation of a diatomic molecule, allowing error correction from small torques and changes in angular momentum. Here, we directly study noise native to atomic and molecular platforms -- spontaneous emission, stray electromagnetic fields, and Raman scattering -- and derive simple necessary and sufficient conditions for codes to protect against such noise. We identify existing and develop new absorption-emission ({\AE}) codes that are more practical than molecular codes, require lower average momentum, can directly protect against photonic processes up to arbitrary order, and are applicable to a broader set of atomic and molecular systems.

}, url = {https://arxiv.org/abs/2311.12324}, author = {Shubham P. Jain and Eric R. Hudson and Wesley C. Campbell and Victor V. Albert} } @article {3078, title = {Accurate and Efficient Quantum Computations of Molecular Properties Using Daubechies Wavelet Molecular Orbitals: A Benchmark Study against Experimental Data}, journal = {PRX Quantum}, volume = {3}, year = {2022}, month = {5/28/2022}, pages = {020360}, abstract = {

Although quantum computation (QC) is regarded as a promising numerical method for computational quantum chemistry, current applications of quantum-chemistry calculations on quantum computers are limited to small molecules. This limitation can be ascribed to technical problems in building and manipulating more qubits and the associated complicated operations of quantum gates in a quantum circuit when the size of the molecular system becomes large. As a result, reducing the number of required qubits is necessary to make QC practical. Currently, the minimal STO-3G basis set is commonly used in benchmark studies because it requires the minimum number of spin orbitals. Nonetheless, the accuracy of using STO-3G is generally low and thus cannot provide useful predictions. We propose to adopt Daubechies wavelet functions as an accurate and efficient method for QCs of molecular electronic properties. We demonstrate that a minimal basis set constructed from Daubechies wavelet basis can yield accurate results through a better description of the molecular Hamiltonian, while keeping the number of spin orbitals minimal. With the improved Hamiltonian through Daubechies wavelets, we calculate vibrational frequencies for H2 and LiH using quantum-computing algorithm to show that the results are in excellent agreement with experimental data. As a result, we achieve quantum calculations in which accuracy is comparable with that of the full configuration interaction calculation using the cc-pVDZ basis set, whereas the computational cost is the same as that of a STO-3G calculation. Thus, our work provides a more efficient and accurate representation of the molecular Hamiltonian for efficient QCs of molecular systems, and for the first time demonstrates that predictions in agreement with experimental measurements are possible to be achieved with quantum resources available in near-term quantum computers.

}, doi = {https://doi.org/10.1103/PRXQuantum.3.020360}, url = {https://arxiv.org/abs/2205.14476}, author = {Cheng-Lin Hong and Ting Tsai and Jyh-Pin Chou and Peng-Jen Chen and Pei-Kai Tsai and Yu-Cheng Chen and En-Jui Kuo and David Srolovitz and Alice Hu and Yuan-Chung Cheng and Hsi-Sheng Goan} } @book {2982, title = {Analogue Quantum Simulation: A New Instrument for Scientific Understanding}, year = {2022}, pages = {83-102}, publisher = {Springer Nature}, organization = {Springer Nature}, abstract = {

Analyzes analogue quantum simulation philosophically.\ Provides a framework to support the goals of scientists.\ Useful to both working scientists and philosophers of science.

}, doi = {https://doi.org/10.1007/978-3-030-87216-8_6}, author = {Dominik Hangleiter and Jacques Carolan and Karim P. Y. Th{\'e}bault} } @article {3001, title = {Approximating Output Probabilities of Shallow Quantum Circuits which are Geometrically-local in any Fixed Dimension}, journal = {Leibniz International Proceedings in Informatics (LIPIcs)}, volume = {232}, year = {2022}, month = {4/7/2022}, pages = {9:1--9:17}, type = {17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)}, abstract = {

We present a classical algorithm that, for any D-dimensional geometrically-local, quantum circuit C of polylogarithmic-depth, and any bit string x\∈0,1n, can compute the quantity |\<x|C|0\⊗n\>|2 to within any inverse-polynomial additive error in quasi-polynomial time, for any fixed dimension D. This is an extension of the result [CC21], which originally proved this result for D=3. To see why this is interesting, note that, while the D=1 case of this result follows from standard use of Matrix Product States, known for decades, the D=2 case required novel and interesting techniques introduced in [BGM19]. Extending to the case D=3 was even more laborious and required further new techniques introduced in [CC21]. Our work here shows that, while handling each new dimension has historically required a new insight, and fixed algorithmic primitive, based on known techniques for D\≤3, we can now handle any fixed dimension D\>3.
Our algorithm uses the Divide-and-Conquer framework of [CC21] to approximate the desired quantity via several instantiations of the same problem type, each involving D-dimensional circuits on about half the number of qubits as the original. This division step is then applied recursively, until the width of the recursively decomposed circuits in the Dth dimension is so small that they can effectively be regarded as (D\−1)-dimensional problems by absorbing the small width in the Dth dimension into the qudit structure at the cost of a moderate increase in runtime. The main technical challenge lies in ensuring that the more involved portions of the recursive circuit decomposition and error analysis from [CC21] still hold in higher dimensions, which requires small modifications to the analysis in some places.

}, keywords = {Computational Complexity (cs.CC), FOS: Computer and information sciences, FOS: Physical sciences, Quantum Physics (quant-ph)}, isbn = {978-3-95977-237-2}, issn = {1868-8969}, doi = {10.48550/ARXIV.2202.08349}, url = {https://arxiv.org/abs/2202.08349}, author = {Dontha, Suchetan and Tan, Shi Jie Samuel and Smith, Stephen and Choi, Sangheon and Matthew Coudron} } @article {3143, title = {Bosonic Qiskit}, year = {2022}, month = {9/22/2022}, abstract = {

The practical benefits of hybrid quantum information processing hardware that contains continuous-variable objects (bosonic modes such as mechanical or electromagnetic oscillators) in addition to traditional (discrete-variable) qubits have recently been demonstrated by experiments with bosonic codes that reach the break-even point for quantum error correction and by efficient Gaussian boson sampling simulation of the Franck-Condon spectra of triatomic molecules that is well beyond the capabilities of current qubit-only hardware. The goal of this Co-design Center for Quantum Advantage (C2QA) project is to develop an instruction set architecture (ISA) for hybrid qubit/bosonic mode systems that contains an inventory of the fundamental operations and measurements that are possible in such hardware. The corresponding abstract machine model (AMM) would also contain a description of the appropriate error models associated with the gates, measurements and time evolution of the hardware. This information has been implemented as an extension of Qiskit. Qiskit is an opensource software development toolkit (SDK) for simulating the quantum state of a quantum circuit on a system with Python 3.7+ and for running the same circuits on prototype hardware within the IBM Quantum Lab. We introduce the Bosonic Qiskit software to enable the simulation of hybrid qubit/bosonic systems using the existing Qiskit software development kit. This implementation can be used for simulating new hybrid systems, verifying proposed physical systems, and modeling systems larger than can currently be constructed. We also cover tutorials and example use cases included within the software to study Jaynes- Cummings models, bosonic Hubbard models, plotting Wigner functions and animations, and calculating maximum likelihood estimations using Wigner functions.

}, keywords = {Emerging Technologies (cs.ET), FOS: Computer and information sciences, FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2209.11153}, url = {https://arxiv.org/abs/2209.11153}, author = {Stavenger, Timothy J and Crane, Eleanor and Smith, Kevin and Kang, Christopher T and Girvin, Steven M and Wiebe, Nathan} } @article {3152, title = {Bounding the Minimum Time of a Quantum Measurement}, year = {2022}, month = {9/13/2022}, abstract = {

Measurements take a singular role in quantum theory. While they are often idealized as an instantaneous process, this is in conflict with all other physical processes in nature. In this Letter, we adopt a standpoint where the interaction with an environment is a crucial ingredient for the occurrence of a measurement. Within this framework, we derive lower bounds on the time needed for a measurement to occur. Our bound scales proportionally to the change in entropy of the measured system, and inversely proportional to the number of possible measurement outcomes and the interaction strength driving the measurement. We evaluate our bound in two examples where the environment is modelled by bosonic modes and the measurement apparatus is modelled by spins or bosons.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2209.06248}, url = {https://arxiv.org/abs/2209.06248}, author = {Shettell, Nathan and Centrone, Federico and Garc{\'\i}a-Pintos, Luis Pedro} } @article {2930, title = {Classification of (2+1)D invertible fermionic topological phases with symmetry}, journal = {Phys. Rev. B}, volume = {105}, year = {2022}, month = {5/30/2022}, abstract = {

We provide a classification of invertible topological phases of interacting fermions with symmetry in two spatial dimensions for general fermionic symmetry groups Gf and general values of the chiral central charge c\−. Here Gf is a central extension of a bosonic symmetry group Gb by fermion parity, (\−1)F, specified by a second cohomology class [ω2]\∈H2(Gb,Z2). Our approach proceeds by gauging fermion parity and classifying the resulting Gb symmetry-enriched topological orders while keeping track of certain additional data and constraints. We perform this analysis through two perspectives, using G-crossed braided tensor categories and Spin(2c\−)1 Chern-Simons theory coupled to a background G gauge field. These results give a way to characterize and classify invertible fermionic topological phases in terms of a concrete set of data and consistency equations, which is more physically transparent and computationally simpler than the more abstract methods using cobordism theory and spectral sequences. Our results also generalize and provide a different approach to the recent classification of fermionic symmetry-protected topological phases by Wang and Gu, which have chiral central charge c\−=0. We show how the 10-fold way classification of topological insulators and superconductors fits into our scheme, along with general non-perturbative constraints due to certain choices of c\− and Gf. Mathematically, our results also suggest an explicit general parameterization of deformation classes of (2+1)D invertible topological quantum field theories with Gf symmetry.\ 

}, doi = {https://doi.org/10.1103/PhysRevB.105.235143}, url = {https://arxiv.org/abs/2109.11039}, author = {Maissam Barkeshli and Yu-An Chen and Po-Shen Hsin and Naren Manjunath} } @article {3082, title = {Closing the Locality and Detection Loopholes in Multiparticle Entanglement Self-Testing}, journal = {Physical Review Letters}, volume = {128}, year = {2022}, month = {06/23/2022}, pages = {250401}, abstract = {

First proposed by Mayers and Yao, self-testing provides a certification method to infer the underlying physics of quantum experiments in a black-box scenario. Numerous demonstrations have been reported to self-test various types of entangled states. However, all the multiparticle self-testing experiments reported so far suffer from both detection and locality loopholes. Here, we report the first experimental realization of multiparticle entanglement self-testing closing the locality loophole in a photonic system, and the detection loophole in a superconducting system, respectively. We certify three-party and four-party GHZ states with at least 0.84 (1) and 0.86 (3) fidelities in a device-independent way. These results can be viewed as a meaningful advance in multiparticle loophole-free self-testing, and also significant progress on the foundations of quantum entanglement certification.

}, doi = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.250401}, url = {https://www.researchgate.net/profile/Dian-Wu/publication/361497881_Closing_the_Locality_and_Detection_Loopholes_in_Multiparticle_Entanglement_Self-Testing/links/62b55a8c1010dc02cc57530c/Closing-the-Locality-and-Detection-Loopholes-in-Multiparticle-Entangl}, author = {Dian Wu and Qi Zhao and Can Wang and Liang Huang and Yang-Fan Jiang and Bing Bai and You Zhou and Xue-Mei Gu and Feng-Ming Liu and Ying-Qiu Mao and Qi-Chao Sun and Ming-Cheng Chen and Jun Zhang and Cheng-Zhi Peng and Xiao-Bo Zhu and Qiang Zhang and Chao-Yang Lu and Jian-Wei Pan} } @article {3144, title = {Codimension-2 defects and higher symmetries in (3+1)D topological phases}, year = {2022}, month = {8/15/2022}, abstract = {

(3+1)D topological phases of matter can host a broad class of non-trivial topological defects of codimension-1, 2, and 3, of which the well-known point charges and flux loops are special cases. The complete algebraic structure of these defects defines a higher category, and can be viewed as an emergent higher symmetry. This plays a crucial role both in the classification of phases of matter and the possible fault-tolerant logical operations in topological quantum error correcting codes. In this paper, we study several examples of such higher codimension defects from distinct perspectives. We mainly study a class of invertible codimension-2 topological defects, which we refer to as twist strings. We provide a number of general constructions for twist strings, in terms of gauging lower dimensional invertible phases, layer constructions, and condensation defects. We study some special examples in the context of Z2 gauge theory with fermionic charges, in Z2\×Z2 gauge theory with bosonic charges, and also in non-Abelian discrete gauge theories based on dihedral (Dn) and alternating (A6) groups. The intersection between twist strings and Abelian flux loops sources Abelian point charges, which defines an H4 cohomology class that characterizes part of an underlying 3-group symmetry of the topological order. The equations involving background gauge fields for the 3-group symmetry have been explicitly written down for various cases. We also study examples of twist strings interacting with non-Abelian flux loops (defining part of a non-invertible higher symmetry), examples of non-invertible codimension-2 defects, and examples of interplay of codimension-2 defects with codimension-1 defects. We also find an example of geometric, not fully topological, twist strings in (3+1)D A6 gauge theory.

}, keywords = {FOS: Mathematics, FOS: Physical sciences, High Energy Physics - Theory (hep-th), Mathematical Physics (math-ph), Quantum Algebra (math.QA), Quantum Physics (quant-ph), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2208.07367}, url = {https://arxiv.org/abs/2208.07367}, author = {Barkeshli, Maissam and Chen, Yu-An and Huang, Sheng-Jie and Kobayashi, Ryohei and Tantivasadakarn, Nathanan and Zhu, Guanyu} } @article {3184, title = {Continuous Symmetry Breaking in a Trapped-Ion Spin Chain}, year = {2022}, month = {11/2/2022}, abstract = {

One-dimensional systems exhibiting a continuous symmetry can host quantum phases of matter with true long-range order only in the presence of sufficiently long-range interactions. In most physical systems, however, the interactions are short-ranged, hindering the emergence of such phases in one dimension. Here we use a one-dimensional trapped-ion quantum simulator to prepare states with long-range spin order that extends over the system size of up to 23 spins and is characteristic of the continuous symmetry-breaking phase of matter. Our preparation relies on simultaneous control over an array of tightly focused individual-addressing laser beams, generating long-range spin-spin interactions. We also observe a disordered phase with frustrated correlations. We further study the phases at different ranges of interaction and the out-of-equilibrium response to symmetry-breaking perturbations. This work opens an avenue to study new quantum phases and out-of-equilibrium dynamics in low-dimensional systems.

}, keywords = {FOS: Physical sciences, Quantum Gases (cond-mat.quant-gas), Quantum Physics (quant-ph), Statistical Mechanics (cond-mat.stat-mech), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2211.01275}, url = {https://arxiv.org/abs/2211.01275}, author = {Feng, Lei and Katz, Or and Haack, Casey and Maghrebi, Mohammad and Gorshkov, Alexey V. and Gong, Zhexuan and Cetina, Marko and Monroe, Christopher} } @article {3072, title = {A Convergence Theory for Over-parameterized Variational Quantum Eigensolvers}, year = {2022}, month = {5/25/2022}, abstract = {

The Variational Quantum Eigensolver (VQE) is a promising candidate for quantum applications on near-term Noisy Intermediate-Scale Quantum (NISQ) computers. Despite a lot of empirical studies and recent progress in theoretical understanding of VQE\&$\#$39;s optimization landscape, the convergence for optimizing VQE is far less understood. We provide the first rigorous analysis of the convergence of VQEs in the over-parameterization regime. By connecting the training dynamics with the Riemannian Gradient Flow on the unit-sphere, we establish a threshold on the sufficient number of parameters for efficient convergence, which depends polynomially on the system dimension and the spectral ratio, a property of the problem Hamiltonian, and could be resilient to gradient noise to some extent. We further illustrate that this overparameterization threshold could be vastly reduced for specific VQE instances by establishing an ansatz-dependent threshold paralleling our main result. We showcase that our ansatz-dependent threshold could serve as a proxy of the trainability of different VQE ansatzes without performing empirical experiments, which hence leads to a principled way of evaluating ansatz design. Finally, we conclude with a comprehensive empirical study that supports our theoretical findings

}, url = {https://arxiv.org/abs/2205.12481}, author = {Xuchen You and Shouvanik Chakrabarti and Xiaodi Wu} } @article {3013, title = {Deconfinement and Error Thresholds in Holography}, year = {2022}, month = {2/9/2022}, abstract = {

We study the error threshold properties of holographic quantum error-correcting codes. We demonstrate that holographic CFTs admit an algebraic threshold, which is related to the confinement-deconfinement phase transition. We then apply geometric intuition from holography and the Hawking-Page phase transition to motivate the CFT result, and comment on potential extensions to other confining theories.

}, keywords = {FOS: Physical sciences, High Energy Physics - Theory (hep-th), Nuclear Theory (nucl-th), Quantum Physics (quant-ph), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2202.04710}, url = {https://arxiv.org/abs/2202.04710}, author = {Bao, Ning and Cao, Charles and Zhu, Guanyu} } @article {3140, title = {Demonstration of three- and four-body interactions between trapped-ion spins}, year = {2022}, month = {9/12/2022}, abstract = {

Quantum processors use the native interactions between effective spins to simulate Hamiltonians or execute quantum gates. In most processors, the native interactions are pairwise, limiting the efficiency of controlling entanglement between many qubits. Here we experimentally demonstrate a new class of native interactions between trapped-ion qubits, extending conventional pairwise interactions to higher order. We realize three- and four-body spin interactions as examples, showing that high-order spin polynomials may serve as a new toolbox for quantum information applications.

}, keywords = {Atomic Physics (physics.atom-ph), FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2209.05691}, url = {https://arxiv.org/abs/2209.05691}, author = {Katz, Or and Feng, Lei and Risinger, Andrew and Monroe, Christopher and Cetina, Marko} } @article {3205, title = {Efficient and practical quantum compiler towards multi-qubit systems with deep reinforcement learning}, year = {2022}, month = {4/14/2022}, abstract = {

Efficient quantum compiling tactics greatly enhance the capability of quantum computers to execute complicated quantum algorithms. Due to its fundamental importance, a plethora of quantum compilers has been designed in past years. However, there are several caveats to current protocols, which are low optimality, high inference time, limited scalability, and lack of universality. To compensate for these defects, here we devise an efficient and practical quantum compiler assisted by advanced deep reinforcement learning (RL) techniques, i.e., data generation, deep Q-learning, and AQ* search. In this way, our protocol is compatible with various quantum machines and can be used to compile multi-qubit operators. We systematically evaluate the performance of our proposal in compiling quantum operators with both inverse-closed and inverse-free universal basis sets. In the task of single-qubit operator compiling, our proposal outperforms other RL-based quantum compilers in the measure of compiling sequence length and inference time. Meanwhile, the output solution is near-optimal, guaranteed by the Solovay-Kitaev theorem. Notably, for the inverse-free universal basis set, the achieved sequence length complexity is comparable with the inverse-based setting and dramatically advances previous methods. These empirical results contribute to improving the inverse-free Solovay-Kitaev theorem. In addition, for the first time, we demonstrate how to leverage RL-based quantum compilers to accomplish two-qubit operator compiling. The achieved results open an avenue for integrating RL with quantum compiling to unify efficiency and practicality and thus facilitate the exploration of quantum advantages.

}, keywords = {FOS: Computer and information sciences, FOS: Physical sciences, Machine Learning (cs.LG), Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2204.06904}, url = {https://arxiv.org/abs/2204.06904}, author = {Chen, Qiuhao and Du, Yuxuan and Zhao, Qi and Jiao, Yuling and Lu, Xiliang and Wu, Xingyao} } @article {2910, title = {Efficient Product Formulas for Commutators and Applications to Quantum Simulation}, journal = {Physical Review Research}, volume = {4}, year = {2022}, month = {03/10/2022}, chapter = {013191}, abstract = {

We construct product formulas for exponentials of commutators and explore their applications. First, we directly construct a third-order product formula with six exponentials by solving polynomial equations obtained using the operator differential method. We then derive higher-order product formulas recursively from the third-order formula. We improve over previous recursive constructions, reducing the number of gates required to achieve the same accuracy. In addition, we demonstrate that the constituent linear terms in the commutator can be included at no extra cost. As an application, we show how to use the product formulas in a digital protocol for counterdiabatic driving, which increases the fidelity for quantum state preparation. We also discuss applications to quantum simulation of one-dimensional fermion chains with nearest- and next-nearest-neighbor hopping terms, and two-dimensional fractional quantum Hall phases.

}, doi = {https://doi.org/10.1103/PhysRevResearch.4.013191}, url = {https://arxiv.org/abs/2111.12177}, author = {Yu-An Chen and Andrew M. Childs and Mohammad Hafezi and Zhang Jiang and Hwanmun Kim and Yijia Xu} } @article {3153, title = {Error-correcting codes for fermionic quantum simulation}, year = {2022}, month = {10/16/2022}, abstract = {

We provide ways to simulate fermions by qubits on 2d lattices using Z2 gauge theories (stabilizer codes). By studying the symplectic automorphisms of the Pauli module over the Laurent polynomial ring, we develop a systematic way to increase the code distances of stabilizer codes. We identify a family of stabilizer codes that can be used to simulate fermions with code distances of d=2,3,4,5,6,7 such that any \⌊d\−12\⌋-qubit error can be corrected. In particular, we demonstrate three stabilizer codes with code distances of d=3, d=4, and d=5, respectively, with all stabilizers and logical operators shown explicitly. The syndromes for all Pauli errors are provided. Finally, we introduce a syndrome-matching method to compute code distances numerically.

}, keywords = {FOS: Mathematics, FOS: Physical sciences, Mathematical Physics (math-ph), Quantum Algebra (math.QA), Quantum Physics (quant-ph), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2210.08411}, url = {https://arxiv.org/abs/2210.08411}, author = {Chen, Yu-An and Alexey V. Gorshkov and Xu, Yijia} } @article {3016, title = {Euler-obstructed Cooper pairing: Nodal superconductivity and hinge Majorana zero modes}, journal = {Physical Review B}, volume = {105}, year = {2022}, month = {3/29/2022}, abstract = {

Since the proposal of monopole Cooper pairing in [Phys. Rev. Lett. 120, 067003 (2018)], considerable research efforts have been dedicated to the study of Cooper pairing order parameters constrained (or obstructed) by the nontrivial normal-state band topology at Fermi surfaces in 3D systems. In the current work, we generalize the topologically obstructed pairings between Chern states (like the monopole Cooper pairing) by proposing Euler obstructed Cooper pairing in 3D systems. The Euler obstructed Cooper pairing widely exists between two Fermi surfaces with nontrivial band topology characterized by nonzero Euler numbers; such Fermi surfaces can exist in 3D PT-protected spinless-Dirac/nodal-line semimetals with negligible spin-orbit coupling, where PT is the space-time inversion symmetry. An Euler obstructed pairing channel must have pairing nodes on the pairing-relevant Fermi surfaces, and the total winding number of the pairing nodes is determined by the sum or difference of the Euler numbers on the Fermi surfaces. In particular, we find that when the normal state is time-reversal invariant and the pairing is weak, a sufficiently-dominant Euler obstructed pairing channel with zero total momentum leads to nodal superconductivity. If the Fermi surface splitting is small, the resultant nodal superconductor hosts hinge Majorana zero modes. The possible dominance of the Euler obstructed pairing channel near the superconducting transition and the robustness of the hinge Majorana zero modes against disorder are explicitly demonstrated using effective or tight-binding models. Our work presents the first class of higher-order nodal superconductivity originating from the topologically obstructed Cooper pairing.

}, doi = {https://doi.org/10.1103\%2Fphysrevb.105.104515}, url = {https://arxiv.org/abs/2109.02685}, author = {Jiabin Yu and Yu-An Chen and Sankar Das Sarma} } @article {3139, title = {Experimental Implementation of an Efficient Test of Quantumness}, year = {2022}, month = {9/28/2022}, abstract = {

A test of quantumness is a protocol where a classical user issues challenges to a quantum device to determine if it exhibits non-classical behavior, under certain cryptographic assumptions. Recent attempts to implement such tests on current quantum computers rely on either interactive challenges with efficient verification, or non-interactive challenges with inefficient (exponential time) verification. In this paper, we execute an efficient non-interactive test of quantumness on an ion-trap quantum computer. Our results significantly exceed the bound for a classical device\&$\#$39;s success.

}, keywords = {FOS: Physical sciences, Other Condensed Matter (cond-mat.other), Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2209.14316}, url = {https://arxiv.org/abs/2209.14316}, author = {Lewis, Laura and Zhu, Daiwei and Gheorghiu, Alexandru and Noel, Crystal and Katz, Or and Harraz, Bahaa and Wang, Qingfeng and Risinger, Andrew and Feng, Lei and Biswas, Debopriyo and Egan, Laird and Vidick, Thomas and Cetina, Marko and Monroe, Christopher} } @article {3122, title = {Extracting Wilson loop operators and fractional statistics from a single bulk ground state}, year = {2022}, month = {9/28/2022}, abstract = {

An essential aspect of topological phases of matter is the existence of Wilson loop operators that keep the ground state subspace invariant. Here we present and implement an unbiased numerical optimization scheme to systematically find the Wilson loop operators given a single ground state wave function of a gapped Hamiltonian on a disk. We then show how these Wilson loop operators can be cut and glued through further optimization to give operators that can create, move, and annihilate anyon excitations. We subsequently use these operators to determine the braiding statistics and topological twists of the anyons, yielding a way to fully extract topological order from a single wave function. We apply our method to the ground state of the perturbed toric code and doubled semion models with a magnetic field that is up to a half of the critical value. From a contemporary perspective, this can be thought of as a machine learning approach to discover emergent 1-form symmetries of a ground state wave function. From an application perspective, our approach can be relevant to find Wilson loop operators in current quantum simulators.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2209.14302}, url = {https://arxiv.org/abs/2209.14302}, author = {Cian, Ze-Pei and Hafezi, Mohammad and Barkeshli, Maissam} } @article {3179, title = {Group coset monogamy games and an application to device-independent continuous-variable QKD}, year = {2022}, month = {12/7/2022}, abstract = {

We develop an extension of a recently introduced subspace coset state monogamy-of-entanglement game [Coladangelo, Liu, Liu, and Zhandry; Crypto\&$\#$39;21] to general group coset states, which are uniform superpositions over elements of a subgroup to which has been applied a group-theoretic generalization of the quantum one-time pad. We give a general bound on the winning probability of a monogamy game constructed from subgroup coset states that applies to a wide range of finite and infinite groups. To study the infinite-group case, we use and further develop a measure-theoretic formalism that allows us to express continuous-variable measurements as operator-valued generalizations of probability measures.
We apply the monogamy game bound to various physically relevant groups, yielding realizations of the game in continuous-variable modes as well as in rotational states of a polyatomic molecule. We obtain explicit strong bounds in the case of specific group-space and subgroup combinations. As an application, we provide the first proof of one sided-device independent security of a squeezed-state continuous-variable quantum key distribution protocol against general coherent attacks.

}, keywords = {Cryptography and Security (cs.CR), FOS: Computer and information sciences, FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2212.03935}, url = {https://arxiv.org/abs/2212.03935}, author = {Culf, Eric and Vidick, Thomas and Victor V. Albert} } @article {2913, title = {Hamiltonian simulation with random inputs}, journal = {Phys. Rev. Lett. 129, 270502}, volume = {129}, year = {2022}, month = {12/30/2022}, abstract = {

The algorithmic error of digital quantum simulations is usually explored in terms of the spectral norm distance between the actual and ideal evolution operators. In practice, this worst-case error analysis may be unnecessarily pessimistic. To address this, we develop a theory of average-case performance of Hamiltonian simulation with random initial states. We relate the average-case error to the Frobenius norm of the multiplicative error and give upper bounds for the product formula (PF) and truncated Taylor series methods. As applications, we estimate average-case error for digital Hamiltonian simulation of general lattice Hamiltonians and k-local Hamiltonians. In particular, for the nearest-neighbor Heisenberg chain with n spins, the error is quadratically reduced from O(n) in the worst case to O(n\−\−\√) on average for both the PF method and the Taylor series method. Numerical evidence suggests that this theory accurately characterizes the average error for concrete models. We also apply our results to error analysis in the simulation of quantum scrambling.

}, doi = {https://doi.org/10.1103/PhysRevLett.129.270502}, url = {https://arxiv.org/abs/2111.04773}, author = {Qi Zhao and You Zhou and Alexander F. Shaw and Tongyang Li and Andrew M. Childs} } @article {3190, title = {Higher-group symmetry in finite gauge theory and stabilizer codes}, year = {2022}, month = {11/21/2022}, abstract = {

A large class of gapped phases of matter can be described by topological finite group gauge theories. In this paper, we derive the d-group global symmetry and its \&$\#$39;t Hooft anomaly for topological finite group gauge theories in (d+1) space-time dimensions, including non-Abelian gauge groups and Dijkgraaf-Witten twists. We focus on the 1-form symmetry generated by invertible (Abelian) magnetic defects and the higher-form symmetries generated by invertible topological defects decorated with lower dimensional gauged symmetry-protected topological (SPT) phases. We show that due to a generalization of the Witten effect and charge-flux attachment, the 1-form symmetry generated by the magnetic defects mixes with other symmetries into a higher group. We describe such higher-group symmetry in various lattice model examples. We discuss several applications, including the classification of fermionic SPT phases in (3+1)D for general fermionic symmetry groups, where we also derive a simpler formula for the [O5]\∈H5(BG,U(1)) obstruction than has appeared in previous work. We also show how the d-group symmetry is related to fault-tolerant non-Pauli logical gates and a refined Clifford hierarchy in stabilizer codes. We construct new logical gates in stabilizer codes using the d-group symmetry, such as the control-Z gate in (3+1)D Z2 toric code.

}, keywords = {FOS: Mathematics, FOS: Physical sciences, High Energy Physics - Theory (hep-th), Quantum Algebra (math.QA), Quantum Physics (quant-ph), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2211.11764}, url = {https://arxiv.org/abs/2211.11764}, author = {Barkeshli, Maissam and Chen, Yu-An and Hsin, Po-Shen and Kobayashi, Ryohei} } @article {2607, title = {Implementing a Fast Unbounded Quantum Fanout Gate Using Power-Law Interactions}, journal = {Phys. Rev. Research}, volume = {4}, year = {2022}, month = {10/27/2022}, abstract = {

The standard circuit model for quantum computation presumes the ability to directly perform gates between arbitrary pairs of qubits, which is unlikely to be practical for large-scale experiments. Power-law interactions with strength decaying as 1/rα in the distance r provide an experimentally realizable resource for information processing, whilst still retaining long-range connectivity. We leverage the power of these interactions to implement a fast quantum fanout gate with an arbitrary number of targets. Our implementation allows the quantum Fourier transform (QFT) and Shor\&$\#$39;s algorithm to be performed on a D-dimensional lattice in time logarithmic in the number of qubits for interactions with α\≤D. As a corollary, we show that power-law systems with α\≤D are difficult to simulate classically even for short times, under a standard assumption that factoring is classically intractable. Complementarily, we develop a new technique to give a general lower bound, linear in the size of the system, on the time required to implement the QFT and the fanout gate in systems that are constrained by a linear light cone. This allows us to prove an asymptotically tighter lower bound for long-range systems than is possible with previously available techniques.\ 

}, doi = {https://doi.org/10.1103/PhysRevResearch.4.L042016}, url = {https://arxiv.org/abs/2007.00662}, author = {Andrew Y. Guo and Abhinav Deshpande and Su-Kuan Chu and Zachary Eldredge and Przemyslaw Bienias and Dhruv Devulapalli and Yuan Su and Andrew M. Childs and Alexey V. Gorshkov} } @article {2814, title = {Kramers{\textquoteright} degeneracy for open systems in thermal equilibrium}, journal = {Phys. Rev. B}, volume = {105}, year = {2022}, month = {3/10/2022}, pages = {L121104}, doi = {https://doi.org/10.1103/PhysRevB.105.L121104}, url = {https://arxiv.org/abs/2105.02888}, author = {Simon Lieu and Max McGinley and Oles Shtanko and Nigel R. Cooper and Alexey V. Gorshkov} } @article {3142, title = {Many-Body Quantum Teleportation via Operator Spreading in the Traversable Wormhole Protocol}, journal = {Physical Review X}, volume = {12}, year = {2022}, month = {8/5/2022}, abstract = {

By leveraging shared entanglement between a pair of qubits, one can teleport a quantum state from one particle to another. Recent advances have uncovered an intrinsically many-body generalization of quantum teleportation, with an elegant and surprising connection to gravity. In particular, the teleportation of quantum information relies on many-body dynamics, which originate from strongly-interacting systems that are holographically dual to gravity; from the gravitational perspective, such quantum teleportation can be understood as the transmission of information through a traversable wormhole. Here, we propose and analyze a new mechanism for many-body quantum teleportation -- dubbed peaked-size teleportation. Intriguingly, peaked-size teleportation utilizes precisely the same type of quantum circuit as traversable wormhole teleportation, yet has a completely distinct microscopic origin: it relies upon the spreading of local operators under generic thermalizing dynamics and not gravitational physics. We demonstrate the ubiquity of peaked-size teleportation, both analytically and numerically, across a diverse landscape of physical systems, including random unitary circuits, the Sachdev-Ye-Kitaev model (at high temperatures), one-dimensional spin chains and a bulk theory of gravity with stringy corrections. Our results pave the way towards using many-body quantum teleportation as a powerful experimental tool for: (i) characterizing the size distributions of operators in strongly-correlated systems and (ii) distinguishing between generic and intrinsically gravitational scrambling dynamics. To this end, we provide a detailed experimental blueprint for realizing many-body quantum teleportation in both trapped ions and Rydberg atom arrays; effects of decoherence and experimental imperfections are analyzed.

}, doi = {10.1103/physrevx.12.031013}, url = {https://arxiv.org/abs/2102.00010}, author = {Thomas Schuster and Bryce Kobrin and Ping Gao and Iris Cong and Emil T. Khabiboulline and Norbert M. Linke and Mikhail D. Lukin and Christopher Monroe and Beni Yoshida and Norman Y. Yao} } @article {3147, title = {Multi-Angle QAOA Does Not Always Need All Its Angles}, year = {2022}, month = {9/23/2022}, abstract = {

Introducing additional tunable parameters to quantum circuits is a powerful way of improving performance without increasing hardware requirements. A recently introduced multi-angle extension of the quantum approximate optimization algorithm (ma-QAOA) significantly improves the solution from QAOA by allowing the parameters for each term in the Hamiltonian to vary independently. However, prior results suggest that there is considerable redundancy in parameters, the removal of which would reduce the cost of parameter optimization. In this work, we show numerically that problem symmetries can be used to reduce the number of parameters used by ma-QAOA without decreasing the solution quality. We study MaxCut on all 7,565 connected, non-isomorphic 8-node graphs with a non-trivial symmetry group and show numerically that in 67.4\% of these graphs, symmetry can be used to reduce the number of parameters with no decrease in the objective, with the average ratio of parameters reduced by 28.1\%. Moreover, we show that in 35.9\% of the graphs this can be achieved by simply using the largest symmetry. For the graphs where reducing the number of parameters leads to a decrease in the objective, the largest symmetry can be used to reduce the parameter count by 37.1\% at the cost of only a 6.1\% decrease in the objective.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2209.11839}, url = {https://arxiv.org/abs/2209.11839}, author = {Shi, Kaiyan and Herrman, Rebekah and Shaydulin, Ruslan and Chakrabarti, Shouvanik and Pistoia, Marco and Larson, Jeffrey} } @article {3141, title = {N-body interactions between trapped ion qubits via spin-dependent squeezing}, journal = {Physical Review Letters}, volume = {129}, year = {2022}, month = {8/5/2022}, abstract = {

We describe a simple protocol for the single-step generation of N-body entangling interactions between trapped atomic ion qubits. We show that qubit state-dependent squeezing operations and displacement forces on the collective atomic motion can generate full N-body interactions. Similar to the M{\o}lmer-S{\o}rensen two-body Ising interaction at the core of most trapped ion quantum computers and simulators, the proposed operation is relatively insensitive to the state of motion. We show how this N-body gate operation allows the single-step implementation of a family of N-bit gate operations such as the powerful N-Toffoli gate, which flips a single qubit if and only if all other N-1 qubits are in a particular state.

}, doi = {10.1103/physrevlett.129.063603}, url = {https://arxiv.org/abs/2202.04230}, author = {Or Katz and Marko Cetina and Christopher Monroe} } @article {3196, title = {Optimal scaling quantum linear systems solver via discrete adiabatic theorem}, journal = {PRX Quantum}, volume = {3}, year = {2022}, month = {10/7/2022}, pages = {040303}, abstract = {

Recently, several approaches to solving linear systems on a quantum computer have been formulated in terms of the quantum adiabatic theorem for a continuously varying Hamiltonian. Such approaches enabled near-linear scaling in the condition number κ of the linear system, without requiring a complicated variable-time amplitude amplification procedure. However, the most efficient of those procedures is still asymptotically sub-optimal by a factor of log(κ). Here, we prove a rigorous form of the adiabatic theorem that bounds the error in terms of the spectral gap for intrinsically discrete time evolutions. We use this discrete adiabatic theorem to develop a quantum algorithm for solving linear systems that is asymptotically optimal, in the sense that the complexity is strictly linear in κ, matching a known lower bound on the complexity. Our O(κlog(1/ϵ)) complexity is also optimal in terms of the combined scaling in κ and the precision ϵ. Compared to existing suboptimal methods, our algorithm is simpler and easier to implement. Moreover, we determine the constant factors in the algorithm, which would be suitable for determining the complexity in terms of gate counts for specific applications.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {https://journals.aps.org/prxquantum/pdf/10.1103/PRXQuantum.3.040303}, url = {https://arxiv.org/abs/2111.08152}, author = {Costa, Pedro C. S. and An, Dong and Sanders, Yuval R. and Su, Yuan and Babbush, Ryan and Berry, Dominic W.} } @article {3015, title = {Pauli Stabilizer Models of Twisted Quantum Doubles}, journal = {PRX Quantum}, volume = {3}, year = {2022}, month = {3/30/2022}, abstract = {

We construct a Pauli stabilizer model for every two-dimensional Abelian topological order that admits a gapped boundary. Our primary example is a Pauli stabilizer model on four-dimensional qudits that belongs to the double semion (DS) phase of matter. The DS stabilizer Hamiltonian is constructed by condensing an emergent boson in a Z4 toric code, where the condensation is implemented by making certain two-body measurements. We rigorously verify the topological order of the DS stabilizer model by identifying an explicit finite-depth quantum circuit (with ancillary qubits) that maps its ground state subspace to that of a DS string-net model. We show that the construction of the DS stabilizer Hamiltonian generalizes to all twisted quantum doubles (TQDs) with Abelian anyons. This yields a Pauli stabilizer code on composite-dimensional qudits for each such TQD, implying that the classification of topological Pauli stabilizer codes extends well beyond stacks of toric codes - in fact, exhausting all Abelian anyon theories that admit a gapped boundary. We also demonstrate that symmetry-protected topological phases of matter characterized by type I and type II cocycles can be modeled by Pauli stabilizer Hamiltonians by gauging certain 1-form symmetries of the TQD stabilizer models.

}, doi = {https://doi.org/10.1103\%2Fprxquantum.3.010353}, url = {https://arxiv.org/abs/2112.11394}, author = {Tyler D. Ellison and Yu-An Chen and Arpit Dua and Wilbur Shirley and Nathanan Tantivasadakarn and Dominic J. Williamson} } @article {3193, title = {Pauli topological subsystem codes from Abelian anyon theories}, year = {2022}, month = {11/7/2022}, abstract = {

We construct Pauli topological subsystem codes characterized by arbitrary two-dimensional Abelian anyon theories--this includes anyon theories with degenerate braiding relations and those without a gapped boundary to the vacuum. Our work both extends the classification of two-dimensional Pauli topological subsystem codes to systems of composite-dimensional qudits and establishes that the classification is at least as rich as that of Abelian anyon theories. We exemplify the construction with topological subsystem codes defined on four-dimensional qudits based on the Z(1)4 anyon theory with degenerate braiding relations and the chiral semion theory--both of which cannot be captured by topological stabilizer codes. The construction proceeds by \"gauging out\" certain anyon types of a topological stabilizer code. This amounts to defining a gauge group generated by the stabilizer group of the topological stabilizer code and a set of anyonic string operators for the anyon types that are gauged out. The resulting topological subsystem code is characterized by an anyon theory containing a proper subset of the anyons of the topological stabilizer code. We thereby show that every Abelian anyon theory is a subtheory of a stack of toric codes and a certain family of twisted quantum doubles that generalize the double semion anyon theory. We further prove a number of general statements about the logical operators of translation invariant topological subsystem codes and define their associated anyon theories in terms of higher-form symmetries.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2211.03798}, url = {https://arxiv.org/abs/2211.03798}, author = {Ellison, Tyler D. and Chen, Yu-An and Dua, Arpit and Shirley, Wilbur and Tantivasadakarn, Nathanan and Williamson, Dominic J.} } @article {3150, title = {Quantum Algorithms for Sampling Log-Concave Distributions and Estimating Normalizing Constants}, journal = {Advances in Neural Information Processing Systems (NeurIPS 2022)}, volume = {35}, year = {2022}, month = {10/12/2022}, keywords = {FOS: Computer and information sciences, FOS: Mathematics, FOS: Physical sciences, Machine Learning (cs.LG), Optimization and Control (math.OC), Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2210.06539}, url = {https://arxiv.org/abs/2210.06539}, author = {Andrew M. Childs and Li, Tongyang and Liu, Jin-Peng and Wang, Chunhao and Zhang, Ruizhe} } @article {3137, title = {Quantum Depth in the Random Oracle Model}, year = {2022}, month = {10/12/2022}, abstract = {

We give a comprehensive characterization of the computational power of shallow quantum circuits combined with classical computation. Specifically, for classes of search problems, we show that the following statements hold, relative to a random oracle:
(a) BPPQNCBPP\≠BQP. This refutes Jozsa\&$\#$39;s conjecture [QIP 05] in the random oracle model. As a result, this gives the first instantiatable separation between the classes by replacing the oracle with a cryptographic hash function, yielding a resolution to one of Aaronson\&$\#$39;s ten semi-grand challenges in quantum computing.
(b) BPPQNC⊈QNCBPP and QNCBPP⊈BPPQNC. This shows that there is a subtle interplay between classical computation and shallow quantum computation. In fact, for the second separation, we establish that, for some problems, the ability to perform adaptive measurements in a single shallow quantum circuit, is more useful than the ability to perform polynomially many shallow quantum circuits without adaptive measurements.
(c) There exists a 2-message proof of quantum depth protocol. Such a protocol allows a classical verifier to efficiently certify that a prover must be performing a computation of some minimum quantum depth. Our proof of quantum depth can be instantiated using the recent proof of quantumness construction by Yamakawa and Zhandry [STOC 22].

}, keywords = {Computational Complexity (cs.CC), Cryptography and Security (cs.CR), FOS: Computer and information sciences, FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2210.06454}, url = {https://arxiv.org/abs/2210.06454}, author = {Arora, Atul Singh and Coladangelo, Andrea and Coudron, Matthew and Gheorghiu, Alexandru and Singh, Uttam and Waldner, Hendrik} } @article {3138, title = {Quantum divide and conquer}, year = {2022}, month = {10/12/2022}, abstract = {

The divide-and-conquer framework, used extensively in classical algorithm design, recursively breaks a problem of size n into smaller subproblems (say, a copies of size n/b each), along with some auxiliary work of cost Caux(n), to give a recurrence relation
C(n)\≤aC(n/b)+Caux(n)
for the classical complexity C(n). We describe a quantum divide-and-conquer framework that, in certain cases, yields an analogous recurrence relation
CQ(n)\≤a\−\−\√CQ(n/b)+O(CauxQ(n))
that characterizes the quantum query complexity. We apply this framework to obtain near-optimal quantum query complexities for various string problems, such as (i) recognizing regular languages; (ii) decision versions of String Rotation and String Suffix; and natural parameterized versions of (iii) Longest Increasing Subsequence and (iv) Longest Common Subsequence.

}, keywords = {Data Structures and Algorithms (cs.DS), FOS: Computer and information sciences, FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2210.06419}, url = {https://arxiv.org/abs/2210.06419}, author = {Andrew M. Childs and Kothari, Robin and Kovacs-Deak, Matt and Sundaram, Aarthi and Wang, Daochen} } @article {2873, title = {Quantum Lego: Building Quantum Error Correction Codes from Tensor Networks}, journal = {PRX Quantum}, volume = {3}, year = {2022}, month = {05/11/2022}, pages = {020332}, abstract = {

We introduce a flexible and graphically intuitive framework that constructs complex quantum error correction codes from simple codes or states, generalizing code concatenation. More specifically, we represent the complex code constructions as tensor networks built from the tensors of simple codes or states in a modular fashion. Using a set of local moves known as operator pushing, one can derive properties of the more complex codes, such as transversal non-Clifford gates, by tracing the flow of operators in the network. The framework endows a network geometry to any code it builds and is valid for constructing stabilizer codes as well as non-stabilizer codes over qubits and qudits. For a contractible tensor network, the sequence of contractions also constructs a decoding/encoding circuit. To highlight the framework\&$\#$39;s range of capabilities and to provide a tutorial, we lay out some examples where we glue together simple stabilizer codes to construct non-trivial codes. These examples include the toric code and its variants, a holographic code with transversal non-Clifford operators, a 3d stabilizer code, and other stabilizer codes with interesting properties. Surprisingly, we find that the surface code is equivalent to the 2d Bacon-Shor code after \"dualizing\" its tensor network encoding map.

}, doi = {https://journals.aps.org/prxquantum/pdf/10.1103/PRXQuantum.3.020332}, url = {https://arxiv.org/abs/2109.08158}, author = {ChunJun Cao and Brad Lackey} } @article {3191, title = {Quantum Natural Proof: A New Perspective of Hybrid Quantum-Classical Program Verification}, year = {2022}, month = {11/11/2022}, abstract = {

Many quantum programs are assured by formal verification, but such verification is usually laborious and time-consuming. This paper proposes quantum natural proof (QNP), an automated proof system for verifying hybrid quantum-classical algorithms. Natural proofs are a subclass of proofs that are amenable to completely automated reasoning, provide sound but incomplete procedures, and capture common reasoning tactics in program verification. The core of QNP is a type-guided quantum proof system, named Qafny, which views quantum operations as some classical array operations that can be modeled as proof rules in a classical separation logic framework, suitable for automated reasoning. We proved the soundness and completeness of the Qafny proof system as well as the soundness of the proof system compilation from Qafny to Dafny. By using the QNP implementation in Dafny, automated verification can be efficiently perform for many hybrid quantum-classical algorithms, including GHZ, Shor\&$\#$39;s, Grover\&$\#$39;s, and quantum walk algorithms, which saves a great amount of human efforts. In addition, quantum programs written in Qafny can be compiled to quantum circuits so that every verified quantum program can be run on a quantum machine.

}, keywords = {FOS: Computer and information sciences, FOS: Physical sciences, Programming Languages (cs.PL), Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2211.06411}, url = {https://arxiv.org/abs/2211.06411}, author = {Li, Liyi and Zhu, Mingwei and Lee, Yi and Chang, Le and Wu, Xiaodi} } @article {2996, title = {Quantum Routing with Teleportation}, year = {2022}, month = {4/8/2022}, abstract = {

We study the problem of implementing arbitrary permutations of qubits under interaction constraints in quantum systems that allow for arbitrarily fast local operations and classical communication (LOCC). In particular, we show examples of speedups over swap-based and more general unitary routing methods by distributing entanglement and using LOCC to perform quantum teleportation. We further describe an example of an interaction graph for which teleportation gives a logarithmic speedup in the worst-case routing time over swap-based routing. We also study limits on the speedup afforded by quantum teleportation - showing an O(NlogN\−\−\−\−\−\−\−\√) upper bound on the separation in routing time for any interaction graph - and give tighter bounds for some common classes of graphs.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2204.04185}, url = {https://arxiv.org/abs/2204.04185}, author = {Devulapalli, Dhruv and Schoute, Eddie and Bapat, Aniruddha and Andrew M. Childs and Alexey V. Gorshkov} } @article {2997, title = {Quantum Simulation for High Energy Physics}, year = {2022}, month = {4/7/2022}, abstract = {

It is for the first time that Quantum Simulation for High Energy Physics (HEP) is studied in the U.S. decadal particle-physics community planning, and in fact until recently, this was not considered a mainstream topic in the community. This fact speaks of a remarkable rate of growth of this subfield over the past few years, stimulated by the impressive advancements in Quantum Information Sciences (QIS) and associated technologies over the past decade, and the significant investment in this area by the government and private sectors in the U.S. and other countries. High-energy physicists have quickly identified problems of importance to our understanding of nature at the most fundamental level, from tiniest distances to cosmological extents, that are intractable with classical computers but may benefit from quantum advantage. They have initiated, and continue to carry out, a vigorous program in theory, algorithm, and hardware co-design for simulations of relevance to the HEP mission. This community whitepaper is an attempt to bring this exciting and yet challenging area of research to the spotlight, and to elaborate on what the promises, requirements, challenges, and potential solutions are over the next decade and beyond.

}, keywords = {FOS: Physical sciences, High Energy Physics - Lattice (hep-lat), High Energy Physics - Phenomenology (hep-ph), High Energy Physics - Theory (hep-th), Nuclear Theory (nucl-th), Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2204.03381}, url = {https://arxiv.org/abs/2204.03381}, author = {Bauer, Christian W. and Davoudi, Zohreh and Balantekin, A. Baha and Bhattacharya, Tanmoy and Carena, Marcela and de Jong, Wibe A. and Draper, Patrick and El-Khadra, Aida and Gemelke, Nate and Hanada, Masanori and Kharzeev, Dmitri and Lamm, Henry and Li, Ying-Ying and Liu, Junyu and Lukin, Mikhail and Meurice, Yannick and Monroe, Christopher and Nachman, Benjamin and Pagano, Guido and Preskill, John and Rinaldi, Enrico and Roggero, Alessandro and Santiago, David I. and Savage, Martin J. and Siddiqi, Irfan and Siopsis, George and Van Zanten, David and Wiebe, Nathan and Yamauchi, Yukari and Yeter-Aydeniz, K{\"u}bra and Zorzetti, Silvia} } @article {3187, title = {Quantum simulation of real-space dynamics}, journal = {Quantum}, volume = {6}, year = {2022}, month = {11/8/2022}, pages = {860}, abstract = {

Quantum simulation is a prominent application of quantum computers. While there is extensive previous work on simulating finite-dimensional systems, less is known about quantum algorithms for real-space dynamics. We conduct a systematic study of such algorithms. In particular, we show that the dynamics of a d-dimensional Schr{\"o}dinger equation with η particles can be simulated with gate complexity O~(ηdFpoly(log(g\′/ϵ))), where ϵ is the discretization error, g\′ controls the higher-order derivatives of the wave function, and F measures the time-integrated strength of the potential. Compared to the best previous results, this exponentially improves the dependence on ϵ and g\′ from poly(g\′/ϵ) to poly(log(g\′/ϵ)) and polynomially improves the dependence on T and d, while maintaining best known performance with respect to η. For the case of Coulomb interactions, we give an algorithm using η3(d+η)Tpoly(log(ηdTg\′/(Δϵ)))/Δ one- and two-qubit gates, and another using η3(4d)d/2Tpoly(log(ηdTg\′/(Δϵ)))/Δ one- and two-qubit gates and QRAM operations, where T is the evolution time and the parameter Δ regulates the unbounded Coulomb interaction. We give applications to several computational problems, including faster real-space simulation of quantum chemistry, rigorous analysis of discretization error for simulation of a uniform electron gas, and a quadratic improvement to a quantum algorithm for escaping saddle points in nonconvex optimization.

}, doi = {https://doi.org/10.22331/q-2022-11-17-860}, url = {https://doi.org/10.22331\%2Fq-2022-11-17-860}, author = {Andrew M. Childs and Jiaqi Leng and Tongyang Li and Jin-Peng Liu and Chenyi Zhang} } @article {3146, title = {Quantum state tomography via non-convex Riemannian gradient descent}, year = {2022}, month = {10/10/2022}, abstract = {

The recovery of an unknown density matrix of large size requires huge computational resources. The recent Factored Gradient Descent (FGD) algorithm and its variants achieved state-of-the-art performance since they could mitigate the dimensionality barrier by utilizing some of the underlying structures of the density matrix. Despite their theoretical guarantee of a linear convergence rate, the convergence in practical scenarios is still slow because the contracting factor of the FGD algorithms depends on the condition number κ of the ground truth state. Consequently, the total number of iterations can be as large as O(κ\−\−\√ln(1ε)) to achieve the estimation error ε. In this work, we derive a quantum state tomography scheme that improves the dependence on κ to the logarithmic scale; namely, our algorithm could achieve the approximation error ε in O(ln(1κε)) steps. The improvement comes from the application of the non-convex Riemannian gradient descent (RGD). The contracting factor in our approach is thus a universal constant that is independent of the given state. Our theoretical results of extremely fast convergence and nearly optimal error bounds are corroborated by numerical results.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2210.04717}, url = {https://arxiv.org/abs/2210.04717}, author = {Hsu, Ming-Chien and Kuo, En-Jui and Yu, Wei-Hsuan and Cai, Jian-Feng and Hsieh, Min-Hsiu} } @article {3009, title = {Self-Testing of a Single Quantum System: Theory and Experiment}, year = {2022}, month = {3/17/2022}, abstract = {

Certifying individual quantum devices with minimal assumptions is crucial for the development of quantum technologies. Here, we investigate how to leverage single-system contextuality to realize self-testing. We develop a robust self-testing protocol based on the simplest contextuality witness for the simplest contextual quantum system, the Klyachko-Can-Binicio{\u g}lu-Shumovsky (KCBS) inequality for the qutrit. We establish a lower bound on the fidelity of the state and the measurements (to an ideal configuration) as a function of the value of the witness under a pragmatic assumption on the measurements we call the KCBS orthogonality condition. We apply the method in an experiment with randomly chosen measurements on a single trapped 40Ca+ and near-perfect detection efficiency. The observed statistics allow us to self-test the system and provide the first experimental demonstration of quantum self-testing of a single system. Further, we quantify and report that deviations from our assumptions are minimal, an aspect previously overlooked by contextuality experiments.

}, keywords = {Atomic Physics (physics.atom-ph), FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {https://doi.org/10.48550/arXiv.2203.09003}, url = {https://arxiv.org/abs/2203.09003}, author = {Hu, Xiao-Min and Xie, Yi and Arora, Atul Singh and Ai, Ming-Zhong and Bharti, Kishor and Zhang, Jie and Wu, Wei and Chen, Ping-Xing and Cui, Jin-Ming and Liu, Bi-Heng and Huang, Yun-Feng and Li, Chuan-Feng and Guo, Guang-Can and Roland, J{\'e}r{\'e}mie and Cabello, Ad{\'a}n and Kwek, Leong-Chuan} } @article {3017, title = {Shadow Distillation: Quantum Error Mitigation with Classical Shadows for Near-Term Quantum Processors}, year = {2022}, month = {3/14/2022}, abstract = {

Mitigating errors in quantum information processing devices is especially important in the absence of fault tolerance. An effective method in suppressing state-preparation errors is using multiple copies to distill the ideal component from a noisy quantum state. Here, we use classical shadows and randomized measurements to circumvent the need for coherent access to multiple copies at an exponential cost. We study the scaling of resources using numerical simulations and find that the overhead is still favorable compared to full state tomography. We optimize measurement resources under realistic experimental constraints and apply our method to an experiment preparing Greenberger-Horne-Zeilinger (GHZ) state with trapped ions. In addition to improving stabilizer measurements, the analysis of the improved results reveals the nature of errors affecting the experiment. Hence, our results provide a directly applicable method for mitigating errors in near-term quantum computers.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2203.07309}, url = {https://arxiv.org/abs/2203.07309}, author = {Seif, Alireza and Cian, Ze-Pei and Zhou, Sisi and Chen, Senrui and Jiang, Liang} } @article {2999, title = {Snowmass 2021 White Paper: Tabletop experiments for infrared quantum gravity}, year = {2022}, month = {3/22/2022}, abstract = {

Progress in the quantum readout and control of mechanical devices from single atoms to large masses may enable a first generation of experiments probing the gravitational interaction in the quantum regime, conceivably within the next decade. In this Snowmass whitepaper, we briefly outline the possibilities and challenges facing the realization of these experiments. In particular, we emphasize the need for detailed theories of modifications to the usual effective QFT of gravitons in the infrared regime E/L3<}, keywords = {FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), High Energy Physics - Phenomenology (hep-ph), Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2203.11846}, url = {https://arxiv.org/abs/2203.11846}, author = {Carney, Daniel and Chen, Yanbei and Geraci, Andrew and M{\"u}ller, Holger and Panda, Cristian D. and Stamp, Philip C. E. and Taylor, Jacob M.} } @article {3000, title = {Snowmass 2021 White Paper: The Windchime Project}, year = {2022}, month = {3/14/2022}, abstract = {

The absence of clear signals from particle dark matter in direct detection experiments motivates new approaches in disparate regions of viable parameter space. In this Snowmass white paper, we outline the Windchime project, a program to build a large array of quantum-enhanced mechanical sensors. The ultimate aim is to build a detector capable of searching for Planck mass-scale dark matter purely through its gravitational coupling to ordinary matter. In the shorter term, we aim to search for a number of other physics targets, especially some ultralight dark matter candidates. Here, we discuss the basic design, open R\&D challenges and opportunities, current experimental efforts, and both short- and long-term physics targets of the Windchime project.

}, keywords = {Cosmology and Nongalactic Astrophysics (astro-ph.CO), FOS: Physical sciences, High Energy Physics - Experiment (hep-ex), High Energy Physics - Phenomenology (hep-ph)}, doi = {10.48550/ARXIV.2203.07242}, url = {https://arxiv.org/abs/2203.07242}, author = {The Windchime Collaboration and Attanasio, Alaina and Bhave, Sunil A. and Blanco, Carlos and Carney, Daniel and Demarteau, Marcel and Elshimy, Bahaa and Febbraro, Michael and Feldman, Matthew A. and Ghosh, Sohitri and Hickin, Abby and Hong, Seongjin and Lang, Rafael F. and Lawrie, Benjamin and Li, Shengchao and Liu, Zhen and Maldonado, Juan P. A. and Marvinney, Claire and Oo, Hein Zay Yar and Pai, Yun-Yi and Pooser, Raphael and Qin, Juehang and Sparmann, Tobias J. and Taylor, Jacob M. and Tian, Hao and Tunnell, Christopher} } @article {3063, title = {Status Report on the Third Round of the NIST Post-Quantum Cryptography Standardization Process}, journal = {NIST}, year = {2022}, month = {7/2022}, abstract = {

The National Institute of Standards and Technology is in the process of selecting publickey cryptographic algorithms through a public, competition-like process. The new publickey cryptography standards will specify additional digital signature, public-key encryption, and key-establishment algorithms to augment Federal Information Processing Standard (FIPS) 186-4, Digital Signature Standard (DSS), as well as NIST Special Publication (SP) 800-56A Revision 3, Recommendation for Pair-Wise Key-Establishment Schemes Using Discrete Logarithm Cryptography, and SP 800-56B Revision 2, Recommendation for Pair-Wise Key Establishment Using Integer Factorization Cryptography. It is intended that these algorithms will be capable of protecting sensitive information well into the foreseeable future, including after the advent of quantum computers.

This report describes the evaluation and selection process of the NIST Post-Quantum Cryptography Standardization process third-round candidates based on public feedback and internal review. The report summarizes each of the 15 third-round candidate algorithms and identifies those selected for standardization, as well as those that will continue to be evaluated in a fourth round of analysis. The public-key encryption and key-establishment algorithm that will be standardized is CRYSTALS\–KYBER. The digital signatures that will be standardized are CRYSTALS\–Dilithium, FALCON, and SPHINCS+. While there are multiple signature algorithms selected, NIST recommends CRYSTALS\–Dilithium as the primary algorithm to be implemented. In addition, four of the alternate key-establishment candidate algorithms will advance to a fourth round of evaluation: BIKE, Classic McEliece, HQC, and SIKE. These candidates are still being considered for future standardization. NIST will also issue a new Call for Proposals for public-key digital signature algorithms to augment and diversify its signature portfolio.

}, doi = {https://doi.org/10.6028/NIST.IR.8413-upd1}, author = {Gorjan Alagic and Daniel Apon and David Cooper and Quynh Dang and Thinh Dang and John Kelsey and Jacob Lichtinger and Carl Miller and Dustin Moody and Rene Peralta and Ray Perlner and Angela Robinson} } @article {3199, title = {Tailoring three-dimensional topological codes for biased noise}, year = {2022}, month = {11/3/2022}, abstract = {

Tailored topological stabilizer codes in two dimensions have been shown to exhibit high storage threshold error rates and improved subthreshold performance under biased Pauli noise. Three-dimensional (3D) topological codes can allow for several advantages including a transversal implementation of non-Clifford logical gates, single-shot decoding strategies, parallelized decoding in the case of fracton codes as well as construction of fractal lattice codes. Motivated by this, we tailor 3D topological codes for enhanced storage performance under biased Pauli noise. We present Clifford deformations of various 3D topological codes, such that they exhibit a threshold error rate of 50\% under infinitely biased Pauli noise. Our examples include the 3D surface code on the cubic lattice, the 3D surface code on a checkerboard lattice that lends itself to a subsystem code with a single-shot decoder, the 3D color code, as well as fracton models such as the X-cube model, the Sierpinski model and the Haah code. We use the belief propagation with ordered statistics decoder (BP-OSD) to study threshold error rates at finite bias. We also present a rotated layout for the 3D surface code, which uses roughly half the number of physical qubits for the same code distance under appropriate boundary conditions. Imposing coprime periodic dimensions on this rotated layout leads to logical operators of weight O(n) at infinite bias and a corresponding exp[\−O(n)] subthreshold scaling of the logical failure rate, where n is the number of physical qubits in the code. Even though this scaling is unstable due to the existence of logical representations with O(1) low-rate Pauli errors, the number of such representations scales only polynomially for the Clifford-deformed code, leading to an enhanced effective distance.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2211.02116}, url = {https://arxiv.org/abs/2211.02116}, author = {Huang, Eric and Pesah, Arthur and Chubb, Christopher T. and Vasmer, Michael and Dua, Arpit} } @article {3012, title = {Three-dimensional quantum cellular automata from chiral semion surface topological order and beyond}, year = {2022}, month = {2/10/2022}, abstract = {

We construct a novel three-dimensional quantum cellular automaton (QCA) based on a system with short-range entangled bulk and chiral semion boundary topological order. We argue that either the QCA is nontrivial, i.e. not a finite-depth circuit of local quantum gates, or there exists a two-dimensional commuting projector Hamiltonian realizing the chiral semion topological order (characterized by U(1)2 Chern-Simons theory). Our QCA is obtained by first constructing the Walker-Wang Hamiltonian of a certain premodular tensor category of order four, then condensing the deconfined bulk boson at the level of lattice operators. We show that the resulting Hamiltonian hosts chiral semion surface topological order in the presence of a boundary and can be realized as a non-Pauli stabilizer code on qubits, from which the QCA is defined. The construction is then generalized to a class of QCAs defined by non-Pauli stabilizer codes on 2n-dimensional qudits that feature surface anyons described by U(1)2n Chern-Simons theory. Our results support the conjecture that the group of nontrivial three-dimensional QCAs is isomorphic to the Witt group of non-degenerate braided fusion categories.

}, keywords = {FOS: Physical sciences, Mathematical Physics (math-ph), Quantum Physics (quant-ph), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2202.05442}, url = {https://arxiv.org/abs/2202.05442}, author = {Shirley, Wilbur and Chen, Yu-An and Dua, Arpit and Ellison, Tyler D. and Tantivasadakarn, Nathanan and Williamson, Dominic J.} } @article {3004, title = {Tweezer-programmable 2D quantum walks in a Hubbard-regime lattice}, journal = {Science}, volume = {377}, year = {2022}, month = {8/18/2022}, pages = {885-889}, abstract = {

Quantum walks provide a framework for understanding and designing quantum algorithms that is both intuitive and universal. To leverage the computational power of these walks, it is important to be able to programmably modify the graph a walker traverses while maintaining coherence. Here, we do this by combining the fast, programmable control provided by optical tweezer arrays with the scalable, homogeneous environment of an optical lattice. Using this new combination of tools we study continuous-time quantum walks of single atoms on a 2D square lattice, and perform proof-of-principle demonstrations of spatial search using these walks. When scaled to more particles, the capabilities demonstrated here can be extended to study a variety of problems in quantum information science and quantum simulation, including the deterministic assembly of ground and excited states in Hubbard models with tunable interactions, and performing versions of spatial search in a larger graph with increased connectivity, where search by quantum walk can be more effective.

}, keywords = {Atomic Physics (physics.atom-ph), FOS: Physical sciences, Quantum Gases (cond-mat.quant-gas), Quantum Physics (quant-ph)}, doi = {https://doi.org/10.1126/science.abo0608}, url = {https://arxiv.org/abs/2202.01204}, author = {Young, Aaron W. and Eckner, William J. and Schine, Nathan and Andrew M. Childs and Kaufman, Adam M.} } @article {2691, title = {Approximate Bacon-Shor Code and Holography}, journal = {Journal of High Energy Physics}, volume = {2021}, year = {2021}, month = {5/14/2021}, abstract = {

We construct an explicit and solvable toy model for the AdS/CFT correspondence in the form of an approximate quantum error correction code with a non-trivial center in the code subalgebra. Specifically, we use the Bacon-Shor codes and perfect tensors to construct a gauge code (or a stabilizer code with gauge-fixing), which we call the holographic hybrid code. This code admits a local log-depth encoding/decoding circuit, and can be represented as a holographic tensor network which satisfies an analog of the Ryu-Takayanagi formula and reproduces features of the sub-region duality. We then construct approximate versions of the holographic hybrid codes by \"skewing\" the code subspace, where the size of skewing is analogous to the size of the gravitational constant in holography. These approximate hybrid codes are not necessarily stabilizer codes, but they can be expressed as the superposition of holographic tensor networks that are stabilizer codes. For such constructions, different logical states, representing different bulk matter content, can \"back-react\" on the emergent geometry, resembling a key feature of gravity. The locality of the bulk degrees of freedom becomes subspace-dependent and approximate. Such subspace-dependence is manifest in the form of bulk operator reconstruction from the boundary. Exact complementary error correction breaks down for certain bipartition of the boundary degrees of freedom; however, a limited, state-dependent form is preserved for particular subspaces. We also construct an example where the connected two-point correlation functions can have a power-law decay. Coupled with known constraints from holography, a weakly back-reacting bulk also forces these skewed tensor network models to the \"large N limit\" where they are built by concatenating a large N number of copies.

}, doi = {https://doi.org/10.1007/JHEP05(2021)127}, url = {https://arxiv.org/abs/2010.05960}, author = {ChunJun Cao and Brad Lackey} } @article {2857, title = {Chiral transport of hot carriers in graphene in the quantum Hall regime}, year = {2021}, month = {10/3/2021}, abstract = {

Photocurrent (PC) measurements can reveal the relaxation dynamics of photo-excited hot carriers beyond the linear response of conventional transport experiments, a regime important for carrier multiplication. In graphene subject to a magnetic field, PC measurements are able to probe the existence of Landau levels with different edge chiralities which is exclusive to relativistic electron systems. Here, we report the accurate measurement of PC in graphene in the quantum Hall regime. Prominent PC oscillations as a function of gate voltage on samples\&$\#$39; edges are observed. These oscillation amplitudes form an envelope which depends on the strength of the magnetic field, as does the PCs\&$\#$39; power dependence and their saturation behavior. We explain these experimental observations through a model using optical Bloch equations, incorporating relaxations through acoustic-, optical- phonons and Coulomb interactions. The simulated PC agrees with our experimental results, leading to a unified understanding of the chiral PC in graphene at various magnetic field strengths, and providing hints for the occurrence of a sizable carrier multiplication.\ 

}, url = {https://arxiv.org/abs/2110.01079}, author = {Bin Cao and Tobias Grass and Olivier Gazzano and Kishan Ashokbhai Patel and Jiuning Hu and Markus M{\"u}ller and Tobias Huber and Luca Anzi and Kenji Watanabe and Takashi Taniguchi and David Newell and Michael Gullans and Roman Sordan and Mohammad Hafezi and Glenn Solomon} } @article {2914, title = {Comment on "Using an atom interferometer to infer gravitational entanglement generation{\textquoteright}{\textquoteright}}, year = {2021}, month = {11/8/2021}, abstract = {

Our paper arXiv:2101.11629 contains a technical error which changes some of the conclusions. We thank Streltsov, Pedernales, and Plenio for bringing the essence of this error to our attention. Here we explain the error, examine its consequences, and suggest methods to overcome the resulting weakness in the proposed experiment.

}, url = {https://arxiv.org/abs/2111.04667}, author = {Daniel Carney and Holger M{\"u}ller and Jacob M. Taylor} } @article {2638, title = {Conformal field theories are magical}, journal = {Physical Review B}, volume = {103}, year = {2021}, month = {2/25/2021}, pages = {075145}, abstract = {

\"Magic\" is the degree to which a state cannot be approximated by Clifford gates. We study mana, a measure of magic, in the ground state of the Z3 Potts model, and argue that it is a broadly useful diagnostic for many-body physics. In particular we find that the q=3 ground state has large mana at the model\&$\#$39;s critical point, and that this mana resides in the system\&$\#$39;s correlations. We explain the form of the mana by a simple tensor-counting calculation based on a MERA representation of the state. Because mana is present at all length scales, we conclude that the conformal field theory describing the 3-state Potts model critical point is magical. These results control the difficulty of preparing the Potts ground state on an error-corrected quantum computer, and constrain tensor network models of AdS-CFT.

}, doi = {https://journals.aps.org/prb/pdf/10.1103/PhysRevB.103.075145}, url = {https://arxiv.org/abs/2007.01303}, author = {Christopher David White and ChunJun Cao and Brian Swingle} } @article {2919, title = {Cross-Platform Comparison of Arbitrary Quantum Computations}, year = {2021}, month = {7/27/2021}, abstract = {

As we approach the era of quantum advantage, when quantum computers (QCs) can outperform any classical computer on particular tasks, there remains the difficult challenge of how to validate their performance. While algorithmic success can be easily verified in some instances such as number factoring or oracular algorithms, these approaches only provide pass/fail information for a single QC. On the other hand, a comparison between different QCs on the same arbitrary circuit provides a lower-bound for generic validation: a quantum computation is only as valid as the agreement between the results produced on different QCs. Such an approach is also at the heart of evaluating metrological standards such as disparate atomic clocks. In this paper, we report a cross-platform QC comparison using randomized and correlated measurements that results in a wealth of information on the QC systems. We execute several quantum circuits on widely different physical QC platforms and analyze the cross-platform fidelities.

}, url = {https://arxiv.org/abs/2107.11387}, author = {Daiwei Zhu and Ze-Pei Cian and Crystal Noel and Andrew Risinger and Debopriyo Biswas and Laird Egan and Yingyue Zhu and Alaina M. Green and Cinthia Huerta Alderete and Nhung H. Nguyen and Qingfeng Wang and Andrii Maksymov and Yunseong Nam and Marko Cetina and Norbert M. Linke and Mohammad Hafezi and Christopher Monroe} } @article {2700, title = {Efficient quantum algorithm for dissipative nonlinear differential equations}, journal = {Proceedings of the National Academy of Sciences}, volume = {118}, year = {2021}, month = {3/1/2021}, chapter = {e2026805118}, abstract = {

While there has been extensive previous work on efficient quantum algorithms for linear differential equations, analogous progress for nonlinear differential equations has been severely limited due to the linearity of quantum mechanics. Despite this obstacle, we develop a quantum algorithm for initial value problems described by dissipative quadratic n-dimensional ordinary differential equations. Assuming R\<1, where R is a parameter characterizing the ratio of the nonlinearity to the linear dissipation, this algorithm has complexity T2poly(logT,logn)/ϵ, where T is the evolution time and ϵ is the allowed error in the output quantum state. This is an exponential improvement over the best previous quantum algorithms, whose complexity is exponential in T. We achieve this improvement using the method of Carleman linearization, for which we give an improved convergence theorem. This method maps a system of nonlinear differential equations to an infinite-dimensional system of linear differential equations, which we discretize, truncate, and solve using the forward Euler method and the quantum linear system algorithm. We also provide a lower bound on the worst-case complexity of quantum algorithms for general quadratic differential equations, showing that the problem is intractable for R\≥2\–\√. Finally, we discuss potential applications of this approach to problems arising in biology as well as in fluid and plasma dynamics.

}, doi = {https://doi.org/10.1073/pnas.2026805118}, url = {https://arxiv.org/abs/2011.03185}, author = {Jin-Peng Liu and Herman {\O}ie Kolden and Hari K. Krovi and Nuno F. Loureiro and Konstantina Trivisa and Andrew M. Childs} } @article {2426, title = {Efficient quantum measurement of Pauli operators}, journal = {Quantum}, volume = {5}, year = {2021}, month = {01/19/2021}, chapter = {385}, abstract = {

Estimating the expectation value of an observable is a fundamental task in quantum computation. Unfortunately, it is often impossible to obtain such estimates directly, as the computer is restricted to measuring in a fixed computational basis. One common solution splits the observable into a weighted sum of Pauli operators and measures each separately, at the cost of many measurements. An improved version first groups mutually commuting Pauli operators together and then measures all operators within each group simultaneously. The effectiveness of this depends on two factors. First, to enable simultaneous measurement, circuits are required to rotate each group to the computational basis. In our work, we present two efficient circuit constructions that suitably rotate any group of k commuting n-qubit Pauli operators using at most kn\−k(k+1)/2 and O(kn/logk) two-qubit gates respectively. Second, metrics that justifiably measure the effectiveness of a grouping are required. In our work, we propose two natural metrics that operate under the assumption that measurements are distributed optimally among groups. Motivated by our new metrics, we introduce SORTED INSERTION, a grouping strategy that is explicitly aware of the weighting of each Pauli operator in the observable. Our methods are numerically illustrated in the context of the Variational Quantum Eigensolver, where the observables in question are molecular Hamiltonians. As measured by our metrics, SORTED INSERTION outperforms four conventional greedy colouring algorithms that seek the minimum number of groups.

}, doi = {https://doi.org/10.22331/q-2021-01-20-385}, url = {https://arxiv.org/abs/1908.06942}, author = {Ophelia Crawford and Barnaby van Straaten and Daochen Wang and Thomas Parks and Earl Campbell and Stephen Brierley} } @article {2725, title = {Energy storage and coherence in closed and open quantum batteries}, journal = {Quantum}, volume = {5}, year = {2021}, month = {7/15/2021}, pages = {505}, abstract = {

We study the role of coherence in closed and open quantum batteries. We obtain upper bounds to the work performed or energy exchanged by both closed and open quantum batteries in terms of coherence. Specifically, we show that the energy storage can be bounded by the Hilbert-Schmidt coherence of the density matrix in the spectral basis of the unitary operator that encodes the evolution of the battery. We also show that an analogous bound can be obtained in terms of the battery\&$\#$39;s Hamiltonian coherence in the basis of the unitary operator by evaluating their commutator. We apply these bounds to a 4-state quantum system and the anisotropic XY Ising model in the closed system case, and the Spin-Boson model in the open case.\ 

}, doi = {https://doi.org/10.22331/q-2021-07-15-505}, url = {https://arxiv.org/abs/2012.15026}, author = {Francesco Caravelli and Bin Yan and Luis Pedro Garc{\'\i}a-Pintos and Alioscia Hamma} } @article {2932, title = {Entangled quantum cellular automata, physical complexity, and Goldilocks rules}, journal = {Quantum Science and Technology}, volume = {6}, year = {2021}, month = {9/29/2021}, pages = {045017}, abstract = {

Cellular automata are interacting classical bits that display diverse emergent behaviors, from fractals to random-number generators to Turing-complete computation. We discover that quantum cellular automata (QCA) can exhibit complexity in the sense of the complexity science that describes biology, sociology, and economics. QCA exhibit complexity when evolving under \"Goldilocks rules\" that we define by balancing activity and stasis. Our Goldilocks rules generate robust dynamical features (entangled breathers), network structure and dynamics consistent with complexity, and persistent entropy fluctuations. Present-day experimental platforms -- Rydberg arrays, trapped ions, and superconducting qubits -- can implement our Goldilocks protocols, making testable the link between complexity science and quantum computation exposed by our QCA.

}, issn = {2058-9565}, doi = {10.1088/2058-9565/ac1c41}, url = {http://dx.doi.org/10.1088/2058-9565/ac1c41}, author = {Hillberry, Logan E and Jones, Matthew T and Vargas, David L and Rall, Patrick and Nicole Yunger Halpern and Bao, Ning and Notarnicola, Simone and Montangero, Simone and Carr, Lincoln D} } @article {2928, title = {Exactly Solvable Lattice Hamiltonians and Gravitational Anomalies}, year = {2021}, month = {10/27/2021}, abstract = {

We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions, whose boundaries are characterized by gravitational anomalies. Examples include the beyond group cohomology invertible phase without symmetry in (4+1)D that has an anomalous boundary Z2 topological order with fermionic particle and fermionic loop excitations that have mutual π statistics. We argue that this construction gives a new non-trivial quantum cellular automaton (QCA) in (4+1)D of order two. We also present an explicit construction of gapped symmetric boundary state for the bosonic beyond group cohomology invertible phase with unitary Z2 symmetry in (4+1)D. We discuss new quantum phase transitions protected by different invertible phases across the transitions.

}, url = {https://arxiv.org/abs/2110.14644}, author = {Yu-An Chen and Po-Shen Hsin} } @article {2605, title = {Faster Digital Quantum Simulation by Symmetry Protection}, journal = {PRX Quantum}, volume = {2}, year = {2021}, month = {2/14/2021}, type = {Report number: FERMILAB-PUB-20-240-QIS-T}, abstract = {

Simulating the dynamics of quantum systems is an important application of quantum computers and has seen a variety of implementations on current hardware. We show that by introducing quantum gates implementing unitary transformations generated by the symmetries of the system, one can induce destructive interference between the errors from different steps of the simulation, effectively giving faster quantum simulation by symmetry protection. We derive rigorous bounds on the error of a symmetry-protected simulation algorithm and identify conditions for optimal symmetry protection. In particular, when the symmetry transformations are chosen as powers of a unitary, the error of the algorithm is approximately projected to the so-called quantum Zeno subspaces. We prove a bound on this approximation error, exponentially improving a recent result of Burgarth, Facchi, Gramegna, and Pascazio. We apply our technique to the simulations of the XXZ Heisenberg interactions with local disorder and the Schwinger model in quantum field theory. For both systems, our algorithm can reduce the simulation error by several orders of magnitude over the unprotected simulation. Finally, we provide numerical evidence suggesting that our technique can also protect simulation against other types of coherent, temporally correlated errors, such as the 1/f noise commonly found in solid-state experiments.

}, issn = {2691-3399}, doi = {http://dx.doi.org/10.1103/PRXQuantum.2.010323}, url = {https://arxiv.org/abs/2006.16248}, author = {Minh C. Tran and Yuan Su and Daniel Carney and J. M. Taylor} } @article {2925, title = {From Quantum Codes to Gravity: A Journey of Gravitizing Quantum Mechanics}, year = {2021}, month = {11/30/2021}, abstract = {

In this note, I review a recent approach to quantum gravity that \"gravitizes\" quantum mechanics by emerging geometry and gravity from complex quantum states. Drawing further insights from tensor network toy models in AdS/CFT, I propose that approximate quantum error correction codes, when re-adapted into the aforementioned framework, also has promise in emerging gravity in near-flat geometries.

}, url = {https://arxiv.org/abs/2112.00199}, author = {ChunJun Cao} } @article {2936, title = {Generalization in quantum machine learning from few training data}, year = {2021}, month = {11/9/2021}, abstract = {

Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i.e., generalizing). In this work, we provide a comprehensive study of generalization performance in QML after training on a limited number N of training data points. We show that the generalization error of a quantum machine learning model with T trainable gates scales at worst as T/N\−\−\−\−\√. When only K<}, url = {https://arxiv.org/abs/2111.05292}, author = {Matthias C. Caro and Hsin-Yuan Huang and M. Cerezo and Kunal Sharma and Andrew Sornborger and Lukasz Cincio and Patrick J. Coles} } @article {2812, title = {Higher cup products on hypercubic lattices: application to lattice models of topological phases}, year = {2021}, month = {6/9/2021}, abstract = {

In this paper, we derive the explicit formula for higher cup products on hypercubic lattices, based on the recently developed geometrical interpretation in the simplicial case. We illustrate how this formalism can elucidate lattice constructions on hypercubic lattices for various models and deriving them from spacetime actions. In particular, we demonstrate explicitly that the (3+1)D SPT S=12\∫w22+w41 (where w1 and w2 are the first and second Stiefel-Whitney classes) is dual to the 3-fermion Walker-Wang model constructed on the cubic lattice by Burnell-Chen-Fidkowski-Vishwanath. Other examples include the double-semion model, and also the {\textquoteleft}fermionic\&$\#$39; toric code in arbitrary dimensions on hypercubic lattices. In addition, we extend previous constructions of exact boson-fermion dualities and the Gu-Wen Grassmann Integral to arbitrary dimensions. Another result which may be of independent interest is a derivation of a cochain-level action for the generalized double-semion model, reproducing a recently derived action on the cohomology level.

}, url = {https://arxiv.org/abs/2106.05274}, author = {Yu-An Chen and Sri Tata} } @article {2543, title = {High-precision quantum algorithms for partial differential equations}, journal = {Quantum 5, 574}, volume = {5}, year = {2021}, month = {11/4/2021}, abstract = {

Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for linear ordinary differential equations are well established, the best previous quantum algorithms for linear partial differential equations (PDEs) have complexity poly(1/ε), where ε is the error tolerance. By developing quantum algorithms based on adaptive-order finite difference methods and spectral methods, we improve the complexity of quantum algorithms for linear PDEs to be poly(d,log(1/ε)), where d is the spatial dimension. Our algorithms apply high-precision quantum linear system algorithms to systems whose condition numbers and approximation errors we bound. We develop a finite difference algorithm for the Poisson equation and a spectral algorithm for more general second-order elliptic equations.\ 

}, doi = {https://doi.org/10.22331/q-2021-11-10-574}, url = {https://arxiv.org/abs/2002.07868}, author = {Andrew M. Childs and Jin-Peng Liu and Aaron Ostrander} } @article {2771, title = {Hyper-Invariant MERA: Approximate Holographic Error Correction Codes with Power-Law Correlations}, year = {2021}, month = {3/15/2021}, abstract = {

We consider a class of holographic tensor networks that are efficiently contractible variational ansatze, manifestly (approximate) quantum error correction codes, and can support power-law correlation functions. In the case when the network consists of a single type of tensor that also acts as an erasure correction code, we show that it cannot be both locally contractible and sustain power-law correlation functions. Motivated by this no-go theorem, and the desirability of local contractibility for an efficient variational ansatz, we provide guidelines for constructing networks consisting of multiple types of tensors that can support power-law correlation. We also provide an explicit construction of one such network, which approximates the holographic HaPPY pentagon code in the limit where variational parameters are taken to be small.

}, url = {https://arxiv.org/abs/2103.08631}, author = {ChunJun Cao and Jason Pollack and Yixu Wang} } @article {2772, title = {On the Impossibility of Post-Quantum Black-Box Zero-Knowledge in Constant Rounds}, year = {2021}, month = {3/20/2021}, abstract = {

We investigate the existence of constant-round post-quantum black-box zero-knowledge protocols for NP. As a main result, we show that there is no constant-round post-quantum black-box zero-knowledge argument for NP unless NP\⊆BQP. As constant-round black-box zero-knowledge arguments for NP exist in the classical setting, our main result points out a fundamental difference between post-quantum and classical zero-knowledge protocols. Combining previous results, we conclude that unless NP\⊆BQP, constant-round post-quantum zero-knowledge protocols for NP exist if and only if we use non-black-box techniques or relax certain security requirements such as relaxing standard zero-knowledge to ϵ-zero-knowledge. Additionally, we also prove that three-round and public-coin constant-round post-quantum black-box ϵ-zero-knowledge arguments for NP do not exist unless NP\⊆BQP.

}, url = {https://arxiv.org/abs/2103.11244}, author = {Nai-Hui Chia and Kai-Min Chung and Qipeng Liu and Takashi Yamakawa} } @article {2908, title = {Interactive Protocols for Classically-Verifiable Quantum Advantage}, year = {2021}, month = {12/9/2021}, abstract = {

Achieving quantum computational advantage requires solving a classically intractable problem on a quantum device. Natural proposals rely upon the intrinsic hardness of classically simulating quantum mechanics; however, verifying the output is itself classically intractable. On the other hand, certain quantum algorithms (e.g. prime factorization via Shor\&$\#$39;s algorithm) are efficiently verifiable, but require more resources than what is available on near-term devices. One way to bridge the gap between verifiability and implementation is to use \"interactions\" between a prover and a verifier. By leveraging cryptographic functions, such protocols enable the classical verifier to enforce consistency in a quantum prover\&$\#$39;s responses across multiple rounds of interaction. In this work, we demonstrate the first implementation of an interactive quantum advantage protocol, using an ion trap quantum computer. We execute two complementary protocols -- one based upon the learning with errors problem and another where the cryptographic construction implements a computational Bell test. To perform multiple rounds of interaction, we implement mid-circuit measurements on a subset of trapped ion qubits, with subsequent coherent evolution. For both protocols, the performance exceeds the asymptotic bound for classical behavior; maintaining this fidelity at scale would conclusively demonstrate verifiable quantum advantage.

}, url = {https://arxiv.org/abs/2112.05156}, author = {Daiwei Zhu and Gregory D. Kahanamoku-Meyer and Laura Lewis and Crystal Noel and Or Katz and Bahaa Harraz and Qingfeng Wang and Andrew Risinger and Lei Feng and Debopriyo Biswas and Laird Egan and Alexandru Gheorghiu and Yunseong Nam and Thomas Vidick and Umesh Vazirani and Norman Y. Yao and Marko Cetina and Christopher Monroe} } @article {2865, title = {Linear and continuous variable spin-wave processing using a cavity-coupled atomic ensemble}, year = {2021}, month = {9/30/2021}, abstract = {

Spin-wave excitations in ensembles of atoms are gaining attention as a quantum information resource. However, current techniques with atomic spin waves do not achieve universal quantum information processing. We conduct a theoretical analysis of methods to create a high-capacity universal quantum processor and network node using an ensemble of laser-cooled atoms, trapped in a one-dimensional periodic potential and coupled to a ring cavity. We describe how to establish linear quantum processing using a lambda-scheme in a rubidium-atom system, calculate the expected experimental operational fidelities. Second, we derive an efficient method to achieve linear controllability with a single ensemble of atoms, rather than two-ensembles as proposed in [K. C. Cox et al. Spin-Wave Quantum Computing with Atoms in a Single-Mode Cavity, preprint 2021]. Finally, we propose to use the spin-wave processor for continuous-variable quantum information processing and present a scheme to generate large dual-rail cluster states useful for deterministic computing.\ 

}, url = {https://arxiv.org/abs/2109.15246}, author = {Kevin C. Cox and Przemyslaw Bienias and David H. Meyer and Donald P. Fahey and Paul D. Kunz and Alexey V. Gorshkov} } @article {2810, title = {Magic State Distillation from Entangled States}, year = {2021}, month = {6/23/2021}, abstract = {

Magic can be distributed non-locally in many-body entangled states, such as the low energy states of condensed matter systems. Using the Bravyi-Kitaev magic state distillation protocol, we find that non-local magic is distillable and can improve the distillation outcome. We analyze a few explicit examples and show that spin squeezing can be used to convert non-distillable states into distillable ones.
Our analysis also suggests that the conventional product input states assumed by magic distillation protocols are extremely atypical among general states with distillable magic. It further justifies the need for studying a diverse range of entangled inputs that yield magic states with high probability.

}, url = {https://arxiv.org/abs/2106.12591}, author = {Ning Bao and ChunJun Cao and Vincent Paul Su} } @article {2777, title = {Maximum Refractive Index of an Atomic Medium}, journal = {Physical Review X}, volume = {11}, year = {2021}, month = {2/18/2021}, abstract = {

It is interesting to observe that all optical materials with a positive refractive index have a value of index that is of order unity. Surprisingly, though, a deep understanding of the mechanisms that lead to this universal behavior seems to be lacking. Moreover, this observation is difficult to reconcile with the fact that a single, isolated atom is known to have a giant optical response, as characterized by a resonant scattering cross section that far exceeds its physical size. Here, we theoretically and numerically investigate the evolution of the optical properties of an ensemble of ideal atoms as a function of density, starting from the dilute gas limit, including the effects of multiple scattering and near-field interactions. Interestingly, despite the giant response of an isolated atom, we find that the maximum index does not indefinitely grow with increasing density, but rather reaches a limiting value n\≈1.7. We propose an explanation based upon strong-disorder renormalization group theory, in which the near-field interaction combined with random atomic positions results in an inhomogeneous broadening of atomic resonance frequencies. This mechanism ensures that regardless of the physical atomic density, light at any given frequency only interacts with at most a few near-resonant atoms per cubic wavelength, thus limiting the maximum index attainable. Our work is a promising first step to understand the limits of refractive index from a bottom-up, atomic physics perspective, and also introduces renormalization group as a powerful tool to understand the generally complex problem of multiple scattering of light overall.

}, doi = {10.1103/PhysRevX.11.011026}, url = {https://arxiv.org/abs/2006.01680}, author = {Andreoli, Francesco and Michael Gullans and High, Alexander A. and Browaeys, Antoine and Chang, Darrick E.} } @article {2935, title = {Noise-induced barren plateaus in variational quantum algorithms}, journal = {Nature Communications}, volume = {12}, year = {2021}, month = {11/29/2021}, pages = {6961}, abstract = {

Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits n if the depth of the ansatz grows linearly with n. These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model.

}, doi = {https://doi.org/10.1038/s41467-021-27045-6}, author = {Samson Wang and Enrico Fontana and M. Cerezo and Kunal Sharma and Akira Sone and Lukasz Cincio and Patrick J. Coles} } @article {2938, title = {On nonlinear transformations in quantum computation}, year = {2021}, month = {12/23/2021}, abstract = {

While quantum computers are naturally well-suited to implementing linear operations, it is less clear how to implement nonlinear operations on quantum computers. However, nonlinear subroutines may prove key to a range of applications of quantum computing from solving nonlinear equations to data processing and quantum machine learning. Here we develop algorithms for implementing nonlinear transformations of input quantum states. Our algorithms are framed around the concept of a weighted state, a mathematical entity describing the output of an operational procedure involving both quantum circuits and classical post-processing.

}, url = {https://arxiv.org/abs/2112.12307}, author = {Zo{\"e} Holmes and Nolan Coble and Andrew T. Sornborger and Yi{\u g}it Suba{\c s}{\i}} } @article {2768, title = {Observation of a prethermal discrete time crystal}, year = {2021}, month = {2/2/2021}, abstract = {

The conventional framework for defining and understanding phases of matter requires thermodynamic equilibrium. Extensions to non-equilibrium systems have led to surprising insights into the nature of many-body thermalization and the discovery of novel phases of matter, often catalyzed by driving the system periodically. The inherent heating from such Floquet drives can be tempered by including strong disorder in the system, but this can also mask the generality of non-equilibrium phases. In this work, we utilize a trapped-ion quantum simulator to observe signatures of a non-equilibrium driven phase without disorder: the prethermal discrete time crystal (PDTC). Here, many-body heating is suppressed not by disorder-induced many-body localization, but instead via high-frequency driving, leading to an expansive time window where non-equilibrium phases can emerge. We observe a number of key features that distinguish the PDTC from its many-body-localized disordered counterpart, such as the drive-frequency control of its lifetime and the dependence of time-crystalline order on the energy density of the initial state. Floquet prethermalization is thus presented as a general strategy for creating, stabilizing and studying intrinsically out-of-equilibrium phases of matter.

}, url = {https://arxiv.org/abs/2102.01695}, author = {Antonis Kyprianidis and Francisco Machado and William Morong and Patrick Becker and Kate S. Collins and Dominic V. Else and Lei Feng and Paul W. Hess and Chetan Nayak and Guido Pagano and Norman Y. Yao and Christopher Monroe} } @article {2805, title = {Observation of measurement-induced quantum phases in a trapped-ion quantum computer}, year = {2021}, month = {6/10/2021}, abstract = {

Many-body open quantum systems balance internal dynamics against decoherence from interactions with an environment. Here, we explore this balance via random quantum circuits implemented on a trapped ion quantum computer, where the system evolution is represented by unitary gates with interspersed projective measurements. As the measurement rate is varied, a purification phase transition is predicted to emerge at a critical point akin to a fault-tolerent threshold. We probe the \"pure\" phase, where the system is rapidly projected to a deterministic state conditioned on the measurement outcomes, and the \"mixed\" or \"coding\" phase, where the initial state becomes partially encoded into a quantum error correcting codespace. We find convincing evidence of the two phases and show numerically that, with modest system scaling, critical properties of the transition clearly emerge.

}, url = {https://arxiv.org/abs/2106.05881}, author = {Crystal Noel and Pradeep Niroula and Daiwei Zhu and Andrew Risinger and Laird Egan and Debopriyo Biswas and Marko Cetina and Alexey V. Gorshkov and Michael Gullans and David A. Huse and Christopher Monroe} } @article {2763, title = {Observation of Stark many-body localization without disorder}, year = {2021}, month = {2/14/2021}, abstract = {

Thermalization is a ubiquitous process of statistical physics, in which details of few-body observables are washed out in favor of a featureless steady state. Even in isolated quantum many-body systems, limited to reversible dynamics, thermalization typically prevails. However, in these systems, there is another possibility: many-body localization (MBL) can result in preservation of a non-thermal state. While disorder has long been considered an essential ingredient for this phenomenon, recent theoretical work has suggested that a quantum many-body system with a uniformly increasing field -- but no disorder -- can also exhibit MBL, resulting in {\textquoteleft}Stark MBL.\&$\#$39; Here we realize Stark MBL in a trapped-ion quantum simulator and demonstrate its key properties: halting of thermalization and slow propagation of correlations. Tailoring the interactions between ionic spins in an effective field gradient, we directly observe their microscopic equilibration for a variety of initial states, and we apply single-site control to measure correlations between separate regions of the spin chain. Further, by engineering a varying gradient, we create a disorder-free system with coexisting long-lived thermalized and nonthermal regions. The results demonstrate the unexpected generality of MBL, with implications about the fundamental requirements for thermalization and with potential uses in engineering long-lived non-equilibrium quantum matter.

}, url = {https://arxiv.org/abs/2102.07250}, author = {W. Morong and F. Liu and P. Becker and K. S. Collins and L. Feng and A. Kyprianidis and G. Pagano and T. You and Alexey V. Gorshkov and C. Monroe} } @article {2926, title = {Optimal scaling quantum linear systems solver via discrete adiabatic theorem}, year = {2021}, month = {11/15/2021}, abstract = {

Recently, several approaches to solving linear systems on a quantum computer have been formulated in terms of the quantum adiabatic theorem for a continuously varying Hamiltonian. Such approaches enabled near-linear scaling in the condition number κ of the linear system, without requiring a complicated variable-time amplitude amplification procedure. However, the most efficient of those procedures is still asymptotically sub-optimal by a factor of log(κ). Here, we prove a rigorous form of the adiabatic theorem that bounds the error in terms of the spectral gap for intrinsically discrete time evolutions. We use this discrete adiabatic theorem to develop a quantum algorithm for solving linear systems that is asymptotically optimal, in the sense that the complexity is strictly linear in κ, matching a known lower bound on the complexity. Our O(κlog(1/ε)) complexity is also optimal in terms of the combined scaling in κ and the precision ε. Compared to existing suboptimal methods, our algorithm is simpler and easier to implement. Moreover, we determine the constant factors in the algorithm, which would be suitable for determining the complexity in terms of gate counts for specific applications.\ 

}, url = {https://arxiv.org/abs/2111.08152}, author = {Pedro C. S. Costa and Dong An and Yuval R. Sanders and Yuan Su and Ryan Babbush and Dominic W. Berry} } @article {2863, title = {Proposal for gravitational direct detection of dark matter}, journal = {Physical Review D}, volume = {102}, year = {2021}, month = {8/23/2021}, abstract = {

The only coupling dark matter is guaranteed to have with the standard model is through gravity. Here we propose a concept for direct dark matter detection using only this gravitational coupling. We suggest that an array of quantum-limited mechanical impulse sensors may be capable of detecting the correlated gravitational force created by a passing dark matter particle. We consider the effects of irreducible noise from couplings of the sensors to the environment and noise due to the quantum measurement process. We show that the signal from Planck-scale dark matter is in principle detectable using a large number of gram-scale sensors in a meter-scale array with sufficiently low quantum noise, and discuss some experimental challenges en route to achieving this target.

}, issn = {2470-0029}, doi = {https://doi.org/10.1103/PhysRevD.102.072003}, url = {https://arxiv.org/abs/1903.00492}, author = {Carney, Daniel and Ghosh, Sohitri and Krnjaic, Gordan and Taylor, Jacob M.} } @article {2942, title = {Proving Quantum Programs Correct}, journal = {12th International Conference on Interactive Theorem Proving (ITP 2021)}, volume = {193}, year = {2021}, month = {06/2021}, pages = {21:1{\textendash}21:19}, abstract = {

As quantum computing progresses steadily from theory into practice, programmers will face
a common problem: How can they be sure that their code does what they intend it to do? This
paper presents encouraging results in the application of mechanized proof to the domain of quantum
programming in the context of the sqir development. It verifies the correctness of a range of a
quantum algorithms including Grover\’s algorithm and quantum phase estimation, a key component
of Shor\’s algorithm. In doing so, it aims to highlight both the successes and challenges of formal
verification in the quantum context and motivate the theorem proving community to target quantum
computing as an application domain.

}, isbn = {978-3-95977-188-7}, issn = {1868-8969}, doi = {10.4230/LIPIcs.ITP.2021.21}, url = {https://drops.dagstuhl.de/opus/volltexte/2021/13916}, author = {Hietala, Kesha and Rand, Robert and Hung, Shih-Han and Li, Liyi and Hicks, Michael}, editor = {Cohen, Liron and Kaliszyk, Cezary} } @article {2917, title = {Quantum circuits for the realization of equivalent forms of one-dimensional discrete-time quantum walks on near-term quantum hardware}, journal = {Physical Review A}, volume = {104}, year = {2021}, month = {12/8/2021}, abstract = {

Quantum walks are a promising framework for developing quantum algorithms and quantum simulations. They represent an important test case for the application of quantum computers. Here we present different forms of discrete-time quantum walks (DTQWs) and show their equivalence for physical realizations. Using an appropriate digital mapping of the position space on which a walker evolves to the multiqubit states of a quantum processor, we present different configurations of quantum circuits for the implementation of DTQWs in one-dimensional position space. We provide example circuits for a five-qubit processor and address scalability to higher dimensions as well as larger quantum processors.

}, issn = {2469-9934}, doi = {https://doi.org/10.1103/PhysRevA.104.062401}, url = {https://arxiv.org/abs/2001.11197}, author = {Singh, Shivani and Alderete, C. Huerta and Balu, Radhakrishnan and Monroe, Christopher and Linke, Norbert M. and Chandrashekar, C. M.} } @article {2633, title = {Quantum exploration algorithms for multi-armed bandits}, journal = {Proceedings of the 35th Conference on Artificial Intelligence (AAAI 2021)}, volume = {35}, year = {2021}, month = {2021}, pages = {10102-10110}, abstract = {

\ Identifying the best arm of a multi-armed bandit is a central problem in bandit optimization. We study a quantum computational version of this problem with coherent oracle access to states encoding the reward probabilities of each arm as quantum amplitudes. Specifically, we show that we can find the best arm with fixed confidence using O~(\∑ni=2Δ\−2i\−\−\−\−\−\−\−\−\√) quantum queries, where Δi represents the difference between the mean reward of the best arm and the ith-best arm. This algorithm, based on variable-time amplitude amplification and estimation, gives a quadratic speedup compared to the best possible classical result. We also prove a matching quantum lower bound (up to poly-logarithmic factors).

}, url = {https://ojs.aaai.org/index.php/AAAI/article/view/17212}, author = {Daochen Wang and Xuchen You and Tongyang Li and Andrew M. Childs} } @article {2875, title = {Quantum Machine Learning for Finance}, year = {2021}, month = {9/9/2021}, abstract = {

Quantum computers are expected to surpass the computational capabilities of classical computers during this decade, and achieve disruptive impact on numerous industry sectors, particularly finance. In fact, finance is estimated to be the first industry sector to benefit from Quantum Computing not only in the medium and long terms, but even in the short term. This review paper presents the state of the art of quantum algorithms for financial applications, with particular focus to those use cases that can be solved via Machine Learning.

}, url = {https://arxiv.org/abs/2109.04298}, author = {Marco Pistoia and Syed Farhan Ahmad and Akshay Ajagekar and Alexander Buts and Shouvanik Chakrabarti and Dylan Herman and Shaohan Hu and Andrew Jena and Pierre Minssen and Pradeep Niroula and Arthur Rattew and Yue Sun and Romina Yalovetzky} } @article {2826, title = {Quantum Meets the Minimum Circuit Size Problem}, year = {2021}, month = {8/6/2021}, abstract = {

In this work, we initiate the study of the Minimum Circuit Size Problem (MCSP) in the quantum setting. MCSP is a problem to compute the circuit complexity of Boolean functions. It is a fascinating problem in complexity theory---its hardness is mysterious, and a better understanding of its hardness can have surprising implications to many fields in computer science.
We first define and investigate the basic complexity-theoretic properties of minimum quantum circuit size problems for three natural objects: Boolean functions, unitaries, and quantum states. We show that these problems are not trivially in NP but in QCMA (or have QCMA protocols). Next, we explore the relations between the three quantum MCSPs and their variants. We discover that some reductions that are not known for classical MCSP exist for quantum MCSPs for unitaries and states, e.g., search-to-decision reduction and self-reduction. Finally, we systematically generalize results known for classical MCSP to the quantum setting (including quantum cryptography, quantum learning theory, quantum circuit lower bounds, and quantum fine-grained complexity) and also find new connections to tomography and quantum gravity. Due to the fundamental differences between classical and quantum circuits, most of our results require extra care and reveal properties and phenomena unique to the quantum setting. Our findings could be of interest for future studies, and we post several open problems for further exploration along this direction.

}, url = {https://arxiv.org/abs/2108.03171}, author = {Nai-Hui Chia and Chi-Ning Chou and Jiayu Zhang and Ruizhe Zhang} } @article {2886, title = {Quantum query complexity with matrix-vector products}, journal = {Proceedings of the 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021), Leibniz International Proceedings in Informatics}, volume = {198}, year = {2021}, month = {3/14/2021}, pages = {55:1-55:19}, abstract = {

We study quantum algorithms that learn properties of a matrix using queries that return its action on an input vector. We show that for various problems, including computing the trace, determinant, or rank of a matrix or solving a linear system that it specifies, quantum computers do not provide an asymptotic speedup over classical computation. On the other hand, we show that for some problems, such as computing the parities of rows or columns or deciding if there are two identical rows or columns, quantum computers provide exponential speedup. We demonstrate this by showing equivalence between models that provide matrix-vector products, vector-matrix products, and vector-matrix-vector products, whereas the power of these models can vary significantly for classical computation.

}, doi = {https://arxiv.org/ct?url=https\%3A\%2F\%2Fdx.doi.org\%2F10.4230\%2FLIPIcs.ICALP.2021.55\&v=2de93347}, url = {https://arxiv.org/abs/2102.11349}, author = {Andrew M. Childs and Shih-Han Hung and Tongyang Li} } @article {2878, title = {Quantum Query Complexity with Matrix-Vector Products}, journal = {48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)}, year = {2021}, month = {2/7/2021}, publisher = {Schloss Dagstuhl {\textendash} Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, abstract = {

We study quantum algorithms that learn properties of a matrix using queries that return its action on an input vector. We show that for various problems, including computing the trace, determinant, or rank of a matrix or solving a linear system that it specifies, quantum computers do not provide an asymptotic speedup over classical computation. On the other hand, we show that for some problems, such as computing the parities of rows or columns or deciding if there are two identical rows or columns, quantum computers provide exponential speedup. We demonstrate this by showing equivalence between models that provide matrix-vector products, vector-matrix products, and vector-matrix-vector products, whereas the power of these models can vary significantly for classical computation.

}, isbn = {978-3-95977-195-5}, doi = {10.4230/LIPIcs.ICALP.2021.55}, url = {https://drops.dagstuhl.de/opus/volltexte/2021/14124}, author = {Andrew M. Childs and Hung, Shih-Han and Li, Tongyang} } @article {2751, title = {Quantum routing with fast reversals}, journal = {Quantum}, volume = {5}, year = {2021}, month = {8/24/2021}, chapter = {533}, abstract = {

We present methods for implementing arbitrary permutations of qubits under interaction constraints. Our protocols make use of previous methods for rapidly reversing the order of qubits along a path. Given nearest-neighbor interactions on a path of length n, we show that there exists a constant ϵ\≈0.034 such that the quantum routing time is at most (1\−ϵ)n, whereas any swap-based protocol needs at least time n\−1. This represents the first known quantum advantage over swap-based routing methods and also gives improved quantum routing times for realistic architectures such as grids. Furthermore, we show that our algorithm approaches a quantum routing time of 2n/3 in expectation for uniformly random permutations, whereas swap-based protocols require time n asymptotically. Additionally, we consider sparse permutations that route k\≤n qubits and give algorithms with quantum routing time at most n/3+O(k2) on paths and at most 2r/3+O(k2) on general graphs with radius r.

}, doi = {https://doi.org/10.22331/q-2021-08-31-533}, url = {https://arxiv.org/abs/2103.03264}, author = {Aniruddha Bapat and Andrew M. Childs and Alexey V. Gorshkov and Samuel King and Eddie Schoute and Hrishee Shastri} } @article {2818, title = {Robust Self-Testing of Multiparticle Entanglement}, journal = {Phys. Rev. Lett. }, volume = {127}, year = {2021}, month = {12/7/2021}, pages = {230503}, abstract = {

Quantum self-testing is a device-independent way to certify quantum states and measurements using only the input-output statistics, with minimal assumptions about the quantum devices. Due to the high demand on tolerable noise, however, experimental self-testing was limited to two-photon systems. Here, we demonstrate the first robust self-testing for multi-particle quantum entanglement. We prepare two examples of four-photon graph states, the Greenberger-Horne-Zeilinger (GHZ) states with a fidelity of 0.957(2) and the linear cluster states with a fidelity of 0.945(2). Based on the observed input-output statistics, we certify the genuine four-photon entanglement and further estimate their qualities with respect to realistic noise in a device-independent manner.

}, doi = {https://doi.org/10.1103/PhysRevLett.127.230503}, url = {https://arxiv.org/abs/2105.10298}, author = {Dian Wu and Qi Zhao and Xue-Mei Gu and Han-Sen Zhong and You Zhou and Li-Chao Peng and Jian Qin and Yi-Han Luo and Kai Chen and Li Li and Nai-Le Liu and Chao-Yang Lu and Jian-Wei Pan} } @article {2864, title = {Spin-Wave Quantum Computing with Atoms in a Single-Mode Cavity}, year = {2021}, month = {9/30/2021}, abstract = {

We present a method for network-capable quantum computing that relies on holographic spin-wave excitations stored collectively in ensembles of qubits. We construct an orthogonal basis of spin waves in a one-dimensional array and show that high-fidelity universal linear controllability can be achieved using only phase shifts, applied in both momentum and position space. Neither single-site addressability nor high single-qubit cooperativity is required, and the spin waves can be read out with high efficiency into a single cavity mode for quantum computing and networking applications.\ 

}, url = {https://arxiv.org/abs/2109.15252}, author = {Kevin C. Cox and Przemyslaw Bienias and David H. Meyer and Paul D. Kunz and Donald P. Fahey and Alexey V. Gorshkov} } @article {2774, title = {Testing quantum gravity with interactive information sensing}, year = {2021}, month = {1/27/2021}, abstract = {

We suggest a test of a central prediction of perturbatively quantized general relativity: the coherent communication of quantum information between massive objects through gravity. To do this, we introduce the concept of interactive quantum information sensing, a protocol tailored to the verification of dynamical entanglement generation between a pair of systems. Concretely, we propose to monitor the periodic wavefunction collapse and revival in an atomic interferometer which is gravitationally coupled to a mechanical oscillator. We prove a theorem which shows that, under the assumption of time-translation invariance, this collapse and revival is possible if and only if the gravitational interaction forms an entangling channel. Remarkably, as this approach improves at moderate temperatures and relies primarily upon atomic coherence, our numerical estimates indicate feasibility with current devices.

}, url = {https://arxiv.org/abs/2101.11629}, author = {Daniel Carney and Holger M{\"u}ller and Jacob M. Taylor} } @article {2506, title = {Theory of Trotter Error with Commutator Scaling}, journal = {Phys. Rev. X}, volume = {11}, year = {2021}, month = {2/1/2021}, pages = {49}, chapter = {011020}, abstract = {

The Lie-Trotter formula, together with its higher-order generalizations, provides a direct approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly understood. We develop a theory of Trotter error that overcomes the limitations of prior approaches based on truncating the Baker-Campbell-Hausdorff expansion. Our analysis directly exploits the commutativity of operator summands, producing tighter error bounds for both real- and imaginary-time evolutions. Whereas previous work achieves similar goals for systems with geometric locality or Lie-algebraic structure, our approach holds in general. We give a host of improved algorithms for digital quantum simulation and quantum Monte Carlo methods, including simulations of second-quantized plane-wave electronic structure, k-local Hamiltonians, rapidly decaying power-law interactions, clustered Hamiltonians, the transverse field Ising model, and quantum ferromagnets, nearly matching or even outperforming the best previous results. We obtain further speedups using the fact that product formulas can preserve the locality of the simulated system. Specifically, we show that local observables can be simulated with complexity independent of the system size for power-law interacting systems, which implies a Lieb-Robinson bound as a byproduct. Our analysis reproduces known tight bounds for first- and second-order formulas. Our higher-order bound overestimates the complexity of simulating a one-dimensional Heisenberg model with an even-odd ordering of terms by only a factor of 5, and is close to tight for power-law interactions and other orderings of terms. This suggests that our theory can accurately characterize Trotter error in terms of both asymptotic scaling and constant prefactor.

}, doi = {https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011020}, url = {https://arxiv.org/abs/1912.08854}, author = {Andrew M. Childs and Yuan Su and Minh C. Tran and Nathan Wiebe and Shuchen Zhu} } @article {2731, title = {A Threshold for Quantum Advantage in Derivative Pricing}, journal = {Quantum}, volume = {5}, year = {2021}, pages = {463}, abstract = {

We give an upper bound on the resources required for valuable quantum advantage in pricing derivatives. To do so, we give the first complete resource estimates for useful quantum derivative pricing, using autocallable and Target Accrual Redemption Forward (TARF) derivatives as benchmark use cases. We uncover blocking challenges in known approaches and introduce a new method for quantum derivative pricing - the re-parameterization method - that avoids them. This method combines pre-trained variational circuits with fault-tolerant quantum computing to dramatically reduce resource requirements. We find that the benchmark use cases we examine require 7.5k logical qubits and a T-depth of 46 million and thus estimate that quantum advantage would require a logical clock speed of 10Mhz. While the resource requirements given here are out of reach of current systems, we hope they will provide a roadmap for further improvements in algorithms, implementations, and planned hardware architectures.\ 

}, doi = {https://doi.org/10.22331/q-2021-06-01-463}, url = {https://arxiv.org/abs/2012.03819}, author = {Shouvanik Chakrabarti and Rajiv Krishnakumar and Guglielmo Mazzola and Nikitas Stamatopoulos and Stefan Woerner and William J. Zeng} } @article {2775, title = {Trading Locality for Time: Certifiable Randomness from Low-Depth Circuits}, journal = {Communications in Mathematical Physics}, volume = {382}, year = {2021}, month = {2/9/2021}, pages = {49 - 86}, abstract = {

The generation of certifiable randomness is the most fundamental informationtheoretic task that meaningfully separates quantum devices from their classical counterparts. We propose a protocol for exponential certified randomness expansion using a\ single quantum device. The protocol calls for the device to implement a simple quantum circuit of constant depth on a 2D lattice of qubits. The output of the circuit can be\ verified classically in linear time, and is guaranteed to contain a polynomial number of\ certified random bits assuming that the device used to generate the output operated using\ a (classical or quantum) circuit of sub-logarithmic depth. This assumption contrasts with\ the locality assumption used for randomness certification based on Bell inequality violation and more recent proposals for randomness certification based on computational\ assumptions. Furthermore, to demonstrate randomness generation it is sufficient for a\ device to sample from the ideal output distribution within constant statistical distance.\ \ Our procedure is inspired by recent work of Bravyi et al. (Science 362(6412):308\–311,\ 2018), who introduced a relational problem that can be solved by a constant-depth quantum circuit, but provably cannot be solved by any classical circuit of sub-logarithmic\ depth. We develop the discovery of Bravyi et al. into a framework for robust randomness\ expansion. Our results lead to a new proposal for a demonstrated quantum advantage\ that has some advantages compared to existing proposals. First, our proposal does not\ rest on any complexity-theoretic conjectures, but relies on the physical assumption that\ the adversarial device being tested implements a circuit of sub-logarithmic depth. Second, success on our task can be easily verified in classical linear time. Finally, our task\ is more noise-tolerant than most other existing proposals that can only tolerate multiplicative error, or require additional conjectures from complexity theory; in contrast, we\ are able to allow a small constant additive error in total variation distance between the\ sampled and ideal distributions.

}, issn = {0010-3616}, doi = {10.1007/s00220-021-03963-w}, url = {https://link.springer.com/content/pdf/10.1007/s00220-021-03963-w.pdf}, author = {Matthew Coudron and Stark, Jalex and Vidick, Thomas} } @article {2764, title = {Trapped electrons and ions as particle detectors}, journal = {Phys. Rev. Lett.}, volume = {127}, year = {2021}, month = {8/5/2021}, abstract = {

Electrons and ions trapped with electromagnetic fields have long served as important high-precision metrological instruments, and more recently have also been proposed as a platform for quantum information processing. Here we point out that these systems can also be used as highly sensitive detectors of passing charged particles, due to the combination of their extreme charge-to-mass ratio and low-noise quantum readout and control. In particular, these systems can be used to detect energy depositions many orders of magnitude below typical ionization scales. As an illustration, we show that current devices can be used to provide competitive sensitivity to models where ambient dark matter particles carry small electric millicharges <}, doi = {https://doi.org/10.1103/PhysRevLett.127.061804}, url = {https://arxiv.org/abs/2104.05737}, author = {Daniel Carney and Hartmut H{\"a}ffner and David C. Moore and J. M. Taylor} } @article {2682, title = {Tunable three-body loss in a nonlinear Rydberg medium}, journal = {Phys. Rev. Lett., in press }, year = {2021}, month = {9/28/2020}, abstract = {

Long-range Rydberg interactions, in combination with electromagnetically induced transparency (EIT), give rise to strongly interacting photons where the strength, sign, and form of the interactions are widely tunable and controllable. Such control can be applied to both coherent and dissipative interactions, which provides the potential to generate novel few-photon states. Recently it has been shown that Rydberg-EIT is a rare system in which three-body interactions can be as strong or stronger than two-body interactions. In this work, we study a three-body scattering loss for Rydberg-EIT in a wide regime of single and two-photon detunings. Our numerical simulations of the full three-body wavefunction and analytical estimates based on Fermi\&$\#$39;s Golden Rule strongly suggest that the observed features in the outgoing photonic correlations are caused by the resonant enhancement of the three-body losses.

}, url = {https://arxiv.org/abs/2009.13599}, author = {Dalia P. Ornelas Huerta and Przemyslaw Bienias and Alexander N. Craddock and Michael Gullans and Andrew J. Hachtel and Marcin Kalinowski and Mary E. Lyon and Alexey V. Gorshkov and Steven L. Rolston and J. V. Porto} } @article {2450, title = {Ultralight dark matter detection with mechanical quantum sensors}, journal = {New Journal of Physics}, volume = {23}, year = {2021}, month = {3/10/2021}, pages = {023041}, abstract = {

We consider the use of quantum-limited mechanical force sensors to detect ultralight (sub-meV) dark matter candidates which are weakly coupled to the standard model. We show that mechanical sensors with masses around or below the milligram scale, operating around the standard quantum limit, would enable novel searches for dark matter with natural frequencies around the kHz scale. This would complement existing strategies based on torsion balances, atom interferometers, and atomic clock systems

}, issn = {1367-2630}, doi = {https://doi.org/10.1088/1367-2630/abd9e7}, url = {https://arxiv.org/abs/1908.04797}, author = {Daniel Carney and Anson Hook and Zhen Liu and J. M. Taylor and Yue Zhao} } @article {2862, title = {Using an Atom Interferometer to Infer Gravitational Entanglement Generation}, journal = {PRX Quantum}, volume = {2}, year = {2021}, month = {8/20/2021}, abstract = {

If gravitational perturbations are quantized into gravitons in analogy with the electromagnetic field and photons, the resulting graviton interactions should lead to an entangling interaction between massive objects. We suggest a test of this prediction. To do this, we introduce the concept of interactive quantum information sensing. This novel sensing protocol is tailored to provable verification of weak dynamical entanglement generation between a pair of systems. We show that this protocol is highly robust to typical thermal noise sources. The sensitivity can moreover be increased both using an initial thermal state and/or an initial phase of entangling via a non-gravitational interaction. We outline a concrete implementation testing the ability of the gravitational field to generate entanglement between an atomic interferometer and mechanical oscillator. Preliminary numerical estimates suggest that near-term devices could feasibly be used to perform the experiment.

}, issn = {2691-3399}, doi = {10.1103/prxquantum.2.030330}, url = {http://dx.doi.org/10.1103/PRXQuantum.2.030330}, author = {Carney, Daniel and M{\"u}ller, Holger and Taylor, Jacob M.} } @article {2449, title = {Auto-tuning of double dot devices in situ with machine learning}, journal = {Phys. Rev. Applied }, volume = {13}, year = {2020}, month = {4/1/2020}, abstract = {

There are myriad quantum computing approaches, each having its own set of challenges to understand and effectively control their operation. Electrons confined in arrays of semiconductor nanostructures, called quantum dots (QDs), is one such approach. The easy access to control parameters, fast measurements, long qubit lifetimes, and the potential for scalability make QDs especially attractive. However, as the size of the QD array grows, so does the number of parameters needed for control and thus the tuning complexity. The current practice of manually tuning the qubits is a relatively time-consuming procedure and is inherently impractical for scaling up and applications. In this work, we report on the in situ implementation of an auto-tuning protocol proposed by Kalantre et al. [arXiv:1712.04914]. In particular, we discuss how to establish a seamless communication protocol between a machine learning (ML)-based auto-tuner and the experimental apparatus. We then show that a ML algorithm trained exclusively on synthetic data coming from a physical model to quantitatively classify the state of the QD device, combined with an optimization routine, can be used to replace manual tuning of gate voltages in devices. A success rate of over 85 \% is determined for tuning to a double quantum dot regime when at least one of the plunger gates is initiated sufficiently close to the desired state. Modifications to the training network, fitness function, and optimizer are discussed as a path towards further improvement in the success rate when starting both near and far detuned from the target double dot range.

}, doi = {https://doi.org/10.1103/PhysRevApplied.13.034075}, url = {https://arxiv.org/abs/1909.08030}, author = {Justyna P. Zwolak and Thomas McJunkin and Sandesh S. Kalantre and J. P. Dodson and E. R. MacQuarrie and D. E. Savage and M. G. Lagally and S. N. Coppersmith and Mark A. Eriksson and J. M. Taylor} } @article {2581, title = {Back-action evading impulse measurement with mechanical quantum sensors}, journal = {Phys. Rev. A}, volume = {102}, year = {2020}, month = {8/28/2020}, type = {FERMILAB-PUB-19-537-T}, abstract = {

The quantum measurement of any observable naturally leads to noise added by the act of measurement. Approaches to evade or reduce this noise can lead to substantial improvements in a wide variety of sensors, from laser interferometers to precision magnetometers and more. In this paper, we develop a measurement protocol based upon pioneering work by the gravitational wave community which allows for reduction of added noise from measurement by coupling an optical field to the momentum of a small mirror. As a specific implementation, we present a continuous measurement protocol using a double-ring optomechanical cavity. We demonstrate that with experimentally-relevant parameters, this protocol can lead to significant back-action noise evasion, yielding measurement noise below the standard quantum limit over many decades of frequency.

}, doi = {https://doi.org/10.1103/PhysRevA.102.023525}, url = {https://arxiv.org/pdf/1910.11892.pdf}, author = {Sohitri Ghosh and Daniel Carney and Peter Shawhan and J. M. Taylor} } @article {2728, title = {A Black-Box Approach to Post-Quantum Zero-Knowledge in Constant Rounds}, year = {2020}, month = {11/5/2020}, abstract = {

In a recent seminal work, Bitansky and Shmueli (STOC \&$\#$39;20) gave the first construction of a constant round zero-knowledge argument for NP secure against quantum attacks. However, their construction has several drawbacks compared to the classical counterparts. Specifically, their construction only achieves computational soundness, requires strong assumptions of quantum hardness of learning with errors (QLWE assumption) and the existence of quantum fully homomorphic encryption (QFHE), and relies on non-black-box simulation. In this paper, we resolve these issues at the cost of weakening the notion of zero-knowledge to what is called ε-zero-knowledge. Concretely, we construct the following protocols: - We construct a constant round interactive proof for NP that satisfies statistical soundness and black-box ε-zero-knowledge against quantum attacks assuming the existence of collapsing hash functions, which is a quantum counterpart of collision-resistant hash functions. Interestingly, this construction is just an adapted version of the classical protocol by Goldreich and Kahan (JoC \&$\#$39;96) though the proof of ε-zero-knowledge property against quantum adversaries requires novel ideas. - We construct a constant round interactive argument for NP that satisfies computational soundness and black-box ε-zero-knowledge against quantum attacks only assuming the existence of post-quantum one-way functions. At the heart of our results is a new quantum rewinding technique that enables a simulator to extract a committed message of a malicious verifier while simulating verifier\&$\#$39;s internal state in an appropriate sense.

}, url = {https://arxiv.org/abs/2011.02670}, author = {Nai-Hui Chia and Kai-Min Chung and Takashi Yamakawa} } @article {2606, title = {Building Bulk Geometry from the Tensor Radon Transform}, journal = {Journal of High Energy Physics}, volume = {2020}, year = {2020}, month = {12/4/2020}, pages = {1-50}, abstract = {

Using the tensor Radon transform and related numerical methods, we study how bulk geometries can be explicitly reconstructed from boundary entanglement entropies in the specific case of AdS3/CFT2. We find that, given the boundary entanglement entropies of a 2d CFT, this framework provides a quantitative measure that detects whether the bulk dual is geometric in the perturbative (near AdS) limit. In the case where a well-defined bulk geometry exists, we explicitly reconstruct the unique bulk metric tensor once a gauge choice is made. We then examine the emergent bulk geometries for static and dynamical scenarios in holography and in many-body systems. Apart from the physics results, our work demonstrates that numerical methods are feasible and effective in the study of bulk reconstruction in AdS/CFT.

}, url = {https://arxiv.org/abs/2007.00004}, author = {ChunJun Cao and Xiao-Liang Q and Brian Swingle and Eugene Tang} } @article {2526, title = {Can graph properties have exponential quantum speedup?}, year = {2020}, month = {1/28/2020}, abstract = {

Quantum computers can sometimes exponentially outperform classical ones, but only for problems with sufficient structure. While it is well known that query problems with full permutation symmetry can have at most polynomial quantum speedup -- even for partial functions -- it is unclear how far this condition must be relaxed to enable exponential speedup. In particular, it is natural to ask whether exponential speedup is possible for (partial) graph properties, in which the input describes a graph and the output can only depend on its isomorphism class. We show that the answer to this question depends strongly on the input model. In the adjacency matrix model, we prove that the bounded-error randomized query complexity R of any graph property P has R(P)=O(Q(P)6), where Q is the bounded-error quantum query complexity. This negatively resolves an open question of Montanaro and de Wolf in the adjacency matrix model. More generally, we prove R(P)=O(Q(P)3l) for any l-uniform hypergraph property P in the adjacency matrix model. In direct contrast, in the adjacency list model for bounded-degree graphs, we exhibit a promise problem that shows an exponential separation between the randomized and quantum query complexities.

}, url = {https://arxiv.org/abs/2001.10520}, author = {Andrew M. Childs and Daochen Wang} } @article {2575, title = {The Character of Motional Modes for Entanglement and Sympathetic Cooling of Mixed-Species Trapped Ion Chains}, year = {2020}, month = {4/16/2020}, abstract = {

Modular mixed-species ion-trap networks are a promising framework for scalable quantum information processing, where one species acts as a memory qubit and another as a communication qubit. This architecture requires high-fidelity mixed-species entangling gates to transfer information from communication to memory qubits through their collective motion. We investigate the character of the motional modes of a mixed-species ion chain for entangling operations and also sympathetic cooling. We find that the laser power required for high-fidelity entangling gates based on transverse modes is at least an order of magnitude higher than that based on axial modes for widely different masses of the two species. We also find that for even moderate mass differences, the transverse modes are much harder to cool than the axial modes regardless of the ion chain configuration. Therefore, transverse modes conventionally used for operations in single-species ion chains may not be well suited for mixed-species chains with widely different masses.

}, url = {https://arxiv.org/abs/2004.08045}, author = {Ksenia Sosnova and Allison Carter and Christopher Monroe} } @article {2573, title = {Computations with Greater Quantum Depth Are Strictly More Powerful (Relative to an Oracle)}, journal = {Accepted to the Symposium on the Theory of Computing (STOC) 2020 conference}, year = {2020}, month = {4/23/2020}, abstract = {

A conjecture of Jozsa [Jozsa06] states that any polynomial-time quantum computation can be simulated by polylogarithmic-depth quantum computation interleaved with polynomial-depth classical computation. Separately, Aaronson [Aaronson05, Aaronson11, Aaronson14] conjectured that there exists an oracle O such that BQPO\≠(BPPBQNC)O. These conjectures are intriguing allusions to the unresolved potential of combining classical and low-depth quantum computation. In this work we show that the Welded Tree Problem, which is an oracle problem that can be solved in quantum polynomial time as shown by Childs et al. [ChildsCDFGS03], cannot be solved in BPPBQNC, nor can it be solved in the class that Jozsa describes. This proves Aaronson\&$\#$39;s oracle separation conjecture and provides a counterpoint to Jozsa\&$\#$39;s conjecture relative to the Welded Tree oracle problem. More precisely, we define two complexity classes, HQC and JC whose languages are decided by two different families of interleaved quantum-classical circuits. HQC contains BPPBQNC and is therefore relevant to Aaronson\&$\#$39;s conjecture, while JC captures the model of computation that Jozsa considers. We show that the Welded Tree Problem gives an oracle separation between either of {JC,HQC} and BQP. Therefore, even when interleaved with arbitrary polynomial-time classical computation, greater \"quantum depth\" leads to strictly greater computational ability in this relativized setting.

}, doi = {https://doi.org/10.1145/3357713.3384269}, url = {https://arxiv.org/abs/1909.10503}, author = {Matthew Coudron and Sanketh Menda} } @article {2695, title = {Confronting lattice parton distributions with global QCD analysis}, year = {2020}, month = {10/1/2020}, abstract = {

We present the first Monte Carlo based global QCD analysis of spin-averaged and spin-dependent parton distribution functions (PDFs) that includes nucleon isovector matrix elements in coordinate space from lattice QCD. We investigate the degree of universality of the extracted PDFs when the lattice and experimental data are treated under the same conditions within the Bayesian likelihood analysis. For the unpolarized sector, we find rather weak constraints from the current lattice data on the phenomenological PDFs, and difficulties in describing the lattice matrix elements at large spatial distances. In contrast, for the polarized PDFs we find good agreement between experiment and lattice data, with the latter providing significant constraints on the spin-dependent isovector quark and antiquark distributions

}, url = {https://arxiv.org/abs/2010.00548}, author = {Jacob Bringewatt and N. Sato and W. Melnitchouk and Jian-Wei Qiu and F. Steffens and M. Constantinou} } @article {2723, title = {Constant-round Blind Classical Verification of Quantum Sampling}, year = {2020}, month = {12/8/2020}, abstract = {

In a recent breakthrough, Mahadev constructed a classical verification of quantum computation (CVQC) protocol for a classical client to delegate decision problems in BQP to an untrusted quantum prover under computational assumptions. In this work, we explore further the feasibility of CVQC with the more general sampling problems in BQP and with the desirable blindness property. We contribute affirmative solutions to both as follows. (1) Motivated by the sampling nature of many quantum applications (e.g., quantum algorithms for machine learning and quantum supremacy tasks), we initiate the study of CVQC for quantum sampling problems (denoted by SampBQP). More precisely, in a CVQC protocol for a SampBQP problem, the prover and the verifier are given an input x\∈{0,1}n and a quantum circuit C, and the goal of the classical client is to learn a sample from the output z\←C(x) up to a small error, from its interaction with an untrusted prover. We demonstrate its feasibility by constructing a four-message CVQC protocol for SampBQP based on the quantum Learning With Error assumption. (2) The blindness of CVQC protocols refers to a property of the protocol where the prover learns nothing, and hence is blind, about the client\&$\#$39;s input. It is a highly desirable property that has been intensively studied for the delegation of quantum computation. We provide a simple yet powerful generic compiler that transforms any CVQC protocol to a blind one while preserving its completeness and soundness errors as well as the number of rounds. Applying our compiler to (a parallel repetition of) Mahadev\&$\#$39;s CVQC protocol for BQP and our CVQC protocol for SampBQP yields the first constant-round blind CVQC protocol for BQP and SampBQP respectively, with negligible completeness and soundness errors.

}, url = {https://arxiv.org/abs/2012.04848}, author = {Kai-Min Chung and Yi Lee and Han-Hsuan Lin and Xiaodi Wu} } @article {2637, title = {Critical Theory for the Breakdown of Photon Blockade}, year = {2020}, month = {6/9/2020}, abstract = {

Photon blockade is the result of the interplay between the quantized nature of light and strong optical nonlinearities, whereby strong photon-photon repulsion prevents a quantum optical system from absorbing multiple photons. We theoretically study a single atom coupled to the light field, described by the resonantly driven Jaynes--Cummings model, in which case the photon blockade breaks down in a second order phase transition at a critical drive strength. We show that this transition is associated to the spontaneous breaking of an anti-unitary PT-symmetry. Within a semiclassical approximation we calculate the expectation values of observables in the steady state. We then move beyond the semiclassical approximation and approach the critical point from the disordered (blockaded) phase by reducing the Lindblad quantum master equation to a classical rate equation that we solve. The width of the steady-state distribution in Fock space is found to diverge as we approach the critical point with a simple power-law, allowing us to calculate the critical scaling of steady state observables without invoking mean-field theory. We propose a simple physical toy model for biased diffusion in the space of occupation numbers, which captures the universal properties of the steady state. We list several experimental platforms where this phenomenon may be observed.

}, url = {https://arxiv.org/abs/2006.05593}, author = {Jonathan B. Curtis and Igor Boettcher and Jeremy T. Young and Mohammad F. Maghrebi and Howard Carmichael and Alexey V. Gorshkov and Michael Foss-Feig} } @article {2514, title = {Destructive Error Interference in Product-Formula Lattice Simulation}, journal = {Phys. Rev. Lett. }, volume = {124}, year = {2020}, month = {6/4/2020}, abstract = {

Quantum computers can efficiently simulate the dynamics of quantum systems. In this paper, we study the cost of digitally simulating the dynamics of several physically relevant systems using the first-order product formula algorithm. We show that the errors from different Trotterization steps in the algorithm can interfere destructively, yielding a much smaller error than previously estimated. In particular, we prove that the total error in simulating a nearest-neighbor interacting system of n sites for time t using the first-order product formula with r time slices is O(nt/r+nt3/r2) when nt2/r is less than a small constant. Given an error tolerance ε, the error bound yields an estimate of max{O(n2t/ε),O(n2t3/2/ε1/2)} for the total gate count of the simulation. The estimate is tighter than previous bounds and matches the empirical performance observed in Childs et al. [PNAS 115, 9456-9461 (2018)]. We also provide numerical evidence for potential improvements and conjecture an even tighter estimate for the gate count.\ 

}, doi = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.220502}, url = {https://arxiv.org/abs/1912.11047}, author = {Minh C. Tran and Su-Kuan Chu and Yuan Su and Andrew M. Childs and Alexey V. Gorshkov} } @article {2457, title = {Entanglement Bounds on the Performance of Quantum Computing Architectures}, journal = {Phys. Rev. Research}, volume = {2}, year = {2020}, month = {9/22/2020}, abstract = {

There are many possible architectures for future quantum computers that designers will need to choose between. However, the process of evaluating a particular connectivity graph\&$\#$39;s performance as a quantum architecture can be difficult. In this paper, we establish a connection between a quantity known as the isoperimetric number and a lower bound on the time required to create highly entangled states. The metric we propose counts resources based on the use of two-qubit unitary operations, while allowing for arbitrarily fast measurements and classical feedback. We describe how these results can be applied to the evaluation of the hierarchical architecture proposed in Phys. Rev. A 98, 062328 (2018). We also show that the time-complexity bound we place on the creation of highly-entangled states can be saturated up to a multiplicative factor logarithmic in the number of qubits.

}, doi = {https://doi.org/10.1103/PhysRevResearch.2.033316}, url = {https://arxiv.org/abs/1908.04802}, author = {Zachary Eldredge and Leo Zhou and Aniruddha Bapat and James R. Garrison and Abhinav Deshpande and Frederic T. Chong and Alexey V. Gorshkov} } @article {2677, title = {Entanglement entropy scaling transition under competing monitoring protocols}, year = {2020}, month = {08/19/2020}, abstract = {

Dissipation generally leads to the decoherence of a quantum state. In contrast, numerous recent proposals have illustrated that dissipation can also be tailored to stabilize many-body entangled quantum states. While the focus of these works has been primarily on engineering the non-equilibrium steady state, we investigate the build-up of entanglement in the quantum trajectories. Specifically, we analyze the competition between two different dissipation channels arising from two incompatible continuous monitoring protocols. The first protocol locks the phase of neighboring sites upon registering a quantum jump, thereby generating a long-range entanglement through the system, while the second one destroys the coherence via dephasing mechanism. By studying the unraveling of stochastic quantum trajectories associated with the continuous monitoring protocols, we present a transition for the scaling of the averaged trajectory entanglement entropies, from critical scaling to area-law behavior. Our work provides novel insights into the occurrence of a measurement-induced phase transition within a continuous monitoring protocol.

}, url = {https://arxiv.org/abs/2008.08619}, author = {Mathias Van Regemortel and Ze-Pei Cian and Alireza Seif and Hossein Dehghani and Mohammad Hafezi} } @article {2567, title = {Exotic photonic molecules via Lennard-Jones-like potentials}, journal = {Phys. Rev. Lett.}, volume = {125}, year = {2020}, month = {9/19/2020}, abstract = {

Ultracold systems offer an unprecedented level of control of interactions between atoms. An important challenge is to achieve a similar level of control of the interactions between photons. Towards this goal, we propose a realization of a novel Lennard-Jones-like potential between photons coupled to the Rydberg states via electromagnetically induced transparency (EIT). This potential is achieved by tuning Rydberg states to a F{{\"o}}rster resonance with other Rydberg states. We consider few-body problems in 1D and 2D geometries and show the existence of self-bound clusters (\"molecules\") of photons. We demonstrate that for a few-body problem, the multi-body interactions have a significant impact on the geometry of the molecular ground state. This leads to phenomena without counterparts in conventional systems: For example, three photons in 2D preferentially arrange themselves in a line-configuration rather than in an equilateral-triangle configuration. Our result opens a new avenue for studies of many-body phenomena with strongly interacting photons.

}, doi = {https://doi.org/10.1103/PhysRevLett.125.093601}, url = {https://arxiv.org/abs/2003.07864}, author = {Przemyslaw Bienias and Michael Gullans and Marcin Kalinowski and Alexander N. Craddock and Dalia P. Ornelas-Huerta and Steven L. Rolston and J. V. Porto and Alexey V. Gorshkov} } @article {2686, title = {Fault-Tolerant Operation of a Quantum Error-Correction Code}, year = {2020}, month = {9/24/2020}, abstract = {

Quantum error correction protects fragile quantum information by encoding it in a larger quantum system whose extra degrees of freedom enable the detection and correction of errors. An encoded logical qubit thus carries increased complexity compared to a bare physical qubit. Fault-tolerant protocols contain the spread of errors and are essential for realizing error suppression with an error-corrected logical qubit. Here we experimentally demonstrate fault-tolerant preparation, rotation, error syndrome extraction, and measurement on a logical qubit encoded in the 9-qubit Bacon-Shor code. For the logical qubit, we measure an average fault-tolerant preparation and measurement error of 0.6\% and a transversal Clifford gate with an error of 0.3\% after error correction. The result is an encoded logical qubit whose logical fidelity exceeds the fidelity of the entangling operations used to create it. We compare these operations with non-fault-tolerant protocols capable of generating arbitrary logical states, and observe the expected increase in error. We directly measure the four Bacon-Shor stabilizer generators and are able to detect single qubit Pauli errors. These results show that fault-tolerant quantum systems are currently capable of logical primitives with error rates lower than their constituent parts. With the future addition of intermediate measurements, the full power of scalable quantum error-correction can be achieved.\ 

}, url = {https://arxiv.org/abs/2009.11482}, author = {Laird Egan and Dripto M. Debroy and Crystal Noel and Andrew Risinger and Daiwei Zhu and Debopriyo Biswas and Michael Newman and Muyuan Li and Kenneth R. Brown and Marko Cetina and Christopher Monroe} } @article {2375, title = {Gravitational Direct Detection of Dark Matter}, journal = {Phys. Rev. D}, volume = {102}, year = {2020}, month = {10/13/2020}, type = {FERMILAB-PUB-19-082-AE-T}, abstract = {

The only coupling dark matter is guaranteed to have with the standard model is through gravity. Here we propose a concept for direct dark matter detection using only this gravitational coupling, enabling a new regime of detection. Leveraging dramatic advances in the ability to create, maintain, and probe quantum states of massive objects, we suggest that an array of quantum-limited impulse sensors may be capable of detecting the correlated gravitational force created by a passing dark matter particle. We present two concrete realizations of this scheme, using either mechanical resonators or freely-falling masses. With currently available technology, a meter-scale apparatus of this type could detect any dark matter candidate around the Planck mass or heavier.

}, doi = {https://doi.org/10.1103/PhysRevD.102.072003}, url = {https://arxiv.org/abs/1903.00492}, author = {Daniel Carney and Sohitri Ghosh and Gordan Krnjaic and J. M. Taylor} } @article {2577, title = {Hierarchy of linear light cones with long-range interactions}, journal = {Physical Review X}, volume = {10}, year = {2020}, month = {5/29/2020}, abstract = {

In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a \"linear light cone,\" which expands at an emergent velocity analogous to the speed of light. Yet most non-relativistic physical systems realized in nature have long-range interactions: two degrees of freedom separated by a distance r interact with potential energy V(r)\∝1/rα. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: at the same α, some quantum information processing tasks are constrained by a linear light cone while others are not. In one spatial dimension, commutators of local operators \⟨ψ|[Ox(t),Oy]|ψ\⟩ are negligible in every state |ψ\⟩ when |x\−y|≳vt, where v is finite when α\>3 (Lieb-Robinson light cone); in a typical state |ψ\⟩ drawn from the infinite temperature ensemble, v is finite when α\>52 (Frobenius light cone); in non-interacting systems, v is finite in every state when α\>2 (free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones, and their tightness, also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that quantum state transfer and many-body quantum chaos are bounded by the Frobenius light cone, and therefore are poorly constrained by all Lieb-Robinson bounds.

}, doi = {https://doi.org/10.1103/PhysRevX.10.031009}, url = {https://arxiv.org/abs/2001.11509}, author = {Minh C. Tran and Chi-Fang Chen and Adam Ehrenberg and Andrew Y. Guo and Abhinav Deshpande and Yifan Hong and Zhe-Xuan Gong and Alexey V. Gorshkov and Andrew Lucas} } @article {2687, title = {Mechanical Quantum Sensing in the Search for Dark Matter}, year = {2020}, month = {8/13/2020}, type = {FERMILAB-PUB-20-378-QIS-T}, abstract = {

Numerous astrophysical and cosmological observations are best explained by the existence of dark matter, a mass density which interacts only very weakly with visible, baryonic matter. Searching for the extremely weak signals produced by this dark matter strongly motivate the development of new, ultra-sensitive detector technologies. Paradigmatic advances in the control and readout of massive mechanical systems, in both the classical and quantum regimes, have enabled unprecedented levels of sensitivity. In this white paper, we outline recent ideas in the potential use of a range of solid-state mechanical sensing technologies to aid in the search for dark matter in a number of energy scales and with a variety of coupling mechanisms.

}, url = {https://arxiv.org/abs/2008.06074}, author = {D. Carney and G. Krnjaic and D. C. Moore and C. A. Regal and G. Afek and S. Bhave and B. Brubaker and T. Corbitt and J. Cripe and N. Crisosto and A.Geraci and S. Ghosh and J. G. E. Harris and A. Hook and E. W. Kolb and J. Kunjummen and R. F. Lang and T. Li and T. Lin and Z. Liu and J. Lykken and L. Magrini and J. Manley and N. Matsumoto and A. Monte and F. Monteiro and T. Purdy and C. J. Riedel and R. Singh and S. Singh and K. Sinha and J. M. Taylor and J. Qin and D. J. Wilson and Y. Zhao} } @article {2692, title = {More of the Bulk from Extremal Area Variations}, journal = {Classical and Quantum Gravity}, volume = {38}, year = {2020}, month = {12/24/2020}, pages = {047001}, abstract = {

It was shown recently, building on work of Alexakis, Balehowksy, and Nachman that the geometry of (some portion of) a manifold with boundary is uniquely fixed by the areas of a foliation of two-dimensional disk-shaped surfaces anchored to the boundary. In the context of AdS/CFT, this implies that (a portion of) a four-dimensional bulk geometry can be fixed uniquely from the entanglement entropies of disk-shaped boundary regions, subject to several constraints. In this Note, we loosen some of these constraints, in particular allowing for the bulk foliation of extremal surfaces to be local and removing the constraint of disk topology; these generalizations ensure uniqueness of more of the deep bulk geometry by allowing for e.g. surfaces anchored on disconnected asymptotic boundaries, or HRT surfaces past a phase transition. We also explore in more depth the generality of the local foliation requirement, showing that even in a highly dynamical geometry like AdS-Vaidya it is satisfied.

}, doi = {https://iopscience.iop.org/article/10.1088/1361-6382/abcfd0/pdf}, url = {https://arxiv.org/abs/2009.07850}, author = {Ning Bao and ChunJun Cao and Sebastian Fischetti and Jason Pollack and Yibo Zhong} } @article {2556, title = {Nearly optimal time-independent reversal of a spin chain}, journal = {accepted for publication in Physical Review Research}, year = {2020}, month = {3/5/2020}, abstract = {

We propose a time-independent Hamiltonian protocol for the reversal of qubit ordering in a chain of N spins. Our protocol has an easily implementable nearest-neighbor, transverse-field Ising model Hamiltonian with time-independent, non-uniform couplings. Under appropriate normalization, we implement this state reversal three times faster than a naive approach using SWAP gates, in time comparable to a protocol of Raussendorf [Phys. Rev. A 72, 052301 (2005)] that requires dynamical control. We also prove lower bounds on state reversal by using results on the entanglement capacity of Hamiltonians and show that we are within a factor 1.502(1+1/N) of the shortest time possible. Our lower bound holds for all nearest-neighbor qubit protocols with arbitrary finite ancilla spaces and local operations and classical communication. Finally, we extend our protocol to an infinite family of nearest-neighbor, time-independent Hamiltonian protocols for state reversal. This includes chains with nearly uniform coupling that may be especially feasible for experimental implementation.\ 

}, url = {https://arxiv.org/abs/2003.02843}, author = {Aniruddha Bapat and Eddie Schoute and Alexey V. Gorshkov and Andrew M. Childs} } @article {2485, title = {Non-interactive classical verification of quantum computation}, journal = {Theory of Cryptography Conference (TCC)}, volume = {Lecture Notes in Computer Science 12552}, year = {2020}, month = {3/9/2020}, pages = {153-180}, abstract = {

In a recent breakthrough, Mahadev constructed an interactive protocol that enables a purely classical party to delegate any quantum computation to an untrusted quantum prover. In this work, we show that this same task can in fact be performed non-interactively and in zero-knowledge.
Our protocols result from a sequence of significant improvements to the original four-message protocol of Mahadev. We begin by making the first message instance-independent and moving it to an offline setup phase. We then establish a parallel repetition theorem for the resulting three-message protocol, with an asymptotically optimal rate. This, in turn, enables an application of the Fiat-Shamir heuristic, eliminating the second message and giving a non-interactive protocol. Finally, we employ classical non-interactive zero-knowledge (NIZK) arguments and classical fully homomorphic encryption (FHE) to give a zero-knowledge variant of this construction. This yields the first purely classical NIZK argument system for QMA, a quantum analogue of NP.
We establish the security of our protocols under standard assumptions in quantum-secure cryptography. Specifically, our protocols are secure in the Quantum Random Oracle Model, under the assumption that Learning with Errors is quantumly hard. The NIZK construction also requires circuit-private FHE.

}, url = {https://arxiv.org/abs/1911.08101}, author = {Gorjan Alagic and Andrew M. Childs and Alex B. Grilo and Shih-Han Hung} } @article {2568, title = {On-demand indistinguishable single photons from an efficient and pure source based on a Rydberg ensemble}, year = {2020}, month = {3/4/2020}, abstract = {

Single photons coupled to atomic systems have shown to be a promising platform for developing quantum technologies. Yet a bright on-demand, highly pure and highly indistinguishable single-photon source compatible with atomic platforms is lacking. In this work, we demonstrate such a source based on a strongly interacting Rydberg system. The large optical nonlinearities in a blockaded Rydberg ensemble convert coherent light into a single-collective excitation that can be coherently retrieved as a quantum field. We observe a single-transverse-mode efficiency up to 0.18(2), g(2)=2.0(1.5)\×10\−4, and indistinguishability of 0.982(7), making this system promising for scalable quantum information applications. Accounting for losses, we infer a generation probability up to 0.40(4). Furthermore, we investigate the effects of contaminant Rydberg excitations on the source efficiency. Finally, we introduce metrics to benchmark the performance of on-demand single-photon sources.\ 

}, url = {https://arxiv.org/abs/2003.02202}, author = {Dalia P. Ornelas-Huerta and Alexander N. Craddock and Elizabeth A. Goldschmidt and Andrew J. Hachtel and Yidan Wang and P. Bienias and Alexey V. Gorshkov and Steve L. Rolston and James V. Porto} } @article {2456, title = {The operator L{\'e}vy flight: light cones in chaotic long-range interacting systems}, journal = {Phys. Rev. Lett. }, volume = {124}, year = {2020}, month = {7/6/2020}, abstract = {

We propose a generic light cone phase diagram for chaotic long-range r\−α interacting systems, where a linear light cone appears for α\≥d+1/2 in d dimension. Utilizing the dephasing nature of quantum chaos, we argue that the universal behavior of the squared commutator is described by a stochastic model, for which the exact phase diagram is known. We provide an interpretation in terms of the L{\'e}vy flights and show that this suffices to capture the scaling of the squared commutator. We verify these phenomena in numerical computation of a long-range spin chain with up to 200 sites.\ 

}, doi = {https://doi.org/10.1103/PhysRevLett.124.180601}, url = {https://arxiv.org/abs/1909.08646}, author = {Tianci Zhou and Shenglong Xu and Xiao Chen and Andrew Guo and Brian Swingle} } @article {2632, title = {Optimal control for quantum detectors}, year = {2020}, month = {5/12/2020}, abstract = {

Quantum systems are promising candidates for sensing of weak signals as they can provide unrivaled performance when estimating parameters of external fields. However, when trying to detect weak signals that are hidden by background noise, the signal-to-noise-ratio is a more relevant metric than raw sensitivity. We identify, under modest assumptions about the statistical properties of the signal and noise, the optimal quantum control to detect an external signal in the presence of background noise using a quantum sensor. Interestingly, for white background noise, the optimal solution is the simple and well-known spin-locking control scheme. We further generalize, using numerical techniques, these results to the background noise being a correlated Lorentzian spectrum. We show that for increasing correlation time, pulse based sequences such as CPMG are also close to the optimal control for detecting the signal, with the crossover dependent on the signal frequency. These results show that an optimal detection scheme can be easily implemented in near-term quantum sensors without the need for complicated pulse shaping.

}, url = {https://arxiv.org/abs/2005.05995}, author = {Paraj Titum and Kevin M. Schultz and Alireza Seif and Gregory D. Quiroz and B. D. Clader} } @article {2582, title = {Position Space Decoherence From Long-Range Interaction With Background Gas}, journal = {Bulletin of the American Physical Society}, year = {2020}, month = {06/05/2020}, type = {Invited paper of the DAMOP20 Meeting of The American Physical Society}, abstract = {

Experiments in matter wave interferometry and optomechanics are increasing the spatial extent of wavefunctions of massive quantum systems; this gives rise to new sources of decoherence that must be characterized. Here\ we calculate the position space decoherence of a quantum particle due to interaction\ with a fluctuating classical background gas for several different force laws. We begin\ with the calculation of this effect for the Newton potential. To our knowledge, this\ calculation has not been done before. We then solve the same problem in the case\ of a Yukawa interaction, which interpolates between our long-range force result and\ the well-studied formula for collisional decoherence from a contact interaction. Unlike the contact interaction case, where the decoherence rate becomes independent\ of distance for large quantum particle separations, we observe that a long-range\ interaction leads to quadratic scaling of the decoherence rate with distance even at\ large separations. This work is relevant to the generation of massive superposition\ in optomechanical and atom beam experiments, and to conclude we comment on\ the use of this decoherence signal for gravitational detection of dark matter.\ 

}, url = {http://meetings.aps.org/Meeting/DAMOP20/Session/S08.5}, author = {Jonathan Kunjummen and Daniel Carney and J. M. Taylor} } @article {2558, title = {On the Principles of Differentiable Quantum Programming Languages}, year = {2020}, month = {4/2/2020}, abstract = {

Variational Quantum Circuits (VQCs), or the so-called quantum neural-networks, are predicted to be one of the most important near-term quantum applications, not only because of their similar promises as classical neural-networks, but also because of their feasibility on near-term noisy intermediate-size quantum (NISQ) machines. The need for gradient information in the training procedure of VQC applications has stimulated the development of auto-differentiation techniques for quantum circuits. We propose the first formalization of this technique, not only in the context of quantum circuits but also for imperative quantum programs (e.g., with controls), inspired by the success of differentiable programming languages in classical machine learning. In particular, we overcome a few unique difficulties caused by exotic quantum features (such as quantum no-cloning) and provide a rigorous formulation of differentiation applied to bounded-loop imperative quantum programs, its code-transformation rules, as well as a sound logic to reason about their correctness. Moreover, we have implemented our code transformation in OCaml and demonstrated the resource-efficiency of our scheme both analytically and empirically. We also conduct a case study of training a VQC instance with controls, which shows the advantage of our scheme over existing auto-differentiation for quantum circuits without controls.

}, doi = {https://doi.org/10.1145/3385412.3386011}, url = {https://arxiv.org/abs/2004.01122}, author = {Shaopeng Zhu and Shih-Han Hung and Shouvanik Chakrabarti and Xiaodi Wu} } @article {2586, title = {Probing XY phase transitions in a Josephson junction array with tunable frustration}, year = {2020}, month = {1/22/2020}, abstract = {

The seminal theoretical works of Berezinskii, Kosterlitz, and Thouless presented a new paradigm for phase transitions in condensed matter that are driven by topological excitations. These transitions have been extensively studied in the context of two-dimensional XY models -- coupled compasses -- and have generated interest in the context of quantum simulation. Here, we use a circuit quantum-electrodynamics architecture to study the critical behavior of engineered XY models through their dynamical response. In particular, we examine not only the unfrustrated case but also the fully-frustrated case which leads to enhanced degeneracy associated with the spin rotational [U(1)] and discrete chiral (Z2) symmetries. The nature of the transition in the frustrated case has posed a challenge for theoretical studies while direct experimental probes remain elusive. Here we identify the transition temperatures for both the unfrustrated and fully-frustrated XY models by probing a Josephson junction array close to equilibrium using weak microwave excitations and measuring the temperature dependence of the effective damping obtained from the complex reflection coefficient. We argue that our probing technique is primarily sensitive to the dynamics of the U(1) part.

}, url = {https://arxiv.org/abs/2001.07877}, author = {R. Cosmic and K. Kawabata and Y. Ashida and H. Ikegami and S. Furukawa and P. Patil and J. M. Taylor and Y. Nakamura} } @article {2726, title = {Programmable Quantum Annealers as Noisy Gibbs Samplers}, year = {2020}, month = {12/16/2020}, abstract = {

Drawing independent samples from high-dimensional probability distributions represents the major computational bottleneck for modern algorithms, including powerful machine learning frameworks such as deep learning. The quest for discovering larger families of distributions for which sampling can be efficiently realized has inspired an exploration beyond established computing methods and turning to novel physical devices that leverage the principles of quantum computation. Quantum annealing embodies a promising computational paradigm that is intimately related to the complexity of energy landscapes in Gibbs distributions, which relate the probabilities of system states to the energies of these states. Here, we study the sampling properties of physical realizations of quantum annealers which are implemented through programmable lattices of superconducting flux qubits. Comprehensive statistical analysis of the data produced by these quantum machines shows that quantum annealers behave as samplers that generate independent configurations from low-temperature noisy Gibbs distributions. We show that the structure of the output distribution probes the intrinsic physical properties of the quantum device such as effective temperature of individual qubits and magnitude of local qubit noise, which result in a non-linear response function and spurious interactions that are absent in the hardware implementation. We anticipate that our methodology will find widespread use in characterization of future generations of quantum annealers and other emerging analog computing devices.

}, url = {https://arxiv.org/abs/2012.08827}, author = {Marc Vuffray and Carleton Coffrin and Yaroslav A. Kharkov and Andrey Y. Lokhov} } @article {2207, title = {Quantum algorithms and lower bounds for convex optimization}, journal = {Quantum}, volume = {4}, year = {2020}, month = {12/18/2019}, abstract = {

While recent work suggests that quantum computers can speed up the solution of semidefinite programs, little is known about the quantum complexity of more general convex optimization. We present a quantum algorithm that can optimize a convex function over an n-dimensional convex body using O~(n) queries to oracles that evaluate the objective function and determine membership in the convex body. This represents a quadratic improvement over the best-known classical algorithm. We also study limitations on the power of quantum computers for general convex optimization, showing that it requires Ω~(n\−\−\√) evaluation queries and Ω(n\−\−\√) membership queries.

}, doi = {https://doi.org/10.22331/q-2020-01-13-221}, url = {https://arxiv.org/abs/1809.01731}, author = {Shouvanik Chakrabarti and Andrew M. Childs and Tongyang Li and Xiaodi Wu} } @article {2557, title = {Quantum Coupon Collector}, journal = {Proceedings of the 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020), Leibniz International Proceedings in Informatics}, volume = {158}, year = {2020}, month = {2/18/2020}, pages = {10:1-10:17}, abstract = {

We study how efficiently a k-element set S\⊆[n] can be learned from a uniform superposition |S\⟩ of its elements. One can think of |S\⟩=\∑i\∈S|i\⟩/|S|\−\−\−\√ as the quantum version of a uniformly random sample over S, as in the classical analysis of the {\textquoteleft}{\textquoteleft}coupon collector problem.\&$\#$39;\&$\#$39; We show that if k is close to n, then we can learn S using asymptotically fewer quantum samples than random samples. In particular, if there are n\−k=O(1) missing elements then O(k) copies of |S\⟩ suffice, in contrast to the Θ(klogk) random samples needed by a classical coupon collector. On the other hand, if n\−k=Ω(k), then Ω(klogk) quantum samples are~necessary. More generally, we give tight bounds on the number of quantum samples needed for every k and n, and we give efficient quantum learning algorithms. We also give tight bounds in the model where we can additionally reflect through |S\⟩. Finally, we relate coupon collection to a known example separating proper and improper PAC learning that turns out to show no separation in the quantum case.

}, doi = {10.4230/LIPIcs.TQC.2020.10}, url = {https://arxiv.org/abs/2002.07688}, author = {Srinivasan Arunachalam and Aleksandrs Belovs and Andrew M. Childs and Robin Kothari and Ansis Rosmanis and Ronald de Wolf} } @article {2333, title = {Quantum spectral methods for differential equations}, journal = {Commun. Math. Phys. }, volume = {375}, year = {2020}, month = {2/18/2020}, pages = {1427-1457}, abstract = {

Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a d-dimensional system of linear equations or linear differential equations with complexity poly(logd). While several of these algorithms approximate the solution to within ε with complexity poly(log(1/ε)), no such algorithm was previously known for differential equations with time-dependent coefficients. Here we develop a quantum algorithm for linear ordinary differential equations based on so-called spectral methods, an alternative to finite difference methods that approximates the solution globally. Using this approach, we give a quantum algorithm for time-dependent initial and boundary value problems with complexity poly(logd,log(1/ε)).

}, doi = {https://doi.org/10.1007/s00220-020-03699-z}, url = {https://arxiv.org/abs/1901.00961}, author = {Andrew M. Childs and Jin-Peng Liu} } @article {2570, title = {Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer}, year = {2020}, month = {2/6/2020}, abstract = {

The quantum walk formalism is a widely used and highly successful framework for modeling quantum systems, such as simulations of the Dirac equation, different dynamics in both the low and high energy regime, and for developing a wide range of quantum algorithms. Here we present the circuit-based implementation of a discrete-time quantum walk in position space on a five-qubit trapped-ion quantum processor. We encode the space of walker positions in particular multi-qubit states and program the system to operate with different quantum walk parameters, experimentally realizing a Dirac cellular automaton with tunable mass parameter. The quantum walk circuits and position state mapping scale favorably to a larger model and physical systems, allowing the implementation of any algorithm based on discrete-time quantum walks algorithm and the dynamics associated with the discretized version of the Dirac equation.

}, url = {https://arxiv.org/abs/2002.02537}, author = {C. Huerta Alderete and Shivani Singh and Nhung H. Nguyen and Daiwei Zhu and Radhakrishnan Balu and Christopher Monroe and C. M. Chandrashekar and Norbert M. Linke} } @article {2716, title = {Quasi-polynomial Time Approximation of Output Probabilities of Constant-depth, Geometrically-local Quantum Circuits}, journal = {Accepted to QIP 2021}, year = {2020}, month = {12/10/2020}, abstract = {

We present a classical algorithm that, for any 3D geometrically-local, constant-depth quantum circuit C, and any bit string x\∈{0,1}n, can compute the quantity |\<x|C|0\⊗n\>|2 to within any inverse-polynomial additive error in quasi-polynomial time. It is known that it is $\#$P-hard to compute this same quantity to within 2\−n2 additive error [Mov20]. The previous best known algorithm for this problem used O(2n1/3poly(1/ε)) time to compute probabilities to within additive error ε [BGM20]. Notably, the [BGM20] paper included an elegant polynomial time algorithm for the same estimation task with 2D circuits, which makes a novel use of 1D Matrix Product States carefully tailored to the 2D geometry of the circuit in question. Surprisingly, it is not clear that it is possible to extend this use of MPS to address the case of 3D circuits in polynomial time. This raises a natural question as to whether the computational complexity of the 3D problem might be drastically higher than that of the 2D problem. In this work we address this question by exhibiting a quasi-polynomial time algorithm for the 3D case. In order to surpass the technical barriers encountered by previously known techniques we are forced to pursue a novel approach: Our algorithm has a Divide-and-Conquer structure, constructing a recursive sub-division of the given 3D circuit using carefully designed block-encodings, each creating a 3D-local circuit on at most half the number of qubits as the original. This division step is then applied recursively, expressing the original quantity as a weighted sum of smaller and smaller 3D-local quantum circuits. A central technical challenge is to control correlations arising from the entanglement that may exist between the different circuit \"pieces\" produced this way.

}, url = {https://arxiv.org/abs/2012.05460}, author = {Nolan J. Coble and Matthew Coudron} } @article {2820, title = {Quasi-polynomial time approximation of output probabilities of geometrically-local, shallow quantum circuits}, year = {2020}, month = {12/10/2020}, abstract = {

We present a classical algorithm that, for any 3D geometrically-local, polylogarithmic-depth quantum circuit C acting on n qubits, and any bit string x\∈{0,1}n, can compute the quantity |\<x|C|0\⊗n\>|2 to within any inverse-polynomial additive error in quasi-polynomial time. It is known that it is $\#$P-hard to compute this same quantity to within 2\−n2 additive error [Mov20, KMM21]. The previous best known algorithm for this problem used O(2n1/3poly(1/ϵ)) time to compute probabilities to within additive error ϵ [BGM20]. Notably, the [BGM20] paper included an elegant polynomial time algorithm for this estimation task restricted to 2D circuits, which makes a novel use of 1D Matrix Product States (MPS) carefully tailored to the 2D geometry of the circuit in question. Surprisingly, it is not clear that it is possible to extend this use of MPS to address the case of 3D circuits in polynomial time. This raises a natural question as to whether the computational complexity of the 3D problem might be drastically higher than that of the 2D problem. In this work we address this question by exhibiting a quasi-polynomial time algorithm for the 3D case. In order to surpass the technical barriers encountered by previously known techniques we are forced to pursue a novel approach.
Our algorithm has a Divide-and-Conquer structure, demonstrating how to approximate the desired quantity via several instantiations of the same problem type, each involving 3D-local circuits on about half the number of qubits as the original. This division step is then applied recursively, expressing the original quantity as a weighted combination of smaller and smaller 3D-local quantum circuits. A central technical challenge is to control correlations arising from entanglement that may exist between the different circuit {\textquoteleft}{\textquoteleft}pieces\" produced this way.

}, url = {https://arxiv.org/abs/2012.05460}, author = {Nolan J. Coble and Matthew Coudron} } @article {2563, title = {Random Quantum Batteries}, journal = {Phys. Rev. Research }, volume = {2}, year = {2020}, month = {5/5/2020}, abstract = {

Quantum nano-devices are fundamental systems in quantum thermodynamics that have been the subject of profound interest in recent years. Among these, quantum batteries play a very important role. In this paper we lay down a theory of random quantum batteries and provide a systematic way of computing the average work and work fluctuations in such devices by investigating their typical behavior. We show that the performance of random quantum batteries exhibits typicality and depends only on the spectral properties of the time evolving operator, the initial state and the measuring Hamiltonian. At given revival times a random quantum battery features a quantum advantage over classical random batteries. Our method is particularly apt to be used both for exactly solvable models like the Jaynes-Cummings model or in perturbation theory, e.g., systems subject to harmonic perturbations. We also study the setting of quantum adiabatic random batteries.

}, doi = {https://doi.org/10.1103/PhysRevResearch.2.023095}, url = {https://arxiv.org/abs/1908.08064}, author = {Francesco Caravelli and Ghislaine Coulter-De Wit and Luis Pedro Garc{\'\i}a-Pintos and Alioscia Hamma} } @article {2727, title = {Raw Image Deblurring}, year = {2020}, month = {12/8/2020}, abstract = {

Deep learning-based blind image deblurring plays an essential role in solving image blur since all existing kernels are limited in modeling the real world blur. Thus far, researchers focus on powerful models to handle the deblurring problem and achieve decent results. For this work, in a new aspect, we discover the great opportunity for image enhancement (e.g., deblurring) directly from RAW images and investigate novel neural network structures benefiting RAW-based learning. However, to the best of our knowledge, there is no available RAW image deblurring dataset. Therefore, we built a new dataset containing both RAW images and processed sRGB images and design a new model to utilize the unique characteristics of RAW images. The proposed deblurring model, trained solely from RAW images, achieves the state-of-art performance and outweighs those trained on processed sRGB images. Furthermore, with fine-tuning, the proposed model, trained on our new dataset, can generalize to other sensors. Additionally, by a series of experiments, we demonstrate that existing deblurring models can also be improved by training on the RAW images in our new dataset. Ultimately, we show a new venue for further opportunities based on the devised novel raw-based deblurring method and the brand-new Deblur-RAW dataset.

}, url = {https://arxiv.org/abs/2012.04264}, author = {Chih-Hung Liang and Yu-An Chen and Yueh-Cheng Liu and Winston H. Hsu} } @article {2681, title = {Resonant enhancement of three-body loss between strongly interacting photons}, year = {2020}, month = {10/19/2020}, abstract = {

Rydberg polaritons provide an example of a rare type of system where three-body interactions can be as strong or even stronger than two-body interactions. The three-body interactions can be either dispersive or dissipative, with both types possibly giving rise to exotic, strongly-interacting, and topological phases of matter. Despite past theoretical and experimental studies of the regime with dispersive interaction, the dissipative regime is still mostly unexplored. Using a renormalization group technique to solve the three-body Schr{\"o}dinger equation, we show how the shape and strength of dissipative three-body forces can be universally enhanced for Rydberg polaritons. We demonstrate how these interactions relate to the transmission through a single-mode cavity, which can be used as a probe of the three-body physics in current experiment

}, url = {https://arxiv.org/abs/2010.09772}, author = {Marcin Kalinowski and Yidan Wang and Przemyslaw Bienias and Michael Gullans and Dalia P. Ornelas-Huerta and Alexander N. Craddock and Steven L. Rolston and J. V. Porto and Hans Peter B{\"u}chler and Alexey V. Gorshkov} } @article {2718, title = {Robust Encoding of a Qubit in a Molecule}, journal = {Phys. Rev. X}, volume = {10}, year = {2020}, month = {9/1/2020}, abstract = {

We construct quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of rotational states of a rigid body. These codes, which protect against both drift in the body\’s orientation and small changes in its angular momentum, may be well suited for robust storage and coherent processing of quantum information using rotational states of a polyatomic molecule. Extensions of such codes to rigid bodies with a symmetry axis are compatible with rotational states of diatomic molecules as well as nuclear states of molecules and atoms. We also describe codes associated with general non-Abelian groups and develop orthogonality relations for coset spaces, laying the groundwork for quantum information processing with exotic configuration spaces.

}, doi = {https://journals.aps.org/prx/abstract/10.1103/PhysRevX.10.031050}, url = {https://arxiv.org/abs/1911.00099}, author = {Victor V. Albert and Jacob P. Covey and John Preskill} } @article {2501, title = {Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning}, journal = {to appear in Proceedings of STOC 2020}, year = {2020}, month = {6/18/2020}, abstract = {

We present an algorithmic framework for quantum-inspired classical algorithms on close-to-low-rank matrices, generalizing the series of results started by Tang\&$\#$39;s breakthrough quantum-inspired algorithm for recommendation systems [STOC\&$\#$39;19]. Motivated by quantum linear algebra algorithms and the quantum singular value transformation (SVT) framework of Gily{\'e}n et al. [STOC\&$\#$39;19], we develop classical algorithms for SVT that run in time independent of input dimension, under suitable quantum-inspired sampling assumptions. Our results give compelling evidence that in the corresponding QRAM data structure input model, quantum SVT does not yield exponential quantum speedups. Since the quantum SVT framework generalizes essentially all known techniques for quantum linear algebra, our results, combined with sampling lemmas from previous work, suffice to generalize all recent results about dequantizing quantum machine learning algorithms. In particular, our classical SVT framework recovers and often improves the dequantization results on recommendation systems, principal component analysis, supervised clustering, support vector machines, low-rank regression, and semidefinite program solving. We also give additional dequantization results on low-rank Hamiltonian simulation and discriminant analysis. Our improvements come from identifying the key feature of the quantum-inspired input model that is at the core of all prior quantum-inspired results: l2-norm sampling can approximate matrix products in time independent of their dimension. We reduce all our main results to this fact, making our exposition concise, self-contained, and intuitive.

}, doi = {https://doi.org/10.1145/3357713.3384314}, url = {https://arxiv.org/abs/1910.06151}, author = {Nai-Hui Chia and Andras Gilyen and Tongyang Li and Han-Hsuan Lin and Ewin Tang and Chunhao Wang} } @article {2693, title = {Search for composite dark matter with optically levitated sensors}, journal = {Phys. Rev. Lett. }, volume = {125}, year = {2020}, month = {11/2/2020}, abstract = {

Results are reported from a search for a class of composite dark matter models with feeble, long-range interactions with normal matter. We search for impulses arising from passing dark matter particles by monitoring the mechanical motion of an optically levitated nanogram mass over the course of several days. Assuming such particles constitute the dominant component of dark matter, this search places upper limits on their interaction with neutrons of αn\≤1.2\×10\−7 at 95\% confidence for dark matter masses between 1--10 TeV and mediator masses mφ\≤0.1 eV. Due to the large enhancement of the cross-section for dark matter to coherently scatter from a nanogram mass (\∼1029 times that for a single neutron) and the ability to detect momentum transfers as small as \∼200 MeV/c, these results provide sensitivity to certain classes of composite dark matter models that substantially exceeds existing searches, including those employing kg-scale or ton-scale targets. Extensions of these techniques can enable directionally-sensitive searches for a broad class of previously inaccessible heavy dark matter candidates.\ 

}, doi = {https://doi.org/10.1103/PhysRevLett.125.181102}, url = {https://arxiv.org/abs/2007.12067}, author = {Fernando Monteiro and Gadi Afek and Daniel Carney and Gordan Krnjaic and Jiaxiang Wang and David C. Moore} } @article {2678, title = {Secure Quantum Two-Party Computation: Impossibility and Constructions}, year = {2020}, month = {10/15/2020}, abstract = {

Secure two-party computation considers the problem of two parties computing a joint function of their private inputs without revealing anything beyond the output of the computation. In this work, we take the first steps towards understanding the setting in which the two parties want to evaluate a joint quantum functionality while using only a classical channel between them. Our first result indicates that it is in general impossible to realize a two-party quantum functionality against malicious adversaries with black-box simulation, relying only on classical channels. The negative result stems from reducing the existence of a black-box simulator to an extractor for classical proof of quantum knowledge, which in turn leads to violation of the quantum no-cloning. Next, we introduce the notion of oblivious quantum function evaluation (OQFE). An OQFE is a two-party quantum cryptographic primitive with one fully classical party (Alice) whose input is (a classical description of a) quantum unitary, U, and a quantum party (Bob) whose input is a quantum state, ψ. In particular, Alice receives a classical output corresponding to the measurement of U(ψ) while Bob receives no output. In OQFE, Bob remains oblivious to Alice\&$\#$39;s input, while Alice learns nothing about ψ more than what can be learned from the output. We present two constructions, one secure against semi-honest parties and the other against malicious parties. Due to the no-go result mentioned above, we consider what is arguably the best possible notion obtainable in our model concerning malicious adversaries: one-sided simulation security. Our protocol relies on the assumption of injective homomorphic trapdoor OWFs, which in turn rely on the LWE problem. As a result, we put forward a first, simple and modular, construction of one-sided quantum two-party computation and quantum oblivious transfer over classical networks.

}, url = {https://arxiv.org/abs/2010.07925}, author = {Michele Ciamp and Alexandru Cojocaru and Elham Kashefi and Atul Mantri} } @article {2610, title = {Security Limitations of Classical-Client Delegated Quantum Computing}, year = {2020}, month = {7/3/2020}, abstract = {

Secure delegated quantum computing allows a computationally weak client to outsource an arbitrary quantum computation to an untrusted quantum server in a privacy-preserving manner. One of the promising candidates to achieve classical delegation of quantum computation is classical-client remote state preparation (RSPCC), where a client remotely prepares a quantum state using a classical channel. However, the privacy loss incurred by employing RSPCC as a sub-module is unclear.
In this work, we investigate this question using the Constructive Cryptography framework by Maurer and Renner (ICS\&$\#$39;11). We first identify the goal of RSPCC as the construction of ideal RSP resources from classical channels and then reveal the security limitations of using RSPCC. First, we uncover a fundamental relationship between constructing ideal RSP resources (from classical channels) and the task of cloning quantum states. Any classically constructed ideal RSP resource must leak to the server the full classical description (possibly in an encoded form) of the generated quantum state, even if we target computational security only. As a consequence, we find that the realization of common RSP resources, without weakening their guarantees drastically, is impossible due to the no-cloning theorem. Second, the above result does not rule out that a specific RSPCC protocol can replace the quantum channel at least in some contexts, such as the Universal Blind Quantum Computing (UBQC) protocol of Broadbent et al. (FOCS \&$\#$39;09). However, we show that the resulting UBQC protocol cannot maintain its proven composable security as soon as RSPCC is used as a subroutine. Third, we show that replacing the quantum channel of the above UBQC protocol by the RSPCC protocol QFactory of Cojocaru et al. (Asiacrypt \&$\#$39;19), preserves the weaker, game-based, security of UBQC.

}, url = {https://arxiv.org/abs/2007.01668}, author = {Christian Badertscher and Alexandru Cojocaru and L{\'e}o Colisson and Elham Kashefi and Dominik Leichtle and Atul Mantri and Petros Wallden} } @article {2403, title = {Signaling and Scrambling with Strongly Long-Range Interactions}, journal = {Physical Review A}, volume = {102}, year = {2020}, month = {7/8/2020}, abstract = {

Strongly long-range interacting quantum systems---those with interactions decaying as a power-law 1/rα in the distance r on a D-dimensional lattice for α\≤D---have received significant interest in recent years. They are present in leading experimental platforms for quantum computation and simulation, as well as in theoretical models of quantum information scrambling and fast entanglement creation. Since no notion of locality is expected in such systems, a general understanding of their dynamics is lacking. As a first step towards rectifying this problem, we prove two new Lieb-Robinson-type bounds that constrain the time for signaling and scrambling in strongly long-range interacting systems, for which no tight bounds were previously known. Our first bound applies to systems mappable to free-particle Hamiltonians with long-range hopping, and is saturable for α\≤D/2. Our second bound pertains to generic long-range interacting spin Hamiltonians, and leads to a tight lower bound for the signaling time to extensive subsets of the system for all α\<D. This result also lower-bounds the scrambling time, and suggests a path towards achieving a tight scrambling bound that can prove the long-standing fast scrambling conjecture.\ 

}, doi = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.102.010401}, url = {https://arxiv.org/abs/1906.02662}, author = {Andrew Y. Guo and Minh C. Tran and Andrew M. Childs and Alexey V. Gorshkov and Zhe-Xuan Gong} } @article {2676, title = {Status Report on the Second Round of the NIST Post-Quantum Cryptography Standardization Process}, journal = {NISTIR 8309}, year = {2020}, month = {07/2020}, abstract = {

The National Institute of Standards and Technology is in the process of selecting one or more public-key cryptographic algorithms through a public, competition-like process. The new public-key cryptography standards will specify one or more additional digital signatures, public-key encryption, and key-establishment algorithms to augment Federal Information Processing Standard (FIPS) 186-4, Digital Signature Standard (DSS), as well as NIST Special Publication (SP) 800-56A Revision 3, Recommendation for Pair-Wise Key-Establishment Schemes Using Discrete Logarithm Cryptography, and SP 800-56B Revision 2, Recommendation for Pair-Wise Key Establishment Using Integer Factorization Cryptography. It is intended that these algorithms will be capable of protecting sensitive information well into the foreseeable future, including after the advent of quantum computers.

The NIST Post-Quantum Cryptography Standardization Process began in 2017 with 69 candidate algorithms that met both the minimum acceptance criteria and submission requirements. The first round lasted until January 2019, during which candidate algorithms were evaluated based on their security, performance, and other characteristics. NIST selected 26 algorithms to advance to the second round for more analysis. This report describes the evaluation and selection process, based on public feedback and internal review, of the second-round candidates. The report summarizes the 26 second-round candidate algorithms and identifies those selected to move forward to the third round of the competition. The third-round finalist public-key encryption and key-establishment algorithms are Classic McEliece, CRYSTALS-KYBER, NTRU, and SABER. The third-round finalists for digital signatures are CRYSTALS-DILITHIUM, FALCON, and Rainbow. These finalists will be considered for standardization at the end of the third round. In addition, eight alternate candidate algorithms will also advance to the third round: BIKE, FrodoKEM, HQC, NTRU Prime, SIKE, GeMSS, Picnic, and SPHINCS+. These additional candidates are still being considered for standardization, although this is unlikely to occur at the end of the third round. NIST hopes that the announcement of these finalists and additional candidates will serve to focus the cryptographic community\’s attention during the next round.

}, doi = {https://doi.org/10.6028/NIST.IR.8309}, author = {Gorjan Alagic and Jacob Alperin-Sheriff and Daniel Apon and David Cooper and Quynh Dang and John Kelsey and Yi-Kai Liu and Carl Miller and Dustin Moody and Rene Peralta and Ray Perlner and Angela Robinson and Daniel Smith-Tone} } @article {2722, title = {Sublinear classical and quantum algorithms for general matrix games}, journal = {To appear in the Thirty-Fifth AAAI Conference on Artificial Intelligence (AAAI 2021)}, year = {2020}, month = {12/11/2020}, abstract = {

We investigate sublinear classical and quantum algorithms for matrix games, a fundamental problem in optimization and machine learning, with provable guarantees. Given a matrix A\∈Rn\×d, sublinear algorithms for the matrix game minx\∈Xmaxy\∈Yy⊤Ax were previously known only for two special cases: (1) Y being the l1-norm unit ball, and (2) X being either the l1- or the l2-norm unit ball. We give a sublinear classical algorithm that can interpolate smoothly between these two cases: for any fixed q\∈(1,2], we solve the matrix game where X is a lq-norm unit ball within additive error ε in time O~((n+d)/ε2). We also provide a corresponding sublinear quantum algorithm that solves the same task in time O~((n\−\−\√+d\−\−\√)poly(1/ε)) with a quadratic improvement in both n and d. Both our classical and quantum algorithms are optimal in the dimension parameters n and d up to poly-logarithmic factors. Finally, we propose sublinear classical and quantum algorithms for the approximate Carath{\'e}odory problem and the lq-margin support vector machines as applications.

}, url = {https://arxiv.org/abs/2012.06519}, author = {Tongyang Li and Chunhao Wang and Shouvanik Chakrabarti and Xiaodi Wu} } @conference {2599, title = {Symmetries, graph properties, and quantum speedups}, booktitle = {Proceedings of the 61st IEEE Symposium on Foundations of Computer Science (FOCS 2020), pp. 649{\textendash}660 (2020)}, year = {2020}, month = {6/23/2020}, abstract = {

Aaronson and Ambainis (2009) and Chailloux (2018) showed that fully symmetric (partial) functions do not admit exponential quantum query speedups. This raises a natural question: how symmetric must a function be before it cannot exhibit a large quantum speedup?
In this work, we prove that hypergraph symmetries in the adjacency matrix model allow at most a polynomial separation between randomized and quantum query complexities. We also show that, remarkably, permutation groups constructed out of these symmetries are essentially the only permutation groups that prevent super-polynomial quantum speedups. We prove this by fully characterizing the primitive permutation groups that allow super-polynomial quantum speedups.
In contrast, in the adjacency list model for bounded-degree graphs (where graph symmetry is manifested differently), we exhibit a property testing problem that shows an exponential quantum speedup. These results resolve open questions posed by Ambainis, Childs, and Liu (2010) and Montanaro and de Wolf (2013).

}, doi = {https://doi.org/10.1109/FOCS46700.2020.00066}, url = {https://arxiv.org/abs/2006.12760}, author = {Shalev Ben-David and Andrew M. Childs and Andras Gilyen and William Kretschmer and Supartha Podder and Daochen Wang} } @article {2402, title = {Time-dependent Hamiltonian simulation with L1-norm scaling}, journal = {Quantum}, volume = {4}, year = {2020}, month = {4/20/2020}, abstract = {

The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation algorithms that exploit this intuition. For the case of sparse Hamiltonian simulation, the gate complexity scales with the L1 norm \∫t0dτ||H(τ)||max, whereas the best previous results scale with tmaxτ\∈[0,t]||H(τ)||max. We also show analogous results for Hamiltonians that are linear combinations of unitaries. Our approaches thus provide an improvement over previous simulation algorithms that can be substantial when the Hamiltonian varies significantly. We introduce two new techniques: a classical sampler of time-dependent Hamiltonians and a rescaling principle for the Schr{\"o}dinger equation. The rescaled Dyson-series algorithm is nearly optimal with respect to all parameters of interest, whereas the sampling-based approach is easier to realize for near-term simulation. By leveraging the L1-norm information, we obtain polynomial speedups for semi-classical simulations of scattering processes in quantum chemistry.

}, doi = {https://doi.org/10.22331/q-2020-04-20-254}, url = {https://arxiv.org/abs/1906.07115}, author = {Dominic W. Berry and Andrew M. Childs and Yuan Su and Xin Wang and Nathan Wiebe} } @article {2578, title = {Universal one-dimensional discrete-time quantum walks and their implementation on near term quantum hardware}, year = {2020}, month = {1/30/2020}, abstract = {

Quantum walks are a promising framework for developing quantum algorithms and quantum simulations. Quantum walks represent an important test case for the application of quantum computers. Here we present different forms of discrete-time quantum walks and show their equivalence for physical realizations. Using an appropriate digital mapping of the position space on which a walker evolves onto the multi-qubit states in a quantum processor, we present different configurations of quantum circuits for the implementation of discrete-time quantum walks in one-dimensional position space. With example circuits for a five qubit machine we address scalability to higher dimensions and larger quantum processors.

}, url = {https://arxiv.org/abs/2001.11197}, author = {Shivani Singh and Cinthia H. Alderete and Radhakrishnan Balu and Christopher Monroe and Norbert M. Linke and C. M. Chandrashekar} } @article {2374, title = {Chaos in a quantum rotor model}, year = {2019}, month = {01/29/2019}, abstract = {

We study scrambling in a model consisting of a number N of M-component quantum rotors coupled by random infinite-range interactions. This model is known to have both a paramagnetic phase and a spin glass phase separated by second order phase transition. We calculate in perturbation theory the squared commutator of rotor fields at different sites in the paramagnetic phase, to leading non-trivial order at large N and large M. This quantity diagnoses the onset of quantum chaos in this system, and we show that the squared commutator grows exponentially with time, with a Lyapunov exponent proportional to 1M. At high temperature, the Lyapunov exponent limits to a value set by the microscopic couplings, while at low temperature, the exponent exhibits a T4 dependence on temperature T.\ 

}, url = {https://arxiv.org/abs/1901.10446}, author = {Gong Cheng and Brian Swingle} } @article {2361, title = {Circuit Transformations for Quantum Architectures}, journal = {Proceedings of TQC 2019, LIPIcs}, volume = {135 }, year = {2019}, month = {02/25/2019}, chapter = {1-3:24}, abstract = {

Quantum computer architectures impose restrictions on qubit interactions. We propose efficient circuit transformations that modify a given quantum circuit to fit an architecture, allowing for any initial and final mapping of circuit qubits to architecture qubits. To achieve this, we first consider the qubit movement subproblem and use the routing via matchings framework to prove tighter bounds on parallel routing. In practice, we only need to perform partial permutations, so we generalize routing via matchings to that setting. We give new routing procedures for common architecture graphs and for the generalized hierarchical product of graphs, which produces subgraphs of the Cartesian product. Secondly, for serial routing, we consider the token swapping framework and extend a 4-approximation algorithm for general graphs to support partial permutations. We apply these routing procedures to give several circuit transformations, using various heuristic qubit placement subroutines. We implement these transformations in software and compare their performance for large quantum circuits on grid and modular architectures, identifying strategies that work well in practice.

}, doi = {https://doi.org/10.4230/LIPIcs.TQC.2019.3}, url = {https://arxiv.org/abs/1902.09102}, author = {Andrew M. Childs and Eddie Schoute and Cem M. Unsal} } @article {2533, title = {Development of Quantum InterConnects for Next-Generation Information Technologies}, year = {2019}, month = {12/13/2019}, abstract = {

Just as classical information technology rests on a foundation built of interconnected information-processing systems, quantum information technology (QIT) must do the same. A critical component of such systems is the interconnect, a device or process that allows transfer of information between disparate physical media, for example, semiconductor electronics, individual atoms, light pulses in optical fiber, or microwave fields. While interconnects have been well engineered for decades in the realm of classical information technology, quantum interconnects (QuICs) present special challenges, as they must allow the transfer of fragile quantum states between different physical parts or degrees of freedom of the system. The diversity of QIT platforms (superconducting, atomic, solid-state color center, optical, etc.) that will form a quantum internet poses additional challenges. As quantum systems scale to larger size, the quantum interconnect bottleneck is imminent, and is emerging as a grand challenge for QIT. For these reasons, it is the position of the community represented by participants of the NSF workshop on Quantum Interconnects that accelerating QuIC research is crucial for sustained development of a national quantum science and technology program. Given the diversity of QIT platforms, materials used, applications, and infrastructure required, a convergent research program including partnership between academia, industry and national laboratories is required. This document is a summary from a U.S. National Science Foundation supported workshop held on 31 October - 1 November 2019 in Alexandria, VA. Attendees were charged to identify the scientific and community needs, opportunities, and significant challenges for quantum interconnects over the next 2-5 years.\ 

}, url = {https://arxiv.org/abs/1912.06642}, author = {David Awschalom and Karl K. Berggren and Hannes Bernien and Sunil Bhave and Lincoln D. Carr and Paul Davids and Sophia E. Economou and Dirk Englund and Andrei Faraon and Marty Fejer and Saikat Guha and Martin V. Gustafsson and Evelyn Hu and Liang Jiang and Jungsang Kim and Boris Korzh and Prem Kumar and Paul G. Kwiat and Marko Lon{\v c}ar and Mikhail D. Lukin and David A. B. Miller and Christopher Monroe and Sae Woo Nam and Prineha Narang and Jason S. Orcutt} } @article {2174, title = {Faster quantum simulation by randomization}, journal = {Quantum }, volume = {3}, year = {2019}, month = {08/28/2019}, abstract = {

Product formulas can be used to simulate Hamiltonian dynamics on a quantum computer by approximating the exponential of a sum of operators by a product of exponentials of the individual summands. This approach is both straightforward and surprisingly efficient. We show that by simply randomizing how the summands are ordered, one can prove stronger bounds on the quality of approximation and thereby give more efficient simulations. Indeed, we show that these bounds can be asymptotically better than previous bounds that exploit commutation between the summands, despite using much less information about the structure of the Hamiltonian. Numerical evidence suggests that our randomized algorithm may be advantageous even for near-term quantum simulation.

}, doi = {https://doi.org/10.22331/q-2019-09-02-182}, url = {https://arxiv.org/abs/1805.08385}, author = {Andrew M. Childs and Aaron Ostrander and Yuan Su} } @article {2369, title = {Ground-state energy estimation of the water molecule on a trapped ion quantum computer}, year = {2019}, month = {03/07/2019}, abstract = {

Quantum computing leverages the quantum resources of superposition and entanglement to efficiently solve computational problems considered intractable for classical computers. Examples include calculating molecular and nuclear structure, simulating strongly-interacting electron systems, and modeling aspects of material function. While substantial theoretical advances have been made in mapping these problems to quantum algorithms, there remains a large gap between the resource requirements for solving such problems and the capabilities of currently available quantum hardware. Bridging this gap will require a co-design approach, where the expression of algorithms is developed in conjunction with the hardware itself to optimize execution. Here, we describe a scalable co-design framework for solving chemistry problems on a trapped ion quantum computer, and apply it to compute the ground-state energy of the water molecule. The robust operation of the trapped ion quantum computer yields energy estimates with errors approaching the chemical accuracy, which is the target threshold necessary for predicting the rates of chemical reaction dynamics.

}, url = {https://arxiv.org/abs/1902.10171}, author = {Yunseong Nam and Jwo-Sy Chen and Neal C. Pisenti and Kenneth Wright and Conor Delaney and Dmitri Maslov and Kenneth R. Brown and Stewart Allen and Jason M. Amini and Joel Apisdorf and Kristin M. Beck and Aleksey Blinov and Vandiver Chaplin and Mika Chmielewski and Coleman Collins and Shantanu Debnath and Andrew M. Ducore and Kai M. Hudek and Matthew Keesan and Sarah M. Kreikemeier and Jonathan Mizrahi and Phil Solomon and Mike Williams and Jaime David Wong-Campos and Christopher Monroe and Jungsang Kim} } @article {2400, title = {How Low Can Vacuum Energy Go When Your Fields Are Finite-Dimensional?}, year = {2019}, month = {05/11/2019}, abstract = {

According to the holographic bound, there is only a finite density of degrees of freedom in space when gravity is taken into account. Conventional quantum field theory does not conform to this bound, since in this framework, infinitely many degrees of freedom may be localized to any given region of space. In this essay, we explore the viewpoint that quantum field theory may emerge from an underlying theory that is locally finite-dimensional, and we construct a locally finite-dimensional version of a Klein-Gordon scalar field using generalized Clifford algebras. Demanding that the finite-dimensional field operators obey a suitable version of the canonical commutation relations makes this construction essentially unique. We then find that enforcing local finite dimensionality in a holographically consistent way leads to a huge suppression of the quantum contribution to vacuum energy, to the point that the theoretical prediction becomes plausibly consistent with observations.

}, url = {https://arxiv.org/abs/1905.11199}, author = {ChunJun Cao and Aidan Chatwin-Davies and Ashmeet Singh} } @article {2195, title = {Locality and digital quantum simulation of power-law interactions}, journal = {Phys. Rev. X 9, 031006}, volume = {9}, year = {2019}, month = {07/10/2019}, abstract = {

The propagation of information in non-relativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound for systems with interactions that decay with distance r as a power law, 1/rα. The bound implies an effective light cone tighter than all previous bounds. Our approach is based on a technique for approximating the time evolution of a system, which was first introduced as part of a quantum simulation algorithm by Haah et al. [arXiv:1801.03922]. To bound the error of the approximation, we use a known Lieb-Robinson bound that is weaker than the bound we establish. This result brings the analysis full circle, suggesting a deep connection between Lieb-Robinson bounds and digital quantum simulation. In addition to the new Lieb-Robinson bound, our analysis also gives an error bound for the Haah et al. quantum simulation algorithm when used to simulate power-law decaying interactions. In particular, we show that the gate count of the algorithm scales with the system size better than existing algorithms when α\>3D (where D is the number of dimensions).

}, doi = {https://doi.org/10.1103/PhysRevX.9.031006}, url = {https://arxiv.org/abs/1808.05225}, author = {Minh C. Tran and Andrew Y. Guo and Yuan Su and James R. Garrison and Zachary Eldredge and Michael Foss-Feig and Andrew M. Childs and Alexey V. Gorshkov} } @article {2332, title = {Nearly optimal lattice simulation by product formulas}, journal = {Phys. Rev. Lett. }, volume = {123}, year = {2019}, month = {12/17/2019}, abstract = {

Product formulas provide a straightforward yet surprisingly efficient approach to quantum simulation. We show that this algorithm can simulate an n-qubit Hamiltonian with nearest-neighbor interactions evolving for time t using only (nt)1+o(1) gates. While it is reasonable to expect this complexity---in particular, this was claimed without rigorous justification by Jordan, Lee, and Preskill---we are not aware of a straightforward proof. Our approach is based on an analysis of the local error structure of product formulas, as introduced by Descombes and Thalhammer and significantly simplified here. We prove error bounds for canonical product formulas, which include well-known constructions such as the Lie-Trotter-Suzuki formulas. We also develop a local error representation for time-dependent Hamiltonian simulation, and we discuss generalizations to periodic boundary conditions, constant-range interactions, and higher dimensions. Combined with a previous lower bound, our result implies that product formulas can simulate lattice Hamiltonians with nearly optimal gate complexity.

}, doi = {https://doi.org/10.1103/PhysRevLett.123.050503}, url = {https://arxiv.org/abs/1901.00564}, author = {Andrew M. Childs and Yuan Su} } @article {2520, title = {Observation of Domain Wall Confinement and Dynamics in a Quantum Simulator}, year = {2019}, month = {12/23/2019}, abstract = {

Confinement is a ubiquitous mechanism in nature, whereby particles feel an attractive force that increases without bound as they separate. A prominent example is color confinement in particle physics, in which baryons and mesons are produced by quark confinement. Analogously, confinement can also occur in low-energy quantum many-body systems when elementary excitations are confined into bound quasiparticles. Here, we report the first observation of magnetic domain wall confinement in interacting spin chains with a trapped-ion quantum simulator. By measuring how correlations spread, we show that confinement can dramatically suppress information propagation and thermalization in such many-body systems. We are able to quantitatively determine the excitation energy of domain wall bound states from non-equilibrium quench dynamics. Furthermore, we study the number of domain wall excitations created for different quench parameters, in a regime that is difficult to model with classical computers. This work demonstrates the capability of quantum simulators for investigating exotic high-energy physics phenomena, such as quark collision and string breaking

}, url = {https://arxiv.org/abs/1912.11117}, author = {W. L. Tan and P. Becker and F. Liu and G. Pagano and K. S. Collins and A. De and L. Feng and H. B. Kaplan and A. Kyprianidis and R. Lundgren and W. Morong and S. Whitsitt and Alexey V. Gorshkov and C. Monroe} } @article {2362, title = {Opportunities for Nuclear Physics \& Quantum Information Science}, year = {2019}, month = {03/13/2019}, abstract = {

his whitepaper is an outcome of the workshop Intersections between Nuclear Physics and Quantum Information held at Argonne National Laboratory on 28-30 March 2018 [www.phy.anl.gov/npqi2018/]. The workshop brought together 116 national and international experts in nuclear physics and quantum information science to explore opportunities for the two fields to collaborate on topics of interest to the U.S. Department of Energy (DOE) Office of Science, Office of Nuclear Physics, and more broadly to U.S. society and industry. The workshop consisted of 22 invited and 10 contributed talks, as well as three panel discussion sessions. Topics discussed included quantum computation, quantum simulation, quantum sensing, nuclear physics detectors, nuclear many-body problem, entanglement at collider energies, and lattice gauge theories.

}, url = {https://arxiv.org/abs/1903.05453}, author = {I. C. Clo{\"e}t and Matthew R. Dietrich and John Arrington and Alexei Bazavov and Michael Bishof and Adam Freese and Alexey V. Gorshkov and Anna Grassellino and Kawtar Hafidi and Zubin Jacob and Michael McGuigan and Yannick Meurice and Zein-Eddine Meziani and Peter Mueller and Christine Muschik and James Osborn and Matthew Otten and Peter Petreczky and Tomas Polakovic and Alan Poon and Raphael Pooser and Alessandro Roggero and Mark Saffman and Brent VanDevender and Jiehang Zhang and Erez Zohar} } @article {2390, title = {Photon pair condensation by engineered dissipation}, journal = {Phys. Rev. Lett. }, volume = {123}, year = {2019}, month = {04/02/2019}, abstract = {

Dissipation can usually induce detrimental decoherence in a quantum system. However, engineered dissipation can be used to prepare and stabilize coherent quantum many-body states. Here, we show that by engineering dissipators containing photon pair operators, one can stabilize an exotic dark state, which is a condensate of photon pairs with a phase-nematic order. In this system, the usual superfluid order parameter, i.e. single-photon correlation, is absent, while the photon pair correlation exhibits long-range order. Although the dark state is not unique due to multiple parity sectors, we devise an additional type of dissipators to stabilize the dark state in a particular parity sector via a diffusive annihilation process which obeys Glauber dynamics in an Ising model. Furthermore, we propose an implementation of these photon-pair dissipators in circuit-QED architecture.\ 

}, doi = {10.1103/PhysRevLett.123.063602}, url = {https://arxiv.org/abs/1904.00016}, author = {Ze-Pei Cian and Guanyu Zhu and Su-Kuan Chu and Alireza Seif and Wade DeGottardi and Liang Jiang and Mohammad Hafezi} } @article {2529, title = {Programmable Quantum Simulations of Spin Systems with Trapped Ions}, year = {2019}, month = {12/17/2019}, abstract = {

Laser-cooled and trapped atomic ions form an ideal standard for the simulation of interacting quantum spin models. Effective spins are represented by appropriate internal energy levels within each ion, and the spins can be measured with near-perfect efficiency using state-dependent fluorescence techniques. By applying optical fields that exert optical dipole forces on the ions, their Coulomb interaction can be modulated in ways that give rise to long-range and tunable spin-spin interactions that can be reconfigured by shaping the spectrum and pattern of the laser fields. Here we review the theoretical mapping of atomic ions to interacting spin systems, the experimental preparation of complex equilibrium states, and the study of dynamical processes of this many-body interacting quantum system. The use of such quantum simulators for studying spin models may inform our understanding of exotic quantum materials and shed light on interacting quantum systems that cannot be modeled with conventional computers.\ 

}, url = {https://arxiv.org/abs/1912.07845}, author = {C. Monroe and W. C. Campbell and L. -M. Duan and Z. -X. Gong and Alexey V. Gorshkov and P. Hess and R. Islam and K. Kim and G. Pagano and P. Richerme and C. Senko and N. Y. Yao} } @article {2131, title = {Quantum Algorithm for Simulating the Wave Equation}, journal = {Phys. Rev. A }, volume = {99 }, year = {2019}, month = {03/24/2019}, abstract = {

We present a quantum algorithm for simulating the wave equation under Dirichlet and Neumann boundary conditions. The algorithm uses Hamiltonian simulation and quantum linear system algorithms as subroutines. It relies on factorizations of discretized Laplacian operators to allow for improved scaling in truncation errors and improved scaling for state preparation relative to general purpose linear differential equation algorithms. We also consider using Hamiltonian simulation for Klein-Gordon equations and Maxwell\&$\#$39;s equations.

}, doi = {https://doi.org/10.1103/PhysRevA.99.012323}, url = {https://arxiv.org/abs/1711.05394}, author = {Pedro C.S. Costa and Stephen P. Jordan and Aaron Ostrander} } @article {2410, title = {Quantum Approximate Optimization with a Trapped-Ion Quantum Simulator}, year = {2019}, month = {06/06/2019}, abstract = {

Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly solving exponentially hard problems, such as optimization and satisfiability. Here we report the first implementation of a shallow-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator to estimate the ground state energy of the transverse field Ising model with tunable long-range interactions. First, we exhaustively search the variational control parameters to approximate the ground state energy with up to 40 trapped-ion qubits. We then interface the quantum simulator with a classical algorithm to more efficiently find the optimal set of parameters that minimizes the resulting energy of the system. We finally sample from the full probability distribution of the QAOA output with single-shot and efficient measurements of every qubit.\ 

}, url = {https://arxiv.org/abs/1906.02700}, author = {G. Pagano and A. Bapat and P. Becker and K. S. Collins and A. De and P. W. Hess and H. B. Kaplan and A. Kyprianidis and W. L. Tan and Christopher L. Baldwin and L. T. Brady and A. Deshpande and F. Liu and S. Jordan and Alexey V. Gorshkov and C. Monroe} } @article {2530, title = {Quantum Computer Systems for Scientific Discovery}, year = {2019}, month = {12/16/2019}, abstract = {

The great promise of quantum computers comes with the dual challenges of building them and finding their useful applications. We argue that these two challenges should be considered together, by co-designing full stack quantum computer systems along with their applications in order to hasten their development and potential for scientific discovery. In this context, we identify scientific and community needs, opportunities, and significant challenges for the development of quantum computers for science over the next 2-10 years. This document is written by a community of university, national laboratory, and industrial researchers in the field of Quantum Information Science and Technology, and is based on a summary from a U.S. National Science Foundation workshop on Quantum Computing held on October 21-22, 2019 in Alexandria, VA.

}, url = {https://arxiv.org/abs/1912.07577}, author = {Yuri Alexeev and Dave Bacon and Kenneth R. Brown and Robert Calderbank and Lincoln D. Carr and Frederic T. Chong and Brian DeMarco and Dirk Englund and Edward Farhi and Bill Fefferman and Alexey V. Gorshkov and Andrew Houck and Jungsang Kim and Shelby Kimmel and Michael Lange and Seth Lloyd and Mikhail D. Lukin and Dmitri Maslov and Peter Maunz and Christopher Monroe and John Preskill and Martin Roetteler and Martin Savage and Jeff Thompson and Umesh Vazirani} } @article {2532, title = {Quantum Simulators: Architectures and Opportunities}, year = {2019}, month = {12/14/2019}, abstract = {

Quantum simulators are a promising technology on the spectrum of quantum devices from specialized quantum experiments to universal quantum computers. These quantum devices utilize entanglement and many-particle behaviors to explore and solve hard scientific, engineering, and computational problems. Rapid development over the last two decades has produced more than 300 quantum simulators in operation worldwide using a wide variety of experimental platforms. Recent advances in several physical architectures promise a golden age of quantum simulators ranging from highly optimized special purpose simulators to flexible programmable devices. These developments have enabled a convergence of ideas drawn from fundamental physics, computer science, and device engineering. They have strong potential to address problems of societal importance, ranging from understanding vital chemical processes, to enabling the design of new materials with enhanced performance, to solving complex computational problems. It is the position of the community, as represented by participants of the NSF workshop on \"Programmable Quantum Simulators,\" that investment in a national quantum simulator program is a high priority in order to accelerate the progress in this field and to result in the first practical applications of quantum machines. Such a program should address two areas of emphasis: (1) support for creating quantum simulator prototypes usable by the broader scientific community, complementary to the present universal quantum computer effort in industry; and (2) support for fundamental research carried out by a blend of multi-investigator, multi-disciplinary collaborations with resources for quantum simulator software, hardware, and education.\ 

}, url = {https://arxiv.org/abs/1912.06938}, author = {Ehud Altman and Kenneth R. Brown and Giuseppe Carleo and Lincoln D. Carr and Eugene Demler and Cheng Chin and Brian DeMarco and Sophia E. Economou and Mark A. Eriksson and Kai-Mei C. Fu and Markus Greiner and Kaden R. A. Hazzard and Randall G. Hulet and Alicia J. Koll{\'a}r and Benjamin L. Lev and Mikhail D. Lukin and Ruichao Ma and Xiao Mi and Shashank Misra and Christopher Monroe and Kater Murch and Zaira Nazario and Kang-Kuen Ni and Andrew C. Potter and Pedram Roushan} } @article {2500, title = {Quantum Wasserstein Generative Adversarial Networks}, journal = {Advances in Neural Information Processing Systems (NIPS)}, volume = {32}, year = {2019}, month = {2019/10/31}, abstract = {

The study of quantum generative models is well-motivated, not only because of its importance in quantum machine learning and quantum chemistry but also because of the perspective of its implementation on near-term quantum machines. Inspired by previous studies on the adversarial training of classical and quantum generative models, we propose the first design of quantum Wasserstein Generative Adversarial Networks (WGANs), which has been shown to improve the robustness and the scalability of the adversarial training of quantum generative models even on noisy quantum hardware. Specifically, we propose a definition of the Wasserstein semimetric between quantum data, which inherits a few key theoretical merits of its classical counterpart. We also demonstrate how to turn the quantum Wasserstein semimetric into a concrete design of quantum WGANs that can be efficiently implemented on quantum machines. Our numerical study, via classical simulation of quantum systems, shows the more robust and scalable numerical performance of our quantum WGANs over other quantum GAN proposals. As a surprising application, our quantum WGAN has been used to generate a 3-qubit quantum circuit of ~50 gates that well approximates a 3-qubit 1-d Hamiltonian simulation circuit that requires over 10k gates using standard techniques.

}, doi = {https://papers.nips.cc/paper/8903-quantum-wasserstein-generative-adversarial-networks.pdf}, url = {https://arxiv.org/abs/1911.00111}, author = {Shouvanik Chakrabarti and Yiming Huang and Tongyang Li and Soheil Feizi and Xiaodi Wu} } @article {2338, title = {Quantum-inspired classical sublinear-time algorithm for solving low-rank semidefinite programming via sampling approaches}, year = {2019}, abstract = {

Semidefinite programming (SDP) is a central topic in mathematical optimization with extensive studies on its efficient solvers. Recently, quantum algorithms with superpolynomial speedups for solving SDPs have been proposed assuming access to its constraint matrices in quantum superposition. Mutually inspired by both classical and quantum SDP solvers, in this paper we present a sublinear classical algorithm for solving low-rank SDPs which is asymptotically as good as existing quantum algorithms. Specifically, given an SDP with m constraint matrices, each of dimension n and rank poly(logn), our algorithm gives a succinct description and any entry of the solution matrix in time O(m\⋅poly(logn,1/ε)) given access to a sample-based low-overhead data structure of the constraint matrices, where ε is the precision of the solution. In addition, we apply our algorithm to a quantum state learning task as an application. Technically, our approach aligns with both the SDP solvers based on the matrix multiplicative weight (MMW) framework and the recent studies of quantum-inspired machine learning algorithms. The cost of solving SDPs by MMW mainly comes from the exponentiation of Hermitian matrices, and we propose two new technical ingredients (compared to previous sample-based algorithms) for this task that may be of independent interest: . Weighted sampling: assuming sampling access to each individual constraint matrix A1,\…,Aτ, we propose a procedure that gives a good approximation of A=A1+...+Aτ. . Symmetric approximation: we propose a sampling procedure that gives low-rank spectral decomposition of a Hermitian matrix A. This improves upon previous sampling procedures that only give low-rank singular value decompositions, losing the signs of eigenvalues.

}, url = {https://arxiv.org/abs/1901.03254}, author = {Nai-Hui Chia and Tongyang Li and Han-Hsuan Lin and Chunhao Wang} } @article {2217, title = {Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator}, journal = {Phys. Rev. Lett}, volume = {122}, year = {2019}, month = {03/27/2019}, abstract = {

The multi-scale entanglement renormalization ansatz (MERA) postulates the existence of quantum circuits that renormalize entanglement in real space at different length scales. Chern insulators, however, cannot have scale-invariant discrete MERA circuits with finite bond dimension. In this Letter, we show that the continuous MERA (cMERA), a modified version of MERA adapted for field theories, possesses a fixed point wavefunction with nonzero Chern number. Additionally, it is well known that reversed MERA circuits can be used to prepare quantum states efficiently in time that scales logarithmically with the size of the system. However, state preparation via MERA typically requires the advent of a full-fledged universal quantum computer. In this Letter, we demonstrate that our cMERA circuit can potentially be realized in existing analog quantum computers, i.e., an ultracold atomic Fermi gas in an optical lattice with light-induced spin-orbit coupling.\ 

}, doi = {https://doi.org/10.1103/PhysRevLett.122.120502}, url = {https://arxiv.org/abs/1807.11486}, author = {Su-Kuan Chu and Guanyu Zhu and James R. Garrison and Zachary Eldredge and Ana Vald{\'e}s Curiel and Przemyslaw Bienias and I. B. Spielman and Alexey V. Gorshkov} } @article {2425, title = {The Speed of Quantum Information Spreading in Chaotic Systems}, year = {2019}, month = {08/19/2019}, abstract = {

We present a general theory of quantum information propagation in chaotic quantum many-body systems. The generic expectation in such systems is that quantum information does not propagate in localized form; instead, it tends to spread out and scramble into a form that is inaccessible to local measurements. To characterize this spreading, we define an information speed via a quench-type experiment and derive a general formula for it as a function of the entanglement density of the initial state. As the entanglement density varies from zero to one, the information speed varies from the entanglement speed to the butterfly speed. We verify that the formula holds both for a quantum chaotic spin chain and in field theories with an AdS/CFT gravity dual. For the second case, we study in detail the dynamics of entanglement in two-sided Vaidya-AdS-Reissner-Nordstrom black branes. We also show that, with an appropriate decoding process, quantum information can be construed as moving at the information speed, and, in the case of AdS/CFT, we show that a locally detectable signal propagates at the information speed in a spatially local variant of the traversable wormhole setup.

}, url = {https://arxiv.org/abs/1908.06993}, author = {Josiah Couch and Stefan Eccles and Phuc Nguyen and Brian Swingle and Shenglong Xu} } @article {2367, title = {Statistical Privacy in Distributed Average Consensus on Bounded Real Inputs}, year = {2019}, month = {03/20/2019}, abstract = {

This paper proposes a privacy protocol for distributed average consensus algorithms on bounded real-valued inputs that guarantees statistical privacy of honest agents\&$\#$39; inputs against colluding (passive adversarial) agents, if the set of colluding agents is not a vertex cut in the underlying communication network. This implies that privacy of agents\&$\#$39; inputs is preserved against t number of arbitrary colluding agents if the connectivity of the communication network is at least (t+1). A similar privacy protocol has been proposed for the case of bounded integral inputs in our previous paper~\cite{gupta2018information}. However, many applications of distributed consensus concerning distributed control or state estimation deal with real-valued inputs. Thus, in this paper we propose an extension of the privacy protocol in~\cite{gupta2018information}, for bounded real-valued agents\&$\#$39; inputs, where bounds are known apriori to all the agents.\ 

}, url = {https://arxiv.org/abs/1903.09315}, author = {Nirupam Gupta and Jonathan Katz and Nikhil Chopra} } @article {2624, title = {Status Report on the First Round of the NIST Post-Quantum Cryptography Standardization Process}, journal = {School: National Institute for Standards and Technology }, year = {2019}, type = {techreport}, abstract = {

The National Institute of Standards and Technology is in the process of selecting one or more
public-key cryptographic algorithms through a public competition-like process. The new publickey cryptography standards will specify one or more additional digital signature, public-key
encryption, and key-establishment algorithms to augment FIPS 186-4, Digital Signature Standard
(DSS), as well as special publications SP 800-56A Revision 2, Recommendation for Pair-Wise
Key Establishment Schemes Using Discrete Logarithm Cryptography, and SP 800-56B,
Recommendation for Pair-Wise Key-Establishment Schemes Using Integer Factorization. It is
intended that these algorithms will be capable of protecting sensitive information well into the
foreseeable future, including after the advent of quantum computers.
In November 2017, 82 candidate algorithms were submitted to NIST for consideration. Among
these, 69 met both the minimum acceptance criteria and our submission requirements, and were
accepted as First-Round Candidates on Dec. 20, 2017, marking the beginning of the First Round
of the NIST Post-Quantum Cryptography Standardization Process. This report describes the
evaluation criteria and selection process, based on public feedback and internal review of the
first-round candidates, and summarizes the 26 candidate algorithms announced on January 30,
2019 for moving forward to the second round of the competition. The 17 Second-Round
Candidate public-key encryption and key-establishment algorithms are BIKE, Classic McEliece,
CRYSTALS-KYBER, FrodoKEM, HQC, LAC, LEDAcrypt (merger of LEDAkem/LEDApkc),
NewHope, NTRU (merger of NTRUEncrypt/NTRU-HRSS-KEM), NTRU Prime, NTS-KEM,
ROLLO (merger of LAKE/LOCKER/Ouroboros-R), Round5 (merger of Hila5/Round2), RQC,
SABER, SIKE, and Three Bears. The 9 Second-Round Candidates for digital signatures are
CRYSTALS-DILITHIUM, FALCON, GeMSS, LUOV, MQDSS, Picnic, qTESLA, Rainbow,
and SPHINCS+.

}, url = {https://nvlpubs.nist.gov/nistpubs/ir/2019/NIST.IR.8240.pdf}, author = {Gorjan Alagic and J. Alperin-Sheriff and D. Apon and D. Cooper and Q. Dang and Carl Miller and D. Moody and R. Peralta and R. Perlner and A. Robinson and D. Smith-Tone and Yi-Kai Liu} } @article {2376, title = {Sublinear quantum algorithms for training linear and kernel-based classifiers}, journal = {Proceedings of the 36th International Conference on Machine Learning (ICML 2019) PMLR }, volume = {97}, year = {2019}, month = {04/03/2019}, pages = {3815-3824}, abstract = {

We investigate quantum algorithms for classification, a fundamental problem in machine learning, with provable guarantees. Given n d-dimensional data points, the state-of-the-art (and optimal) classical algorithm for training classifiers with constant margin runs in O~(n+d) time. We design sublinear quantum algorithms for the same task running in O~(n\−\−\√+d\−\−\√) time, a quadratic improvement in both n and d. Moreover, our algorithms use the standard quantization of the classical input and generate the same classical output, suggesting minimal overheads when used as subroutines for end-to-end applications. We also demonstrate a tight lower bound (up to poly-log factors) and discuss the possibility of implementation on near-term quantum machines. As a side result, we also give sublinear quantum algorithms for approximating the equilibria of n-dimensional matrix zero-sum games with optimal complexity Θ~(n\−\−\√).\ 

}, url = {https://arxiv.org/abs/1904.02276}, author = {Tongyang Li and Shouvanik Chakrabarti and Xiaodi Wu} } @article {2401, title = {Towards Bulk Metric Reconstruction from Extremal Area Variations}, year = {2019}, month = {04/09/19}, abstract = {

The Ryu-Takayanagi and Hubeny-Rangamani-Takayanagi formulae suggest that bulk geometry emerges from the entanglement structure of the boundary theory. Using these formulae, we build on a result of Alexakis, Balehowsky, and Nachman to show that in four bulk dimensions, the entanglement entropies of boundary regions of disk topology uniquely fix the bulk metric in any region foliated by the corresponding HRT surfaces. More generally, for a bulk of any dimension , knowledge of the (variations of the) areas of two-dimensional boundary-anchored extremal surfaces of disk topology uniquely fixes the bulk metric wherever these surfaces reach. This result is covariant and not reliant on any symmetry assumptions; its applicability thus includes regions of strong dynamical gravity such as the early-time interior of black holes formed from collapse. While we only show uniqueness of the metric, the approach we present provides a clear path towards an\textit {explicit} spacetime metric reconstruction.

}, url = {https://arxiv.org/abs/1904.04834}, author = {Ning Bao and ChunJun Cao and Sebastian Fischetti and Cynthia Keeler} } @article {2067, title = {Automated optimization of large quantum circuits with continuous parameters}, journal = {npj:Quantum Information}, volume = {4}, year = {2018}, month = {2017/10/19}, abstract = {

We develop and implement automated methods for optimizing quantum circuits of the size and type expected in quantum computations that outperform classical computers. We show how to handle continuous gate parameters and report a collection of fast algorithms capable of optimizing large-scale quantum circuits. For the suite of benchmarks considered, we obtain substantial reductions in gate counts. In particular, we provide better optimization in significantly less time than previous approaches, while making minimal structural changes so as to preserve the basic layout of the underlying quantum algorithms. Our results help bridge the gap between the computations that can be run on existing hardware and those that are expected to outperform classical computers.\ 

}, doi = {https://doi.org/10.1038/s41534-018-0072-4}, url = {https://arxiv.org/abs/1710.07345}, author = {Yunseong Nam and Neil J. Ross and Yuan Su and Andrew M. Childs and Dmitri Maslov} } @article {2298, title = {Black Hole Microstate Cosmology}, year = {2018}, abstract = {

In this note, we explore the possibility that certain high-energy holographic CFT states correspond to black hole microstates with a geometrical behind-the-horizon region, modelled by a portion of a second asymptotic region terminating at an end-of-the-world (ETW) brane. We study the time-dependent physics of this behind-the-horizon region, whose ETW boundary geometry takes the form of a closed FRW spacetime. We show that in many cases, this behind-the-horizon physics can be probed directly by looking at the time dependence of entanglement entropy for sufficiently large spatial CFT subsystems. We study in particular states defined via Euclidean evolution from conformal boundary states and give specific predictions for the behavior of the entanglement entropy in this case. We perform analogous calculations for the SYK model and find qualitative agreement with our expectations. A fascinating possibility is that for certain states, we might have gravity localized to the ETW brane as in the Randall-Sundrum II scenario for cosmology. In this case, the effective description of physics beyond the horizon could be a big bang/big crunch cosmology of the same dimensionality as the CFT. In this case, the d-dimensional CFT describing the black hole microstate would give a precise, microscopic description of the d-dimensional cosmological physics.\ 

}, url = {https://arxiv.org/abs/1810.10601}, author = {Sean Cooper and Moshe Rozali and Brian Swingle and Mark Van Raamsdonk and Christopher Waddell and David Wakeham} } @article {2272, title = {Circuit QED-based measurement of vortex lattice order in a Josephson junction array}, journal = {Phys. Rev. B 98, 060501}, year = {2018}, month = {2018/03/12}, abstract = {

Superconductivity provides a canonical example of a quantum phase of matter. When superconducting islands are connected by Josephson junctions in a lattice, the low temperature state of the system can map to the celebrated XY model and its associated universality classes. This has been used to experimentally implement realizations of Mott insulator and Berezinskii--Kosterlitz--Thouless (BKT) transitions to vortex dynamics analogous to those in type-II superconductors. When an external magnetic field is added, the effective spins of the XY model become frustrated, leading to the formation of topological defects (vortices). Here we observe the many-body dynamics of such an array, including frustration, via its coupling to a superconducting microwave cavity. We take the design of the transmon qubit, but replace the single junction between two antenna pads with the complete array. This allows us to probe the system at 10 mK with minimal self-heating by using weak coherent states at the single (microwave) photon level to probe the resonance frequency of the cavity. We observe signatures of ordered vortex lattice at rational flux fillings of the array.\ 

}, doi = {https://doi.org/10.1103/PhysRevB.98.060501}, url = {https://arxiv.org/abs/1803.04113}, author = {R. Cosmic and Hiroki Ikegami and Zhirong Lin and Kunihiro Inomata and J. M. Taylor and Yasunobu Nakamura} } @article {2282, title = {Experimentally Generated Randomness Certified by the Impossibility of Superluminal Signals}, journal = {Nature}, volume = {556}, year = {2018}, month = {2018/04/11}, pages = {223-226}, abstract = {

From dice to modern complex circuits, there have been many attempts to build increasingly better devices to generate random numbers. Today, randomness is fundamental to security and cryptographic systems, as well as safeguarding privacy. A key challenge with random number generators is that it is hard to ensure that their outputs are unpredictable. For a random number generator based on a physical process, such as a noisy classical system or an elementary quantum measurement, a detailed model describing the underlying physics is required to assert unpredictability. Such a model must make a number of assumptions that may not be valid, thereby compromising the integrity of the device. However, it is possible to exploit the phenomenon of quantum nonlocality with a loophole-free Bell test to build a random number generator that can produce output that is unpredictable to any adversary limited only by general physical principles. With recent technological developments, it is now possible to carry out such a loophole-free Bell test. Here we present certified randomness obtained from a photonic Bell experiment and extract 1024 random bits uniform to within 10\−12. These random bits could not have been predicted within any physical theory that prohibits superluminal signaling and allows one to make independent measurement choices. To certify and quantify the randomness, we describe a new protocol that is optimized for apparatuses characterized by a low per-trial violation of Bell inequalities. We thus enlisted an experimental result that fundamentally challenges the notion of determinism to build a system that can increase trust in random sources. In the future, random number generators based on loophole-free Bell tests may play a role in increasing the security and trust of our cryptographic systems and infrastructure.

}, doi = {https://doi.org/10.1038/s41586-018-0019-0}, url = {https://arxiv.org/abs/1803.06219}, author = {Peter Bierhorst and Emanuel Knill and Scott Glancy and Yanbao Zhang and Alan Mink and Stephen Jordan and Andrea Rommal and Yi-Kai Liu and Bradley Christensen and Sae Woo Nam and Martin J. Stevens and Lynden K. Shalm} } @article {2109, title = {Geometry of the quantum set of correlations}, journal = {Physical Review A}, volume = {97}, year = {2018}, month = {2018/02/07}, pages = {022104}, abstract = {

It is well known that correlations predicted by quantum mechanics cannot be explained by any classical (local-realistic) theory. The relative strength of quantum and classical correlations is usually studied in the context of Bell inequalities, but this tells us little about the geometry of the quantum set of correlations. In other words, we do not have good intuition about what the quantum set actually looks like. In this paper we study the geometry of the quantum set using standard tools from convex geometry. We find explicit examples of rather counter-intuitive features in the simplest non-trivial Bell scenario (two parties, two inputs and two outputs) and illustrate them using 2-dimensional slice plots. We also show that even more complex features appear in Bell scenarios with more inputs or more parties. Finally, we discuss the limitations that the geometry of the quantum set imposes on the task of self-testing.

}, doi = {10.1103/PhysRevA.97.022104}, url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.022104}, author = {Koon Tong Goh and Jedrzej Kaniewski and Elie Wolfe and Tam{\'a}s V{\'e}rtesi and Xingyao Wu and Yu Cai and Yeong-Cherng Liang and Valerio Scarani} } @article {2302, title = {High Purity Single Photons Entangled with an Atomic Memory}, year = {2018}, abstract = {

Trapped atomic ions are an ideal candidate for quantum network nodes, with long-lived identical qubit memories that can be locally entangled through their Coulomb interaction and remotely entangled through photonic channels. The integrity of this photonic interface is generally reliant on purity of single photons produced by the quantum memory. Here we demonstrate a single-photon source for quantum networking based on a trapped 138Ba+ ion with a single photon purity of g2(0)=(8.1\±2.3)\×10\−5 without background subtraction. We further optimize the tradeoff between the photonic generation rate and the memory-photon entanglement fidelity for the case of polarization photonic qubits by tailoring the spatial mode of the collected light.\ 

}, url = {https://arxiv.org/abs/1812.01749}, author = {Clayton Crocker and Martin Lichtman and Ksenia Sosnova and Allison Carter and Sophia Scarano and Christopher Monroe} } @article {2368, title = {Information-Theoretic Privacy For Distributed Average Consensus: Bounded Integral Inputs}, year = {2018}, month = {03/28/2019}, abstract = {

We propose an asynchronous distributed average consensus algorithm that guarantees information-theoretic privacy of honest agents\&$\#$39; inputs against colluding passive adversarial agents, as long as the set of colluding passive adversarial agents is not a vertex cut in the underlying communication network. This implies that a network with (t+1)-connectivity guarantees information-theoretic privacy of honest agents\&$\#$39; inputs against any t colluding agents. The proposed protocol is formed by composing a distributed privacy mechanism we provide with any (non-private) distributed average consensus algorithm. The agent\&$\#$39; inputs are bounded integers, where the bounds are apriori known to all the agents.

}, url = {https://arxiv.org/abs/1809.01794}, author = {Nirupam Gupta and Jonathan Katz and Nikhil Chopra} } @article {2212, title = {Information-Theoretic Privacy in Distributed Average Consensus}, year = {2018}, abstract = {

We propose an asynchronous distributed average consensus algorithm that guarantees information-theoretic privacy of honest agents\&$\#$39; inputs against colluding semi-honest (passively adversarial) agents, as long as the set of colluding semi-honest agents is not a vertex cut in the underlying communication network. This implies that a network with\ (t+1)-connectivity guarantees information-theoretic privacy of honest agents\&$\#$39; inputs against any\ t\ colluding semi-honest agents. The proposed protocol is formed by composing a distributed privacy mechanism we provide with any (non-private) distributed average consensus algorithm.\ 

}, url = {https://arxiv.org/abs/1809.01794}, author = {Nirupam Gupta and Jonathan Katz and Nikhil Chopra} } @article {1994, title = {Keyring models: an approach to steerability}, journal = {Journal of Mathematical Physics}, volume = {59}, year = {2018}, month = {2018/01/02}, pages = {022103}, abstract = {

If a measurement is made on one half of a bipartite system then, conditioned on the outcome, the other half has a new reduced state. If these reduced states defy classical explanation \— that is, if shared randomness cannot produce these reduced states for all possible measurements \— the bipartite state is said to be steerable. Determining which states are steerable is a challenging problem even for low dimensions. In the case of two-qubit systems a criterion is known for T-states (that is, those with maximally mixed marginals) under projective measurements. In the current work we introduce the concept of keyring models \— a special class of local hidden state model. When the measurements made correspond to real projectors, these allow us to study steerability beyond T-states. Using keyring models, we completely solve the steering problem for real projective measurements when the state arises from mixing a pure two-qubit state with uniform noise. We also give a partial solution in the case when the uniform noise is replaced by independent depolarizing channels. Our results imply that Werner states, which are a special case of the previous states, are unsteerable under real projective measurements if and only if their efficiency is at most 2/π.

}, doi = {10.1063/1.5006199}, url = {http://aip.scitation.org/doi/full/10.1063/1.5006199}, author = {Carl Miller and Roger Colbeck and Yaoyun Shi} } @article {2214, title = {More is Less: Perfectly Secure Oblivious Algorithms in the Multi-Server Setting}, year = {2018}, abstract = {

The problem of Oblivious RAM (ORAM) has traditionally been studied in a single-server setting, but more recently the multi-server setting has also been considered. Yet it is still unclear whether the multi-server setting has any inherent advantages, e.g., whether the multi-server setting can be used to achieve stronger security goals or provably better efficiency than is possible in the single-server case. In this work, we construct a perfectly secure 3-server ORAM scheme that outperforms the best known single-server scheme by a logarithmic factor. In the process, we also show, for the first time, that there exist specific algorithms for which multiple servers can overcome known lower bounds in the single-server setting.\ 

}, url = {https://arxiv.org/abs/1809.00825}, author = {Hubert Chan and Jonathan Katz and Kartik Nayak and Antigoni Polychroniadou and Elaine Shi} } @article {2251, title = {Multiparty quantum data hiding with enhanced security and remote deletion}, year = {2018}, pages = {5}, abstract = {

One of the applications of quantum technology is to use quantum states and measurements to communicate which offers more reliable security promises. Quantum data hiding, which gives the source party the ability of sharing data among multiple receivers and revealing it at a later time depending on his/her will, is one of the promising information sharing schemes which may address practical security issues. In this work, we propose a novel quantum data hiding protocol. By concatenating different subprotocols which apply to rather symmetric hiding scenarios, we cover a variety of more general hiding scenarios. We provide the general requirements for constructing such protocols and give explicit examples of encoding states for five parties. We also proved the security of the protocol in sense that the achievable information by unauthorized operations asymptotically goes to zero. In addition, due to the capability of the sender to manipulate his/her subsystem, the sender is able to abort the protocol remotely at any time before he/she reveals the information.

}, url = {https://arxiv.org/abs/1804.01982}, author = {Xingyao Wu and Jianxin Chen} } @article {2312, title = {On the need for soft dressing}, journal = {High Energ. Phys. }, volume = {121}, year = {2018}, month = {2018}, abstract = {

In order to deal with IR divergences arising in QED or perturbative quantum gravity scattering processes, one can either calculate inclusive quantities or use dressed asymptotic states. We consider incoming superpositions of momentum eigenstates and show that in calculations of cross-sections these two approaches yield different answers: in the inclusive formalism no interference occurs for incoming finite superpositions and wavepackets do not scatter at all, while the dressed formalism yields the expected interference terms. This suggests that rather than Fock space states, one should use Faddeev-Kulish-type dressed states to correctly describe physical processes involving incoming superpositions. We interpret this in terms of selection rules due to large U(1) gauge symmetries and BMS supertranslations.

}, author = {Daniel Carney and Laurent Chaurette and Dominik Neuenfeld and Gordon Semenoff} } @article {2206, title = {Observation of bound state self-interaction in a nano-eV atom collider}, journal = {Nature Communications }, volume = {9}, year = {2018}, month = {2018/11/20}, abstract = {

Quantum mechanical scattering resonances for colliding particles occur when a continuum scattering state couples to a discrete bound state between them. The coupling also causes the bound state to interact with itself via the continuum and leads to a shift in the bound state energy, but, lacking knowledge of the bare bound state energy, measuring this self-energy via the resonance position has remained elusive. Here, we report on the direct observation of self-interaction by using a nano-eV atom collider to track the position of a magnetically-tunable Feshbach resonance through a parameter space spanned by energy and magnetic field. Our system of potassium and rubidium atoms displays a strongly non-monotonic resonance trajectory with an exceptionally large self-interaction energy arising from an interplay between the Feshbach bound state and a different, virtual bound state at a fixed energy near threshold.

}, doi = {https://doi.org/10.1038/s41467-018-07375-8}, url = {https://arxiv.org/abs/1807.01174}, author = {Ryan Thomas and Matthew Chilcott and Eite Tiesinga and Amita B. Deb and Niels Kj{\ae}rgaard} } @article {2060, title = {Observation of three-photon bound states in a quantum nonlinear medium}, journal = {Science}, volume = {359}, year = {2018}, month = {2018/02/16}, pages = {783-786}, abstract = {

Bound states of massive particles, such as nuclei, atoms or molecules, are ubiquitous in nature and constitute the bulk of the visible world around us. In contrast, photons typically only weakly influence each other due to their very weak interactions and vanishing mass. We report the observation of traveling three-photon bound states in a quantum nonlinear medium where the interactions between photons are mediated by atomic Rydberg states. In particular, photon correlation and conditional phase measurements reveal the distinct features associated with three-photon and two-photon bound states. Such photonic trimers and dimers can be viewed as quantum solitons with shape-preserving wavefunctions that depend on the constituent photon number. The observed bunching and strongly nonlinear optical phase are quantitatively described by an effective field theory (EFT) of Rydberg-induced photon-photon interactions, which demonstrates the presence of a substantial effective three-body force between the photons. These observations pave the way towards the realization, studies, and control of strongly interacting quantum many-body states of light.

}, doi = {10.1126/science.aao7293}, url = {http://science.sciencemag.org/content/359/6377/783}, author = {Qi-Yu Liang and Aditya V. Venkatramani and Sergio H. Cantu and Travis L. Nicholson and Michael Gullans and Alexey V. Gorshkov and Jeff D. Thompson and Cheng Chin and Mikhail D. Lukin and Vladan Vuletic} } @article {2209, title = {Optimization of photon storage fidelity in ordered atomic arrays}, journal = {New Journal of Physics}, volume = {20}, year = {2018}, month = {2018/08/31}, abstract = {

A major application for atomic ensembles consists of a quantum memory for light, in which an optical state can be reversibly converted to a collective atomic excitation on demand. There exists a well-known fundamental bound on the storage error, when the ensemble is describable by a continuous medium governed by the Maxwell-Bloch equations. The validity of this model can break down, however, in systems such as dense, ordered atomic arrays, where strong interference in emission can give rise to phenomena such as subradiance and \"selective\" radiance. Here, we develop a general formalism that finds the maximum storage efficiency for a collection of atoms with discrete, known positions, and a given spatial mode in which an optical field is sent. As an example, we apply this technique to study a finite two-dimensional square array of atoms. We show that such a system enables a storage error that scales with atom number Na like \∼(logNa)2/N2a, and that, remarkably, an array of just 4\×4 atoms in principle allows for an efficiency comparable to a disordered ensemble with optical depth of around 600.

}, doi = {https://doi.org/10.1088/1367-2630/aadb74}, url = {https://arxiv.org/abs/1710.06312}, author = {M. T. Manzoni and M. Moreno-Cardoner and A. Asenjo-Garcia and J. V. Porto and Alexey V. Gorshkov and D. E. Chang} } @article {2218, title = {Photon propagation through dissipative Rydberg media at large input rates}, year = {2018}, abstract = {

We study the dissipative propagation of quantized light in interacting Rydberg media under the conditions of electromagnetically induced transparency (EIT). Rydberg blockade physics in optically dense atomic media leads to strong dissipative interactions between single photons. The regime of high incoming photon flux constitutes a challenging many-body dissipative problem. We experimentally study in detail for the first time the pulse shapes and the second-order correlation function of the outgoing field and compare our data with simulations based on two novel theoretical approaches well-suited to treat this many-photon limit. At low incoming flux, we report good agreement between both theories and the experiment. For higher input flux, the intensity of the outgoing light is lower than that obtained from theoretical predictions. We explain this discrepancy using a simple phenomenological model taking into account pollutants, which are nearly-stationary Rydberg excitations coming from the reabsorption of scattered probe photons. At high incoming photon rates, the blockade physics results in unconventional shapes of measured correlation functions.\ 

}, url = {https://arxiv.org/abs/1807.07586}, author = {Przemyslaw Bienias and James Douglas and Asaf Paris-Mandoki and Paraj Titum and Ivan Mirgorodskiy and Christoph Tresp and Emil Zeuthen and Michael Gullans and Marco Manzoni and Sebastian Hofferberth and Darrick Chang and Alexey V. Gorshkov} } @article {1922, title = {Quantum algorithm for multivariate polynomial interpolation}, journal = {Proceedings of The Royal Society A}, volume = {474}, year = {2018}, month = {2018/01/17}, abstract = {

How many quantum queries are required to determine the coefficients of a degree-d polynomial in n variables? We present and analyze quantum algorithms for this multivariate polynomial interpolation problem over the fields Fq, R, and C. We show that kC and 2kC queries suffice to achieve probability 1 for C and R, respectively, where kC = \⌈ 1 n+1 ( n+d d )\⌉ except for d = 2 and four other special cases. For Fq, we show that \⌈ d n+d ( n+d d )\⌉ queries suffice to achieve probability approaching 1 for large field order q. The classical query complexity of this problem is ( n+d d ), so our result provides a speedup by a factor of n + 1, n+1 2 , and n+d d for C, R, and Fq, respectively. Thus we find a much larger gap between classical and quantum algorithms than the univariate case, where the speedup is by a factor of 2. For the case of Fq, we conjecture that 2kC queries also suffice to achieve probability approaching 1 for large field order q, although we leave this as an open problem.

}, doi = {10.1098/rspa.2017.0480}, url = {http://rspa.royalsocietypublishing.org/content/474/2209/20170480}, author = {Jianxin Chen and Andrew M. Childs and Shih-Han Hung} } @article {2213, title = {Single-photon bound states in atomic ensembles}, year = {2018}, abstract = {

We illustrate the existence of single-excitation bound states for propagating photons interacting with N two-level atoms. These bound states can be calculated from an effective spin model, and their existence relies on dissipation in the system. The appearance of these bound states is in a one-to-one correspondence with zeros in the single-photon transmission and with divergent bunching in the second-order photon-photon correlation function. We also formulate a dissipative version of Levinson\&$\#$39;s theorem for this system by looking at the relation between the number of bound states and the winding number of the transmission phases. This theorem allows a direct experimental measurement of the number of bound states using the measured transmission phases.

}, url = {https://arxiv.org/abs/1809.01147}, author = {Yidan Wang and Michael Gullans and Antoine Browaeys and J. V. Porto and Darrick E. Chang and Alexey V. Gorshkov} } @article {1837, title = {Spectrum estimation of density operators with alkaline-earth atoms}, volume = {120}, year = {2018}, month = {2018/01/09}, abstract = {

We show that Ramsey spectroscopy of fermionic alkaline-earth atoms in a square-well trap provides an efficient and accurate estimate for the eigenspectrum of a density matrix whose n copies are stored in the nuclear spins of n such atoms. This spectrum estimation is enabled by the high symmetry of the interaction Hamiltonian, dictated, in turn, by the decoupling of the nuclear spin from the electrons and by the shape of the square-well trap. Practical performance of this procedure and its potential applications to quantum computing, quantum simulation, and time-keeping with alkalineearth atoms are discussed.

}, doi = {https://doi.org/10.1103/PhysRevLett.120.025301}, url = {http://arxiv.org/abs/1608.02045}, author = {Michael E. Beverland and Jeongwan Haah and Gorjan Alagic and Gretchen K. Campbell and Ana Maria Rey and Alexey V. Gorshkov} } @article {2257, title = {Structure of Correlated Worldline Theories of Quantum Gravity}, journal = {Phys. Rev.}, volume = {D}, year = {2018}, month = {2018/06/21}, pages = {084052}, abstract = {

We consider the general form of \"Correlated Worldline\" (CWL) theories of quantum gravity. We show that one can have 2 different kinds of CWL theory, in which the generating functional is written as either a sum or a product over multiple copies of the coupled matter and gravitational fields. In both versions, the paths in a functional formulation are correlated via gravity itself, causing a breakdown of the superposition principle; however, the product form survives consistency tests not satisfied by the summed form. To better understand the structure of these two theories, we show how to perform diagrammatic expansions in the gravitational coupling for each version of CWL theory, using particle propagation and scalar fields as examples. We explicitly calculate contributions to 2-point and 4-point functions, again for each version of the theory, up to 2nd-order in the gravitational coupling.

}, doi = {https://doi.org/10.1103/PhysRevD.98.084052}, url = {https://arxiv.org/abs/1806.08043}, author = {Andrei O. Barvinsky and Daniel Carney and Philip C. E. Stamp} } @article {2270, title = {Tabletop experiments for quantum gravity: a user{\textquoteright}s manual}, year = {2018}, abstract = {

Recent advances in cooling, control, and measurement of mechanical systems in the quantum regime have opened the possibility of the first direct observation of quantum gravity, at scales achievable in experiments. This paper gives a broad overview of this idea, using some matter-wave and optomechanical systems to illustrate the predictions of a variety of models of low-energy quantum gravity. We first review the treatment of perturbatively quantized general relativity as an effective quantum field theory, and consider the particular challenges of observing quantum effects in this framework. We then move on to a variety of alternative models, such as those in which gravity is classical, emergent, or responsible for a breakdown of quantum mechanics.

}, url = {https://arxiv.org/abs/1807.11494}, author = {Daniel Carney and Philip C. E. Stamp and J. M. Taylor} } @article {2204, title = {Tabletop experiments for quantum gravity: a user{\textquoteright}s manual}, year = {2018}, abstract = {

Recent advances in cooling, control, and measurement of mechanical systems in the quantum regime have opened the possibility of the first direct observation of quantum gravity, at scales achievable in experiments. This paper gives a broad overview of this idea, using some matter-wave and optomechanical systems to illustrate the predictions of a variety of models of low-energy quantum gravity. We first review the treatment of perturbatively quantized general relativity as an effective quantum field theory, and consider the particular challenges of observing quantum effects in this framework. We then move on to a variety of alternative models, such as those in which gravity is classical, emergent, or responsible for a breakdown of quantum mechanics.

}, url = {https://arxiv.org/abs/1807.11494}, author = {Daniel Carney and Philip C. E. Stamp and J. M. Taylor} } @article {2220, title = {Toward the first quantum simulation with quantum speedup}, journal = {Proceedings of the National Academy of Sciences}, volume = {115 }, year = {2018}, pages = {9456-9461}, abstract = {

With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical computers, but that requires the fewest resources for a quantum computer. We consider quantum simulation of spin systems, which could be applied to understand condensed matter phenomena. We synthesize explicit circuits for three leading quantum simulation algorithms, using diverse techniques to tighten error bounds and optimize circuit implementations. Quantum signal processing appears to be preferred among algorithms with rigorous performance guarantees, whereas higher-order product formulas prevail if empirical error estimates suffice. Our circuits are orders of magnitude smaller than those for the simplest classically infeasible instances of factoring and quantum chemistry, bringing practical quantum computation closer to reality.

}, doi = {https://doi.org/10.1073/pnas.1801723115}, url = {https://arxiv.org/abs/1711.10980}, author = {Andrew M. Childs and Dmitri Maslov and Yunseong Nam and Neil J. Ross and Yuan Su} } @article {2463, title = {Two-Dimensional Dilaton Gravity Theory and Lattice Schwarzian Theory}, year = {2018}, abstract = {
We report a holographic study of a two-dimensional dilaton gravity theory with the Dirichlet boundary condition for the cases of non-vanishing and vanishing cosmological constants. Our result shows that the boundary theory of the two-dimensional dilaton gravity theory with the Dirichlet boundary condition for the case of non-vanishing cosmological constants is the Schwarzian term coupled to a dilaton field, while for the case of vanishing cosmological constant, a theory does not have a kinetic term. We also include the higher derivative term R2, where R is the scalar curvature that is coupled to a dilaton field. We find that the form of the boundary theory is not modified perturbatively. Finally, we show that a lattice holographic picture is realized up to the second-order perturbation of boundary cut-off ε2 under a constant boundary dilaton field and the non-vanishing cosmological constant by identifying the lattice spacing a of a lattice Schwarzian theory with the boundary cut-off ε of the two-dimensional dilaton gravity theory.\ 
}, url = {https://arxiv.org/abs/1802.04599}, author = {Su-Kuan Chu and Chen-Te Ma and Chih-Hung Wu} } @article {2215, title = {Unitary Entanglement Construction in Hierarchical Networks}, year = {2018}, abstract = {

The construction of large-scale quantum computers will require modular architectures that allow physical resources to be localized in easy-to-manage packages. In this work, we examine the impact of different graph structures on the preparation of entangled states. We begin by explaining a formal framework, the hierarchical product, in which modular graphs can be easily constructed. This framework naturally leads us to suggest a class of graphs, which we dub hierarchies. We argue that such graphs have favorable properties for quantum information processing, such as a small diameter and small total edge weight, and use the concept of Pareto efficiency to identify promising quantum graph architectures. We present numerical and analytical results on the speed at which large entangled states can be created on nearest-neighbor grids and hierarchy graphs. We also present a scheme for performing circuit placement--the translation from circuit diagrams to machine qubits--on quantum systems whose connectivity is described by hierarchies.

}, url = {https://arxiv.org/abs/1808.07876}, author = {Aniruddha Bapat and Zachary Eldredge and James R. Garrison and Abhinav Desphande and Frederic T. Chong and Alexey V. Gorshkov} } @article {2056, title = {Computational Notions of Quantum Min-Entropy}, year = {2017}, month = {2017/09/09}, abstract = {

We initiate the study of computational entropy in the quantum setting. We investigate to what extent the classical notions of computational entropy generalize to the quantum setting, and whether quantum analogues of classical theorems hold. Our main results are as follows. (1) The classical Leakage Chain Rule for pseudoentropy can be extended to the case that the leakage information is quantum (while the source remains classical). Specifically, if the source has pseudoentropy at least k, then it has pseudoentropy at least k \− l conditioned on an l- qubit leakage. (2) As an application of the Leakage Chain Rule, we construct the first quantum leakage-resilient stream-cipher in the bounded-quantum-storage model, assuming the existence of a quantum-secure pseudorandom generator. (3) We show that the general form of the classical Dense Model Theorem (interpreted as the equivalence between two definitions of pseudo-relativemin-entropy) does not extend to quantum states. Along the way, we develop quantum analogues of some classical techniques (e.g., the Leakage Simulation Lemma, which is proven by a Nonuniform Min-Max Theorem or Boosting). On the other hand, we also identify some classical techniques (e.g., Gap Amplification) that do not work in the quantum setting. Moreover, we introduce a variety of notions that combine quantum information and quantum complexity, and this raises several directions for future work.

}, url = {https://arxiv.org/abs/1704.07309}, author = {Yi-Hsiu Chen and Kai-Min Chung and Ching-Yi Lai and Salil P. Vadhan and Xiaodi Wu} } @article {1985, title = {Domination with decay in triangular matchstick arrangement graphs}, journal = {Involve, a Journal of Mathematics}, volume = {10}, year = {2017}, month = {2017/05/14}, pages = {749 - 766}, abstract = {

We provide results for the exponential dominating numbers and total exponential dominating numbers of a family of triangular grid graphs. We then prove inequalities for these numbers and compare them with inequalities that hold more generally for exponential dominating numbers of graphs.

}, issn = {1944-4176}, doi = {10.2140/involve10.2140/involve.2017.10-510.2140/involve.2017.10.749}, url = {http://msp.org/involve/http://msp.org/involve/2017/10-5/index.xhtmlhttp://msp.org/involve/2017/10-5/p03.xhtmlhttp://msp.org/involve/2017/10-5/involve-v10-n5-p03-s.pdf}, author = {Jill Cochran and Terry Henderson and Aaron Ostrander and Ron Taylor} } @article {1902, title = {Efficient simulation of sparse Markovian quantum dynamics}, journal = {Quantum Information and Computation}, volume = {17}, year = {2017}, month = {2017/09/01}, pages = {901-947}, abstract = {

Quantum algorithms for simulating Hamiltonian dynamics have been extensively developed, but there has been much less work on quantum algorithms for simulating the dynamics of open quantum systems. We give the first efficient quantum algorithms for simulating Markovian quantum dynamics generated by Lindbladians that are not necessarily local. We introduce two approaches to simulating sparse Lindbladians. First, we show how to simulate Lindbladians that act within small invariant subspaces using a quantum algorithm to implement sparse Stinespring isometries. Second, we develop a method for simulating sparse Lindblad operators by concatenating a sequence of short-time evolutions. We also show limitations on Lindbladian simulation by proving a no-fast-forwarding theorem for simulating sparse Lindbladians in a black-box model.

}, doi = {10.26421/QIC17.11-12}, url = {https://arxiv.org/abs/1611.05543}, author = {Andrew M. Childs and Tongyang Li} } @article {2301, title = {Entanglement Wedge Reconstruction via Universal Recovery Channels}, year = {2017}, abstract = {

We apply and extend the theory of universal recovery channels from quantum information theory to address the problem of entanglement wedge reconstruction in AdS/CFT. It has recently been proposed that any low-energy local bulk operators in a CFT boundary region\&$\#$39;s entanglement wedge can be reconstructed on that boundary region itself. Existing work arguing for this proposal relies on algebraic consequences of the exact equivalence between bulk and boundary relative entropies, namely the theory of operator algebra quantum error correction. However, bulk and boundary relative entropies are only approximately equal in bulk effective field theory, and in similar situations it is known that predictions from exact entropic equalities can be qualitatively incorrect. The framework of universal recovery channels provides a robust demonstration of the entanglement wedge reconstruction conjecture in addition to new physical insights. Most notably, we find that a bulk operator acting in a given boundary region\&$\#$39;s entanglement wedge can be expressed as the response of the boundary region\&$\#$39;s modular Hamiltonian to a perturbation of the bulk state in the direction of the bulk operator. This formula can be interpreted as a noncommutative version of Bayes\&$\#$39; rule that attempts to undo the noise induced by restricting to only a portion of the boundary, and has an integral representation in terms of modular flows. To reach these conclusions, we extend the theory of universal recovery channels to finite-dimensional operator algebras and demonstrate that recovery channels approximately preserve the multiplicative structure of the operator algebra

}, url = {https://arxiv.org/abs/1704.05839}, author = {Jordan Cotler and Patrick Hayden and Geoffrey Penington and Grant Salton and Brian Swingle and Michael Walter} } @article {1945, title = {Experimentally Generated Random Numbers Certified by the Impossibility of Superluminal Signaling}, year = {2017}, month = {2017/02/16}, abstract = {

Random numbers are an important resource for applications such as numerical simulation and secure communication. However, it is difficult to certify whether a physical random number generator is truly unpredictable. Here, we exploit the phenomenon of quantum nonlocality in a loophole-free photonic Bell test experiment for the generation of randomness that cannot be predicted within any physical theory that allows one to make independent measurement choices and prohibits superluminal signaling. To certify and quantify the randomness, we describe a new protocol that performs well in an experimental regime characterized by low violation of Bell inequalities. Applying an extractor function to our data, we obtained 256 new random bits, uniform to within 0.001.

}, url = {https://arxiv.org/abs/1702.05178$\#$}, author = {Peter Bierhorst and Emanuel Knill and Scott Glancy and Alan Mink and Stephen P. Jordan and Andrea Rommal and Yi-Kai Liu and Bradley Christensen and Sae Woo Nam and Lynden K. Shalm} } @article {2107, title = {Provable quantum state tomography via non-convex methods}, year = {2017}, month = {2017/11/19}, abstract = {

With nowadays steadily growing quantum processors, it is required to develop new quantum tomography tools that are tailored for high-dimensional systems. In this work, we describe such a computational tool, based on recent ideas from non-convex optimization. The algorithm excels in the compressed-sensing-like setting, where only a few data points are measured from a lowrank or highly-pure quantum state of a high-dimensional system. We show that the algorithm can practically be used in quantum tomography problems that are beyond the reach of convex solvers, and, moreover, is faster than other state-of-the-art non-convex approaches. Crucially, we prove that, despite being a non-convex program, under mild conditions, the algorithm is guaranteed to converge to the global minimum of the problem; thus, it constitutes a provable quantum state tomography protocol.

}, url = {https://arxiv.org/abs/1711.02524}, author = {Anastasios Kyrillidis and Amir Kalev and Dohuyng Park and Srinadh Bhojanapalli and Constantine Caramanis and Sujay Sanghavi} } @article {1923, title = {Quantum algorithm for linear differential equations with exponentially improved dependence on precision}, journal = {Communications in Mathematical Physics}, volume = {356}, year = {2017}, month = {2017/12/01}, pages = {1057-1081}, abstract = {

We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time. The complexity of the algorithm is polynomial in the logarithm of the inverse error, an exponential improvement over previous quantum algorithms for this problem. Our result builds upon recent advances in quantum linear systems algorithms by encoding the simulation into a sparse, well-conditioned linear system that approximates evolution according to the propagator using a Taylor series. Unlike with finite difference methods, our approach does not require additional hypotheses to ensure numerical stability.

}, url = {https://arxiv.org/abs/1701.03684}, author = {Dominic W. Berry and Andrew M. Childs and Aaron Ostrander and Guoming Wang} } @article {1605, title = {Quantum algorithm for systems of linear equations with exponentially improved dependence on precision}, journal = {SIAM Journal on Computing}, volume = {46}, year = {2017}, month = {2017/12/21}, pages = {1920-1950}, abstract = {

Harrow, Hassidim, and Lloyd showed that for a suitably specified N\×N matrix A and N-dimensional vector b⃗ , there is a quantum algorithm that outputs a quantum state proportional to the solution of the linear system of equations Ax⃗ =b⃗ . If A is sparse and well-conditioned, their algorithm runs in time poly(logN,1/ϵ), where ϵ is the desired precision in the output state. We improve this to an algorithm whose running time is polynomial in log(1/ϵ), exponentially improving the dependence on precision while keeping essentially the same dependence on other parameters. Our algorithm is based on a general technique for implementing any operator with a suitable Fourier or Chebyshev series representation. This allows us to bypass the quantum phase estimation algorithm, whose dependence on ϵ is prohibitive.

}, doi = {10.1137/16M1087072}, url = {http://epubs.siam.org/doi/10.1137/16M1087072}, author = {Andrew M. Childs and Robin Kothari and Rolando D. Somma} } @article {1787, title = {Quantum state tomography via reduced density matrices}, journal = {Physical Review Letters}, volume = {118}, year = {2017}, month = {2017/01/09}, pages = {020401}, abstract = {

Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this work we demonstrate for the first time a class of states that are UD by their RDMs under the assumption that the global state is pure, but fail to be UD in the absence of that assumption. This discovery allows us to classify quantum states according to their UD properties, with the requirement that each class be treated distinctly in the practice of simplifying quantum state tomography. Additionally we experimentally test the feasibility and stability of performing quantum state tomography via the measurement of local RDMs for each class. These theoretical and experimental results advance the project of performing efficient and accurate quantum state tomography in practice.

}, doi = {10.1103/PhysRevLett.118.020401}, url = {http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.020401}, author = {Tao Xin and Dawei Lu and Joel Klassen and Nengkun Yu and Zhengfeng Ji and Jianxin Chen and Xian Ma and Guilu Long and Bei Zeng and Raymond Laflamme} } @article {1234, title = {Complexity of the XY antiferromagnet at fixed magnetization}, journal = {Quantum Information and Computation}, volume = {16}, year = {2016}, month = {2016/01/01}, pages = {1-18}, abstract = { We prove that approximating the ground energy of the antiferromagnetic XY model on a simple graph at fixed magnetization (given as part of the instance specification) is QMA-complete. To show this, we strengthen a previous result by establishing QMA-completeness for approximating the ground energy of the Bose-Hubbard model on simple graphs. Using a connection between the XY and Bose-Hubbard models that we exploited in previous work, this establishes QMA-completeness of the XY model. }, url = {http://arxiv.org/abs/1503.07083v1}, author = {Andrew M. Childs and David Gosset and Zak Webb} } @article {1452, title = {Detecting Consistency of Overlapping Quantum Marginals by Separability}, journal = {Physical Review A}, volume = {93}, year = {2016}, month = {2016/03/03}, pages = {032105}, abstract = { The quantum marginal problem asks whether a set of given density matrices are consistent, i.e., whether they can be the reduced density matrices of a global quantum state. Not many non-trivial analytic necessary (or sufficient) conditions are known for the problem in general. We propose a method to detect consistency of overlapping quantum marginals by considering the separability of some derived states. Our method works well for the $k$-symmetric extension problem in general, and for the general overlapping marginal problems in some cases. Our work is, in some sense, the converse to the well-known $k$-symmetric extension criterion for separability. }, doi = {10.1103/PhysRevA.93.032105}, url = {http://arxiv.org/abs/1509.06591}, author = {Jianxin Chen and Zhengfeng Ji and Nengkun Yu and Bei Zeng} } @article {2004, title = {Entanglement and spin-squeezing without infinite-range interactions}, year = {2016}, month = {2016/12/22}, abstract = {

Infinite-range interactions are known to facilitate the production of highly entangled states with applications in quantum information and metrology. However, many experimental systems have interactions that decay with distance, and the achievable benefits in this context are much less clear. Combining recent exact solutions with a controlled expansion in the system size, we analyze quench dynamics in Ising models with power-law (1/r α ) interactions in D dimensions, thereby expanding the understanding of spin squeezing into a broad and experimentally relevant context. In spatially homogeneous systems, we show that for small α the scaling of squeezing with system size is identical to the infinite-range (α = 0) case. This indifference to the interaction range persists up to a critical value α = 2D/3, above which squeezing degrades continuously. Boundaryinduced inhomogeneities present in most experimental systems modify this picture, but it nevertheless remains qualitatively correct for finite-sized systems.

}, url = {https://arxiv.org/abs/1612.07805}, author = {Michael Foss-Feig and Zhe-Xuan Gong and Alexey V. Gorshkov and Charles W. Clark} } @article {1925, title = {A finite presentation of CNOT-dihedral operators}, year = {2016}, month = {2016/12/31}, abstract = {

We give a finite presentation by generators and relations of unitary operators expressible over the {CNOT, T, X} gate set, also known as CNOT-dihedral operators. To this end, we introduce a notion of normal form for CNOT-dihedral circuits and prove that every CNOT-dihedral operator admits a unique normal form. Moreover, we show that in the presence of certain structural rules only finitely many circuit identities are required to reduce an arbitrary CNOT-dihedral circuit to its normal form. By appropriately restricting our relations, we obtain a finite presentation of unitary operators expressible over the {CNOT, T } gate set as a corollary.

}, url = {https://arxiv.org/abs/1701.00140}, author = {Matthew Amy and Jianxin Chen and Neil J. Ross} } @article {1783, title = {Joint product numerical range and geometry of reduced density matrices}, year = {2016}, month = {2016/06/23}, abstract = {The reduced density matrices of a many-body quantum system form a convex set, whose three-dimensional projection Θ is convex in R3. The boundary ∂Θ of Θ may exhibit nontrivial geometry, in particular ruled surfaces. Two physical mechanisms are known for the origins of ruled surfaces: symmetry breaking and gapless. In this work, we study the emergence of ruled surfaces for systems with local Hamiltonians in infinite spatial dimension, where the reduced density matrices are known to be separable as a consequence of the quantum de Finetti{\textquoteright}s theorem. This allows us to identify the reduced density matrix geometry with joint product numerical range Π of the Hamiltonian interaction terms. We focus on the case where the interaction terms have certain structures, such that ruled surface emerge naturally when taking a convex hull of Π. We show that, a ruled surface on ∂Θ sitting in Π has a gapless origin, otherwise it has a symmetry breaking origin. As an example, we demonstrate that a famous ruled surface, known as the oloid, is a possible shape of Θ, with two boundary pieces of symmetry breaking origin separated by two gapless lines.}, url = {http://arxiv.org/abs/1606.07422}, author = {Jianxin Chen and Cheng Guo and Zhengfeng Ji and Yiu-Tung Poon and Nengkun Yu and Bei Zeng and Jie Zhou} } @article {1774, title = {Mapping constrained optimization problems to quantum annealing with application to fault diagnosis}, year = {2016}, abstract = {Current quantum annealing (QA) hardware suffers from practical limitations such as finite temperature, sparse connectivity, small qubit numbers, and control error. We propose new algorithms for mapping boolean constraint satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In particular we develop a new embedding algorithm for mapping a CSP onto a hardware Ising model with a fixed sparse set of interactions, and propose two new decomposition algorithms for solving problems too large to map directly into hardware. The mapping technique is locally-structured, as hardware compatible Ising models are generated for each problem constraint, and variables appearing in different constraints are chained together using ferromagnetic couplings. In contrast, global embedding techniques generate a hardware independent Ising model for all the constraints, and then use a minor-embedding algorithm to generate a hardware compatible Ising model. We give an example of a class of CSPs for which the scaling performance of D-Wave{\textquoteright}s QA hardware using the local mapping technique is significantly better than global embedding. We validate the approach by applying D-Wave{\textquoteright}s hardware to circuit-based fault-diagnosis. For circuits that embed directly, we find that the hardware is typically able to find all solutions from a min-fault diagnosis set of size N using 1000N samples, using an annealing rate that is 25 times faster than a leading SAT-based sampling method. Further, we apply decomposition algorithms to find min-cardinality faults for circuits that are up to 5 times larger than can be solved directly on current hardware.}, url = {http://arxiv.org/abs/1603.03111}, author = {Bian, Zhengbing and Chudak, Fabian and Israel, Robert and Lackey, Brad and Macready, William G and Roy, Aidan} } @article {1859, title = {Mapping contrained optimization problems to quantum annealing with application to fault diagnosis}, journal = {Frontiers in ICT}, volume = {3}, year = {2016}, month = {2016/07/28}, pages = {14}, abstract = {

Current quantum annealing (QA) hardware suffers from practical limitations such as finite\ temperature, sparse connectivity, small qubit numbers, and control error. We propose new algorithms for\ mapping Boolean constraint satisfaction problems (CSPs) onto QA hardware mitigating these limitations.\ In particular, we develop a new embedding algorithm for mapping a CSP onto a hardware Ising model with\ a fixed sparse set of interactions and propose two new decomposition algorithms for solving problems too\ large to map directly into hardware. The mapping technique is locally structured, as hardware compatible\ Ising models are generated for each problem constraint, and variables appearing in different constraints are\ chained together using ferromagnetic couplings. By contrast, global embedding techniques generate a\ hardware-independent Ising model for all the constraints, and then use a minor-embedding algorithm to\ generate\ a hardware compatible Ising model. We give an example of a class of CSPs for which the scaling\ performance\ of the D-Wave hardware using the local mapping technique is significantly better than global\ embedding. We validate\ the approach by applying D- Wave\’s QA hardware to circuit-based fault diagnosis.\ For circuits that embed directly, we\ find that the hardware is typically able to find all solutions from a\ min-fault diagnosis set of size N using 1000 N samples,\ using an annealing rate that is 25 times faster than\ a leading SAT-based sampling method. Furthermore, we apply\ decomposition algorithms to find min-cardinality\ faults for circuits that are up to 5 times larger than can be solved directly on current hardware.

}, url = {http://journal.frontiersin.org/article/10.3389/fict.2016.00014/full}, author = {Bian, Zhengbing and Chudak, Fabian and Robert Brian Israel and Brad Lackey and Macready, William G and Aiden Roy} } @article {1554, title = {Optimal quantum algorithm for polynomial interpolation}, journal = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)}, volume = {55}, year = {2016}, month = {2016/03/01}, pages = {16:1--16:13}, abstract = {

We consider the number of quantum queries required to determine the coefficients of a degree-d polynomial over GF(q). A lower bound shown independently by Kane and Kutin and by Meyer and Pommersheim shows that d/2+1/2 quantum queries are needed to solve this problem with bounded error, whereas an algorithm of Boneh and Zhandry shows that d quantum queries are sufficient. We show that the lower bound is achievable: d/2+1/2 quantum queries suffice to determine the polynomial with bounded error. Furthermore, we show that d/2+1 queries suffice to achieve probability approaching 1 for large q. These upper bounds improve results of Boneh and Zhandry on the insecurity of cryptographic protocols against quantum attacks. We also show that our algorithm\&$\#$39;s success probability as a function of the number of queries is precisely optimal. Furthermore, the algorithm can be implemented with gate complexity poly(log q) with negligible decrease in the success probability.

}, isbn = {978-3-95977-013-2}, issn = {1868-8969}, doi = {http://dx.doi.org/10.4230/LIPIcs.ICALP.2016.16}, url = {http://arxiv.org/abs/1509.09271}, author = {Andrew M. Childs and Wim van Dam and Shih-Han Hung and Igor E. Shparlinski} } @article {1235, title = {Optimal state discrimination and unstructured search in nonlinear quantum mechanics}, journal = {Physical Review A}, volume = {93}, year = {2016}, month = {2016/02/11}, pages = {022314}, abstract = { Nonlinear variants of quantum mechanics can solve tasks that are impossible in standard quantum theory, such as perfectly distinguishing nonorthogonal states. Here we derive the optimal protocol for distinguishing two states of a qubit using the Gross-Pitaevskii equation, a model of nonlinear quantum mechanics that arises as an effective description of Bose-Einstein condensates. Using this protocol, we present an algorithm for unstructured search in the Gross-Pitaevskii model, obtaining an exponential improvement over a previous algorithm of Meyer and Wong. This result establishes a limitation on the effectiveness of the Gross-Pitaevskii approximation. More generally, we demonstrate similar behavior under a family of related nonlinearities, giving evidence that the ability to quickly discriminate nonorthogonal states and thereby solve unstructured search is a generic feature of nonlinear quantum mechanics. }, doi = {10.1103/PhysRevA.93.022314}, url = {http://arxiv.org/abs/1507.06334}, author = {Andrew M. Childs and Joshua Young} } @article {1706, title = {Pure-state tomography with the expectation value of Pauli operators}, journal = {Physical Review A}, volume = {93}, year = {2016}, month = {2016/03/31}, pages = {032140}, abstract = {

We examine the problem of finding the minimum number of Pauli measurements needed to uniquely determine an arbitrary n-qubit pure state among all quantum states. We show that only 11 Pauli measurements are needed to determine an arbitrary two-qubit pure state compared to the full quantum state tomography with 16 measurements, and only 31 Pauli measurements are needed to determine an arbitrary three-qubit pure state compared to the full quantum state tomography with 64 measurements. We demonstrate that our protocol is robust under depolarizing error with simulated random pure states. We experimentally test the protocol on two- and three-qubit systems with nuclear magnetic resonance techniques. We show that the pure state tomography protocol saves us a number of measurements without considerable loss of fidelity. We compare our protocol with same-size sets of randomly selected Pauli operators and find that our selected set of Pauli measurements significantly outperforms those random sampling sets. As a direct application, our scheme can also be used to reduce the number of settings needed for pure-state tomography in quantum optical systems.

}, doi = {http://dx.doi.org/10.1103/PhysRevA.93.032140}, url = {http://arxiv.org/abs/1601.05379}, author = {Xian Ma and Tyler Jackson and Hui Zhou and Jianxin Chen and Dawei Lu and Michael D. Mazurek and Kent A.G. Fisher and Xinhua Peng and David Kribs and Kevin J. Resch and Zhengfeng Ji and Bei Zeng and Raymond Laflamme} } @article {1707, title = {Quantifying the coherence of pure quantum states}, journal = {Physical Review A}, volume = {94}, year = {2016}, month = {2016/10/07}, pages = {042313}, abstract = {

In recent years, several measures have been proposed for characterizing the coherence of a given quantum state. We derive several results that illuminate how these measures behave when restricted to pure states. Notably, we present an explicit characterization of the closest incoherent state to a given pure state under the trace distance measure of coherence, and we affirm a recent conjecture that the l1 measure of coherence of a pure state is never smaller than its relative entropy of coherence. We then use our result to show that the states maximizing the trace distance of coherence are exactly the maximally coherent states, and we derive a new inequality relating the negativity and distillable entanglement of pure states.

}, doi = {10.1103/PhysRevA.94.042313}, url = {https://doi.org/10.1103/PhysRevA.94.042313}, author = {Jianxin Chen and Nathaniel Johnston and Chi-Kwong Li and Sarah Plosker} } @article {1772, title = {Self-organization of atoms coupled to a chiral reservoir}, journal = {Physical Review A}, volume = {94}, year = {2016}, month = {2016/11/29}, pages = {053855}, abstract = {

Tightly confined modes of light, as in optical nanofibers or photonic crystal waveguides, can lead to large optical coupling in atomic systems, which mediates long-range interactions between atoms. These one-dimensional systems can naturally possess couplings that are asymmetric between modes propagating in different directions. Strong long-range interaction among atoms via these modes can drive them to a self-organized periodic distribution. In this paper, we examine the self-organizing behavior of atoms in one dimension coupled to a chiral reservoir. We determine the solution to the equations of motion in different parameter regimes, relative to both the detuning of the pump laser that initializes the atomic dipole-dipole interactions and the degree of reservoir chirality. In addition, we calculate possible experimental signatures such as reflectivity from self-organized atoms and motional sidebands.

}, doi = {10.1103/PhysRevA.94.053855}, url = {http://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.053855}, author = {Zachary Eldredge and Pablo Solano and Darrick Chang and Alexey V. Gorshkov} } @article {2006, title = {Subwavelength-width optical tunnel junctions for ultracold atoms}, journal = {Physical Review A}, volume = {94}, year = {2016}, month = {2016/12/27}, pages = {063422}, abstract = {

We propose a method for creating far-field optical barrier potentials for ultracold atoms with widths that are narrower than the diffraction limit and can approach tens of nanometers. The reduced widths stem from the nonlinear atomic response to control fields that create spatially varying dark resonances. The subwavelength barrier is the result of the geometric scalar potential experienced by an atom prepared in such a spatially varying dark state. The performance of this technique, as well as its applications to the study of many-body physics and to the implementation of quantum-information protocols with ultracold atoms, are discussed, with a focus on the implementation of tunnel junctions.

}, doi = {10.1103/PhysRevA.94.063422}, url = {http://link.aps.org/doi/10.1103/PhysRevA.94.063422}, author = {Jendrzejewski, F. and Eckel, S. and Tiecke, T. G. and G. Juzeliunas and Campbell, G. K. and Jiang, Liang and Alexey V. Gorshkov} } @article {1689, title = {Tomography is necessary for universal entanglement detection with single-copy observables}, journal = {Physical Review Letters}, volume = {116}, year = {2016}, month = {2016/06/07}, pages = {230501}, abstract = {Entanglement, one of the central mysteries of quantum mechanics, plays an essential role in numerous applications of quantum information theory. A natural question of both theoretical and experimental importance is whether universal entanglement detection is possible without full state tomography. In this work, we prove a no-go theorem that rules out this possibility for any non-adaptive schemes that employ single-copy measurements only. We also examine in detail a previously implemented experiment, which claimed to detect entanglement of two-qubit states via adaptive single-copy measurements without full state tomography. By performing the experiment and analyzing the data, we demonstrate that the information gathered is indeed sufficient to reconstruct the state. These results reveal a fundamental limit for single-copy measurements in entanglement detection, and provides a general framework to study the detection of other interesting properties of quantum states, such as the positivity of partial transpose and the k-symmetric extendibility.}, doi = {10.1103/PhysRevLett.116.230501}, url = {http://arxiv.org/abs/1511.00581}, author = {Dawei Lu and Tao Xin and Nengkun Yu and Zhengfeng Ji and Jianxin Chen and Guilu Long and Jonathan Baugh and Xinhua Peng and Bei Zeng and Raymond Laflamme} } @article {1838, title = {Atom induced cavities and tunable long-range interactions between atoms trapped near photonic crystals}, journal = {Nature Photon. 9, 326 (2015)}, year = {2015}, month = {2015/03/03}, abstract = {

Using cold atoms to simulate strongly interacting quantum systems represents an exciting frontier of physics. However, achieving tunable, coherent long-range interactions between atoms is an outstanding challenge, which currently leaves a large class of models inaccessible to quantum simulation. Here, we propose a solution exploiting the powerful new platform of cold atoms trapped near nano-photonic systems. We show that the dielectric contrast of an atom trapped near a photonic crystal can seed a localized cavity mode around the atomic position. In a dynamic form of \“all-atomic\” cavity QED, the length of these cavity modes can be tuned, and atoms separated by the order of the e\↵ective cavity length can interact coherently with each other. Considering realistic conditions such as fabrication disorder and photon losses, coherent long-range potentials or spin interactions can be dominant in the system over length scales up to hundreds of wavelengths.

}, doi = {doi:10.1038/nphoton.2015.57}, url = {http://www.nature.com/nphoton/journal/v9/n5/full/nphoton.2015.57.html}, author = {J S Douglas and H Habibian and Alexey V. Gorshkov and H J Kimble and D E Chang} } @article {1507, title = {Coulomb bound states of strongly interacting photons}, journal = {Physical Review Letters}, volume = {115}, year = {2015}, month = {2015/09/16}, pages = {123601}, abstract = { We show that two photons coupled to Rydberg states via electromagnetically induced transparency can interact via an effective Coulomb potential. This interaction gives rise to a continuum of two-body bound states. Within the continuum, metastable bound states are distinguished in analogy with quasi-bound states tunneling through a potential barrier. We find multiple branches of metastable bound states whose energy spectrum is governed by the Coulomb potential, thus obtaining a photonic analogue of the hydrogen atom. Under certain conditions, the wavefunction resembles that of a diatomic molecule in which the two polaritons are separated by a finite "bond length." These states propagate with a negative group velocity in the medium, allowing for a simple preparation and detection scheme, before they slowly decay to pairs of bound Rydberg atoms. }, doi = {10.1103/PhysRevLett.115.123601}, url = {http://arxiv.org/abs/1505.03859v1}, author = {Mohammad F. Maghrebi and Michael Gullans and P. Bienias and S. Choi and I. Martin and O. Firstenberg and M. D. Lukin and H. P. B{\"u}chler and Alexey V. Gorshkov} } @article {1515, title = {Demonstration of Robust Quantum Gate Tomography via Randomized Benchmarking}, journal = {New Journal of Physics}, volume = {17}, year = {2015}, month = {2015/11/05}, pages = {113019}, abstract = { Typical quantum gate tomography protocols struggle with a self-consistency problem: the gate operation cannot be reconstructed without knowledge of the initial state and final measurement, but such knowledge cannot be obtained without well-characterized gates. A recently proposed technique, known as randomized benchmarking tomography (RBT), sidesteps this self-consistency problem by designing experiments to be insensitive to preparation and measurement imperfections. We implement this proposal in a superconducting qubit system, using a number of experimental improvements including implementing each of the elements of the Clifford group in single {\textquoteleft}atomic{\textquoteright} pulses and custom control hardware to enable large overhead protocols. We show a robust reconstruction of several single-qubit quantum gates, including a unitary outside the Clifford group. We demonstrate that RBT yields physical gate reconstructions that are consistent with fidelities obtained by randomized benchmarking. }, doi = {10.1088/1367-2630/17/11/113019}, url = {http://arxiv.org/abs/1505.06686}, author = {Blake R. Johnson and Marcus P. da Silva and Colm A. Ryan and Shelby Kimmel and Jerry M. Chow and Thomas A. Ohki} } @article {1462, title = {Discontinuity of Maximum Entropy Inference and Quantum Phase Transitions}, journal = {New Journal of Physics}, volume = {17}, year = {2015}, month = {2015/08/10}, pages = {083019}, abstract = { In this paper, we discuss the connection between two genuinely quantum phenomena --- the discontinuity of quantum maximum entropy inference and quantum phase transitions at zero temperature. It is shown that the discontinuity of the maximum entropy inference of local observable measurements signals the non-local type of transitions, where local density matrices of the ground state change smoothly at the transition point. We then propose to use the quantum conditional mutual information of the ground state as an indicator to detect the discontinuity and the non-local type of quantum phase transitions in the thermodynamic limit. }, doi = {10.1088/1367-2630/17/8/083019}, url = {http://arxiv.org/abs/1406.5046v2}, author = {Jianxin Chen and Zhengfeng Ji and Chi-Kwong Li and Yiu-Tung Poon and Yi Shen and Nengkun Yu and Bei Zeng and Duanlu Zhou} } @article {1247, title = {Hamiltonian simulation with nearly optimal dependence on all parameters}, journal = {Proceedings of the 56th IEEE Symposium on Foundations of Computer Science}, year = {2015}, month = {2015/01/08}, pages = {792-809}, abstract = { We present an algorithm for sparse Hamiltonian simulation that has optimal dependence on all parameters of interest (up to log factors). Previous algorithms had optimal or near-optimal scaling in some parameters at the cost of poor scaling in others. Hamiltonian simulation via a quantum walk has optimal dependence on the sparsity $d$ at the expense of poor scaling in the allowed error $\epsilon$. In contrast, an approach based on fractional-query simulation provides optimal scaling in $\epsilon$ at the expense of poor scaling in $d$. Here we combine the two approaches, achieving the best features of both. By implementing a linear combination of quantum walk steps with coefficients given by Bessel functions, our algorithm achieves near-linear scaling in $\tau := d \|H\|_{\max} t$ and sublogarithmic scaling in $1/\epsilon$. Our dependence on $\epsilon$ is optimal, and we prove a new lower bound showing that no algorithm can have sublinear dependence on $\tau$. }, doi = {10.1109/FOCS.2015.54}, url = {http://arxiv.org/abs/1501.01715}, author = {Dominic W. Berry and Andrew M. Childs and Robin Kothari} } @article {1440, title = {The Minimum Size of Unextendible Product Bases in the Bipartite Case (and Some Multipartite Cases) }, journal = {Communications in Mathematical Physics}, volume = {333}, year = {2015}, month = {2014/10/10}, pages = {351 - 365}, abstract = { A long-standing open question asks for the minimum number of vectors needed to form an unextendible product basis in a given bipartite or multipartite Hilbert space. A partial solution was found by Alon and Lovasz in 2001, but since then only a few other cases have been solved. We solve all remaining bipartite cases, as well as a large family of multipartite cases. }, doi = {10.1007/s00220-014-2186-7}, url = {http://arxiv.org/abs/1301.1406v1}, author = {Jianxin Chen and Nathaniel Johnston} } @article {1259, title = {Momentum switches}, journal = {Quantum Information and Computation}, volume = {15}, year = {2015}, month = {2015/05/01}, pages = {601-621}, abstract = { Certain continuous-time quantum walks can be viewed as scattering processes. These processes can perform quantum computations, but it is challenging to design graphs with desired scattering behavior. In this paper, we study and construct momentum switches, graphs that route particles depending on their momenta. We also give an example where there is no exact momentum switch, although we construct an arbitrarily good approximation. }, url = {http://arxiv.org/abs/1406.4510v1}, author = {Andrew M. Childs and David Gosset and Daniel Nagaj and Mouktik Raha and Zak Webb} } @article {1178, title = {Nearly-linear light cones in long-range interacting quantum systems}, journal = {Physical Review Letters}, volume = {114}, year = {2015}, month = {2015/04/13}, pages = {157201}, abstract = { In non-relativistic quantum theories with short-range Hamiltonians, a velocity $v$ can be chosen such that the influence of any local perturbation is approximately confined to within a distance $r$ until a time $t \sim r/v$, thereby defining a linear light cone and giving rise to an emergent notion of locality. In systems with power-law ($1/r^{\alpha}$) interactions, when $\alpha$ exceeds the dimension $D$, an analogous bound confines influences to within a distance $r$ only until a time $t\sim(\alpha/v)\log r$, suggesting that the velocity, as calculated from the slope of the light cone, may grow exponentially in time. We rule out this possibility; light cones of power-law interacting systems are algebraic for $\alpha>2D$, becoming linear as $\alpha\rightarrow\infty$. Our results impose strong new constraints on the growth of correlations and the production of entangled states in a variety of rapidly emerging, long-range interacting atomic, molecular, and optical systems. }, doi = {10.1103/PhysRevLett.114.157201}, url = {http://arxiv.org/abs/1410.3466v1}, author = {Michael Foss-Feig and Zhe-Xuan Gong and Charles W. Clark and Alexey V. Gorshkov} } @article {1333, title = {Optomechanical reference accelerometer}, journal = {Metrologia}, volume = {52}, year = {2015}, month = {2015/09/08}, pages = {654}, abstract = {

We present an optomechanical accelerometer with high dynamic range, high bandwidth and read-out noise levels below 8 ${\mu}$g/$\sqrt{\mathrm{Hz}}$. The straightforward assembly and low cost of our device make it a prime candidate for on-site reference calibrations and autonomous navigation. We present experimental data taken with a vacuum sealed, portable prototype and deduce the achieved bias stability and scale factor accuracy. Additionally, we present a comprehensive model of the device physics that we use to analyze the fundamental noise sources and accuracy limitations of such devices.

}, doi = {10.1088/0026-1394/52/5/654}, url = {http://iopscience.iop.org/article/10.1088/0026-1394/52/5/654/meta;jsessionid=C2B417A5CD50B9B57EE14C78E1783802.ip-10-40-1-105}, author = {Oliver Gerberding and Felipe Guzman Cervantes and John Melcher and Jon R. Pratt and J. M. Taylor} } @article {1189, title = {Parafermionic zero modes in ultracold bosonic systems}, journal = {Physical Review Letters}, volume = {115}, year = {2015}, month = {2015/08/06}, pages = {065301}, abstract = { Exotic topologically protected zero modes with parafermionic statistics (also called fractionalized Majorana modes) have been proposed to emerge in devices fabricated from a fractional quantum Hall system and a superconductor. The fractionalized statistics of these modes takes them an important step beyond the simplest non-Abelian anyons, Majorana fermions. Building on recent advances towards the realization of fractional quantum Hall states of bosonic ultracold atoms, we propose a realization of parafermions in a system consisting of Bose-Einstein-condensate trenches within a bosonic fractional quantum Hall state. We show that parafermionic zero modes emerge at the endpoints of the trenches and give rise to a topologically protected degeneracy. We also discuss methods for preparing and detecting these modes. }, doi = {10.1103/PhysRevLett.115.065301}, url = {http://arxiv.org/abs/1504.04012v2}, author = {Mohammad F. Maghrebi and Sriram Ganeshan and David J. Clarke and Alexey V. Gorshkov and Jay D. Sau} } @article {1675, title = {Quantum many-body models with cold atoms coupled to photonic crystals}, journal = {Nature Photonics}, volume = {9}, year = {2015}, month = {2015/04/04}, pages = {326 - 331}, issn = {1749-4885}, doi = {10.1038/nphoton.2015.57}, url = {http://www.nature.com/doifinder/10.1038/nphoton.2015.57}, author = {Douglas, J. S. and Habibian, H. and Hung, C.-L. and Alexey V. Gorshkov and Kimble, H. J. and Chang, D. E.} } @article {1304, title = {Self-heterodyne detection of the {\it in-situ} phase of an atomic-SQUID}, journal = {Physical Review A}, volume = {92}, year = {2015}, month = {2015/09/03}, pages = {033602}, abstract = { We present theoretical and experimental analysis of an interferometric measurement of the {\it in-situ} phase drop across and current flow through a rotating barrier in a toroidal Bose-Einstein condensate (BEC). This experiment is the atomic analog of the rf-superconducting quantum interference device (SQUID). The phase drop is extracted from a spiral-shaped density profile created by the spatial interference of the expanding toroidal BEC and a reference BEC after release from all trapping potentials. We characterize the interferometer when it contains a single particle, which is initially in a coherent superposition of a torus and reference state, as well as when it contains a many-body state in the mean-field approximation. The single-particle picture is sufficient to explain the origin of the spirals, to relate the phase-drop across the barrier to the geometry of a spiral, and to bound the expansion times for which the {\it in-situ} phase can be accurately determined. Mean-field estimates and numerical simulations show that the inter-atomic interactions shorten the expansion time scales compared to the single-particle case. Finally, we compare the mean-field simulations with our experimental data and confirm that the interferometer indeed accurately measures the {\it in-situ} phase drop. }, doi = {10.1103/PhysRevA.92.033602}, url = {http://arxiv.org/abs/1506.09149v2}, author = {Ranchu Mathew and Avinash Kumar and Stephen Eckel and Fred Jendrzejewski and Gretchen K. Campbell and Mark Edwards and Eite Tiesinga} } @article {1265, title = {Simulating Hamiltonian dynamics with a truncated Taylor series}, journal = {Physical Review Letters}, volume = {114}, year = {2015}, month = {2015/03/03}, pages = {090502}, abstract = { We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of physical systems. As in another recent algorithm, the cost of our method depends only logarithmically on the inverse of the desired precision, which is optimal. However, we simplify the algorithm and its analysis by using a method for implementing linear combinations of unitary operations to directly apply the truncated Taylor series. }, doi = {10.1103/PhysRevLett.114.090502}, url = {http://arxiv.org/abs/1412.4687v1}, author = {Dominic W. Berry and Andrew M. Childs and Richard Cleve and Robin Kothari and Rolando D. Somma} } @article {1450, title = {Universal Subspaces for Local Unitary Groups of Fermionic Systems}, journal = {Communications in Mathematical Physics}, volume = {333}, year = {2015}, month = {2014/10/10}, pages = {541 - 563}, abstract = { Let $\mathcal{V}=\wedge^N V$ be the $N$-fermion Hilbert space with $M$-dimensional single particle space $V$ and $2N\le M$. We refer to the unitary group $G$ of $V$ as the local unitary (LU) group. We fix an orthonormal (o.n.) basis $\ket{v_1},...,\ket{v_M}$ of $V$. Then the Slater determinants $e_{i_1,...,i_N}:= \ket{v_{i_1}\we v_{i_2}\we...\we v_{i_N}}$ with $i_1<...3. If $M$ is even, the well known BCS states are not LU-equivalent to any single occupancy state. Our main result is that for N=3 and $M$ even there is a universal subspace $\cW\subseteq\cS$ spanned by $M(M-1)(M-5)/6$ states $e_{i_1,...,i_N}$. Moreover the number $M(M-1)(M-5)/6$ is minimal. }, doi = {10.1007/s00220-014-2187-6}, url = {http://arxiv.org/abs/1301.3421v2}, author = {Lin Chen and Jianxin Chen and Dragomir Z. Djokovic and Bei Zeng} } @article {1232, title = {The Bose-Hubbard model is QMA-complete}, journal = {Proceedings of the 41st International Colloquium on Automata, Languages, and Programming (ICALP 2014)}, volume = {8572}, year = {2014}, month = {2014/07/08}, pages = {308-319}, abstract = { The Bose-Hubbard model is a system of interacting bosons that live on the vertices of a graph. The particles can move between adjacent vertices and experience a repulsive on-site interaction. The Hamiltonian is determined by a choice of graph that specifies the geometry in which the particles move and interact. We prove that approximating the ground energy of the Bose-Hubbard model on a graph at fixed particle number is QMA-complete. In our QMA-hardness proof, we encode the history of an n-qubit computation in the subspace with at most one particle per site (i.e., hard-core bosons). This feature, along with the well-known mapping between hard-core bosons and spin systems, lets us prove a related result for a class of 2-local Hamiltonians defined by graphs that generalizes the XY model. By avoiding the use of perturbation theory in our analysis, we circumvent the need to multiply terms in the Hamiltonian by large coefficients. }, doi = {10.1007/978-3-662-43948-7_26}, url = {http://arxiv.org/abs/1311.3297v1}, author = {Andrew M. Childs and David Gosset and Zak Webb} } @article {1230, title = {The computational power of matchgates and the XY interaction on arbitrary graphs}, journal = {Quantum Information and Computation}, volume = {14}, year = {2014}, month = {2014/09/01}, pages = {901-916}, abstract = { Matchgates are a restricted set of two-qubit gates known to be classically simulable when acting on nearest-neighbor qubits on a path, but universal for quantum computation when the qubits are arranged on certain other graphs. Here we characterize the power of matchgates acting on arbitrary graphs. Specifically, we show that they are universal on any connected graph other than a path or a cycle, and that they are classically simulable on a cycle. We also prove the same dichotomy for the XY interaction, a proper subset of matchgates related to some implementations of quantum computing. }, url = {http://arxiv.org/abs/1308.1463v1}, author = {Daniel J. Brod and Andrew M. Childs} } @article {1226, title = {Constructing elliptic curve isogenies in quantum subexponential time}, journal = {Journal of Mathematical Cryptology}, volume = {8}, year = {2014}, month = {2014/01/01}, pages = {1 - 29}, abstract = { Given two elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit an isogeny between them, but finding such an isogeny is believed to be computationally difficult. The fastest known classical algorithm takes exponential time, and prior to our work no faster quantum algorithm was known. Recently, public-key cryptosystems based on the presumed hardness of this problem have been proposed as candidates for post-quantum cryptography. In this paper, we give a subexponential-time quantum algorithm for constructing isogenies, assuming the Generalized Riemann Hypothesis (but with no other assumptions). Our algorithm is based on a reduction to a hidden shift problem, together with a new subexponential-time algorithm for evaluating isogenies from kernel ideals (under only GRH), and represents the first nontrivial application of Kuperberg{\textquoteright}s quantum algorithm for the hidden shift problem. This result suggests that isogeny-based cryptosystems may be uncompetitive with more mainstream quantum-resistant cryptosystems such as lattice-based cryptosystems. }, doi = {10.1515/jmc-2012-0016}, url = {http://arxiv.org/abs/1012.4019v2}, author = {Andrew M. Childs and David Jao and Vladimir Soukharev} } @article {1516, title = {Different Strategies for Optimization Using the Quantum Adiabatic Algorithm }, year = {2014}, month = {2014/01/28}, abstract = { We present the results of a numerical study, with 20 qubits, of the performance of the Quantum Adiabatic Algorithm on randomly generated instances of MAX 2-SAT with a unique assignment that maximizes the number of satisfied clauses. The probability of obtaining this assignment at the end of the quantum evolution measures the success of the algorithm. Here we report three strategies which consistently increase the success probability for the hardest instances in our ensemble: decreasing the overall evolution time, initializing the system in excited states, and adding a random local Hamiltonian to the middle of the evolution. }, url = {http://arxiv.org/abs/1401.7320v1}, author = {Elizabeth Crosson and Edward Farhi and Cedric Yen-Yu Lin and Han-Hsuan Lin and Peter Shor} } @article {bian2014discrete, title = {Discrete optimization using quantum annealing on sparse Ising models}, journal = {Frontiers in Physics}, volume = {2}, year = {2014}, month = {2014/09/01}, pages = {56}, publisher = {Frontiers}, abstract = {This paper discusses techniques for solving discrete optimization problems using quantum annealing. Practical issues likely to affect the computation include precision limitations, finite temperature, bounded energy range, sparse connectivity, and small numbers of qubits. To address these concerns we propose a way of finding energy representations with large classical gaps between ground and first excited states, efficient algorithms for mapping non-compatible Ising models into the hardware, and the use of decomposition methods for problems that are too large to fit in hardware. We validate the approach by describing experiments with D-Wave quantum hardware for low density parity check decoding with up to 1000 variables.}, author = {Bian, Zhengbing and Chudak, Fabian and Israel, Robert and Brad Lackey and Macready, William G and Roy, Aidan} } @article {1264, title = {Exponential improvement in precision for simulating sparse Hamiltonians}, journal = {Proceedings of the 46th ACM Symposium on Theory of Computing (STOC 2014)}, year = {2014}, month = {2014/05/31}, pages = {283-292}, abstract = { We provide a quantum algorithm for simulating the dynamics of sparse Hamiltonians with complexity sublogarithmic in the inverse error, an exponential improvement over previous methods. Specifically, we show that a $d$-sparse Hamiltonian $H$ acting on $n$ qubits can be simulated for time $t$ with precision $\epsilon$ using $O\big(\tau \frac{\log(\tau/\epsilon)}{\log\log(\tau/\epsilon)}\big)$ queries and $O\big(\tau \frac{\log^2(\tau/\epsilon)}{\log\log(\tau/\epsilon)}n\big)$ additional 2-qubit gates, where $\tau = d^2 \|{H}\|_{\max} t$. Unlike previous approaches based on product formulas, the query complexity is independent of the number of qubits acted on, and for time-varying Hamiltonians, the gate complexity is logarithmic in the norm of the derivative of the Hamiltonian. Our algorithm is based on a significantly improved simulation of the continuous- and fractional-query models using discrete quantum queries, showing that the former models are not much more powerful than the discrete model even for very small error. We also simplify the analysis of this conversion, avoiding the need for a complex fault correction procedure. Our simplification relies on a new form of "oblivious amplitude amplification" that can be applied even though the reflection about the input state is unavailable. Finally, we prove new lower bounds showing that our algorithms are optimal as a function of the error. }, isbn = {978-1-4503-2710-7}, doi = {10.1145/2591796.2591854}, url = {http://arxiv.org/abs/1312.1414v2}, author = {Dominic W. Berry and Andrew M. Childs and Richard Cleve and Robin Kothari and Rolando D. Somma} } @article {1480, title = {Many-body dynamics of dipolar molecules in an optical lattice}, journal = {Physical Review Letters}, volume = {113}, year = {2014}, month = {2014/11/7}, abstract = { Understanding the many-body dynamics of isolated quantum systems is one of the central challenges in modern physics. To this end, the direct experimental realization of strongly correlated quantum systems allows one to gain insights into the emergence of complex phenomena. Such insights enable the development of theoretical tools that broaden our understanding. Here, we theoretically model and experimentally probe with Ramsey spectroscopy the quantum dynamics of disordered, dipolar-interacting, ultracold molecules in a partially filled optical lattice. We report the capability to control the dipolar interaction strength, and we demonstrate that the many-body dynamics extends well beyond a nearest-neighbor or mean-field picture, and cannot be quantitatively described using previously available theoretical tools. We develop a novel cluster expansion technique and demonstrate that our theoretical method accurately captures the measured dependence of the spin dynamics on molecule number and on the dipolar interaction strength. In the spirit of quantum simulation, this agreement simultaneously benchmarks the new theoretical method and verifies our microscopic understanding of the experiment. Our findings pave the way for numerous applications in quantum information science, metrology, and condensed matter physics. }, doi = {10.1103/PhysRevLett.113.195302}, url = {http://arxiv.org/abs/1402.2354v1}, author = {Kaden R. A. Hazzard and Bryce Gadway and Michael Foss-Feig and Bo Yan and Steven A. Moses and Jacob P. Covey and Norman Y. Yao and Mikhail D. Lukin and Jun Ye and Deborah S. Jin and Ana Maria Rey} } @article {1231, title = {Quantum computation of discrete logarithms in semigroups}, journal = {Journal of Mathematical Cryptology}, volume = {8}, year = {2014}, month = {2014/01/1}, abstract = { We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor{\textquoteright}s algorithms for period finding and discrete log as subroutines. Thus proposed cryptosystems based on the presumed hardness of discrete logarithms in semigroups are insecure against quantum attacks. In contrast, we show that some generalizations of the discrete log problem are hard in semigroups despite being easy in groups. We relate a shifted version of the discrete log problem in semigroups to the dihedral hidden subgroup problem, and we show that the constructive membership problem with respect to $k \ge 2$ generators in a black-box abelian semigroup of order $N$ requires $\tilde \Theta(N^{\frac{1}{2}-\frac{1}{2k}})$ quantum queries. }, doi = {10.1515/jmc-2013-0038}, url = {http://arxiv.org/abs/1310.6238v2}, author = {Andrew M. Childs and G{\'a}bor Ivanyos} } @article {1506, title = {Scattering resonances and bound states for strongly interacting Rydberg polaritons }, journal = {Physical Review A}, volume = {90}, year = {2014}, month = {2014/11/3}, abstract = { We provide a theoretical framework describing slow-light polaritons interacting via atomic Rydberg states. We use a diagrammatic method to analytically derive the scattering properties of two polaritons. We identify parameter regimes where polariton-polariton interactions are repulsive. Furthermore, in the regime of attractive interactions, we identify multiple two-polariton bound states, calculate their dispersion, and study the resulting scattering resonances. Finally, the two-particle scattering properties allow us to derive the effective low-energy many-body Hamiltonian. This theoretical platform is applicable to ongoing experiments. }, doi = {10.1103/PhysRevA.90.053804}, url = {http://arxiv.org/abs/1402.7333v1}, author = {P. Bienias and S. Choi and O. Firstenberg and Mohammad F. Maghrebi and Michael Gullans and M. D. Lukin and Alexey V. Gorshkov and H. P. B{\"u}chler} } @article {1233, title = {Spatial search by continuous-time quantum walks on crystal lattices}, journal = {Physical Review A}, volume = {89}, year = {2014}, month = {2014/5/30}, abstract = { We consider the problem of searching a general $d$-dimensional lattice of $N$ vertices for a single marked item using a continuous-time quantum walk. We demand locality, but allow the walk to vary periodically on a small scale. By constructing lattice Hamiltonians exhibiting Dirac points in their dispersion relations and exploiting the linear behaviour near a Dirac point, we develop algorithms that solve the problem in a time of $O(\sqrt N)$ for $d>2$ and $O(\sqrt N \log N)$ in $d=2$. In particular, we show that such algorithms exist even for hypercubic lattices in any dimension. Unlike previous continuous-time quantum walk algorithms on hypercubic lattices in low dimensions, our approach does not use external memory. }, doi = {10.1103/PhysRevA.89.052337}, url = {http://arxiv.org/abs/1403.2676v2}, author = {Andrew M. Childs and Yimin Ge} } @article {1479, title = {Suppressing the loss of ultracold molecules via the continuous quantum Zeno effect }, journal = {Physical Review Letters}, volume = {112}, year = {2014}, month = {2014/2/20}, abstract = { We investigate theoretically the suppression of two-body losses when the on-site loss rate is larger than all other energy scales in a lattice. This work quantitatively explains the recently observed suppression of chemical reactions between two rotational states of fermionic KRb molecules confined in one-dimensional tubes with a weak lattice along the tubes [Yan et al., Nature 501, 521-525 (2013)]. New loss rate measurements performed for different lattice parameters but under controlled initial conditions allow us to show that the loss suppression is a consequence of the combined effects of lattice confinement and the continuous quantum Zeno effect. A key finding, relevant for generic strongly reactive systems, is that while a single-band theory can qualitatively describe the data, a quantitative analysis must include multiband effects. Accounting for these effects reduces the inferred molecule filling fraction by a factor of five. A rate equation can describe much of the data, but to properly reproduce the loss dynamics with a fixed filling fraction for all lattice parameters we develop a mean-field model and benchmark it with numerically exact time-dependent density matrix renormalization group calculations. }, doi = {10.1103/PhysRevLett.112.070404}, url = {http://arxiv.org/abs/1310.2221v2}, author = {Bihui Zhu and Bryce Gadway and Michael Foss-Feig and Johannes Schachenmayer and Michael Wall and Kaden R. A. Hazzard and Bo Yan and Steven A. Moses and Jacob P. Covey and Deborah S. Jin and Jun Ye and Murray Holland and Ana Maria Rey} } @article {1451, title = {Symmetric Extension of Two-Qubit States}, journal = {Physical Review A}, volume = {90}, year = {2014}, month = {2014/9/17}, abstract = { Quantum key distribution uses public discussion protocols to establish shared secret keys. In the exploration of ultimate limits to such protocols, the property of symmetric extendibility of underlying bipartite states $\rho_{AB}$ plays an important role. A bipartite state $\rho_{AB}$ is symmetric extendible if there exits a tripartite state $\rho_{ABB{\textquoteright}}$, such that the $AB$ marginal state is identical to the $AB{\textquoteright}$ marginal state, i.e. $\rho_{AB{\textquoteright}}=\rho_{AB}$. For a symmetric extendible state $\rho_{AB}$, the first task of the public discussion protocol is to break this symmetric extendibility. Therefore to characterize all bi-partite quantum states that possess symmetric extensions is of vital importance. We prove a simple analytical formula that a two-qubit state $\rho_{AB}$ admits a symmetric extension if and only if $\tr(\rho_B^2)\geq \tr(\rho_{AB}^2)-4\sqrt{\det{\rho_{AB}}}$. Given the intimate relationship between the symmetric extension problem and the quantum marginal problem, our result also provides the first analytical necessary and sufficient condition for the quantum marginal problem with overlapping marginals. }, doi = {10.1103/PhysRevA.90.032318}, url = {http://arxiv.org/abs/1310.3530v2}, author = {Jianxin Chen and Zhengfeng Ji and David Kribs and Norbert L{\"u}tkenhaus and Bei Zeng} } @article {1445, title = {Unextendible Product Basis for Fermionic Systems}, journal = {Journal of Mathematical Physics}, volume = {55}, year = {2014}, month = {2014/01/01}, pages = {082207}, abstract = { We discuss the concept of unextendible product basis (UPB) and generalized UPB for fermionic systems, using Slater determinants as an analogue of product states, in the antisymmetric subspace $\wedge^ N \bC^M$. We construct an explicit example of generalized fermionic unextendible product basis (FUPB) of minimum cardinality $N(M-N)+1$ for any $N\ge2,M\ge4$. We also show that any bipartite antisymmetric space $\wedge^ 2 \bC^M$ of codimension two is spanned by Slater determinants, and the spaces of higher codimension may not be spanned by Slater determinants. Furthermore, we construct an example of complex FUPB of $N=2,M=4$ with minimum cardinality $5$. In contrast, we show that a real FUPB does not exist for $N=2,M=4$ . Finally we provide a systematic construction for FUPBs of higher dimensions using FUPBs and UPBs of lower dimensions. }, doi = {10.1063/1.4893358}, url = {http://arxiv.org/abs/1312.4218v1}, author = {Jianxin Chen and Lin Chen and Bei Zeng} } @article {1505, title = {All-Optical Switch and Transistor Gated by One Stored Photon}, journal = {Science}, volume = {341}, year = {2013}, month = {2013/07/04}, pages = {768 - 770}, abstract = { The realization of an all-optical transistor where one {\textquoteright}gate{\textquoteright} photon controls a {\textquoteright}source{\textquoteright} light beam, is a long-standing goal in optics. By stopping a light pulse in an atomic ensemble contained inside an optical resonator, we realize a device in which one stored gate photon controls the resonator transmission of subsequently applied source photons. A weak gate pulse induces bimodal transmission distribution, corresponding to zero and one gate photons. One stored gate photon produces fivefold source attenuation, and can be retrieved from the atomic ensemble after switching more than one source photon. Without retrieval, one stored gate photon can switch several hundred source photons. With improved storage and retrieval efficiency, our work may enable various new applications, including photonic quantum gates, and deterministic multiphoton entanglement. }, doi = {10.1126/science.1238169}, url = {http://arxiv.org/abs/1401.3194v1}, author = {Wenlan Chen and Kristin M. Beck and Robert B{\"u}cker and Michael Gullans and Mikhail D. Lukin and Haruka Tanji-Suzuki and Vladan Vuletic} } @article {1475, title = {Dynamical quantum correlations of Ising models on an arbitrary lattice and their resilience to decoherence }, journal = {New Journal of Physics}, volume = {15}, year = {2013}, month = {2013/11/07}, pages = {113008}, abstract = { Ising models, and the physical systems described by them, play a central role in generating entangled states for use in quantum metrology and quantum information. In particular, ultracold atomic gases, trapped ion systems, and Rydberg atoms realize long-ranged Ising models, which even in the absence of a transverse field can give rise to highly non-classical dynamics and long-range quantum correlations. In the first part of this paper, we present a detailed theoretical framework for studying the dynamics of such systems driven (at time t=0) into arbitrary unentangled non-equilibrium states, thus greatly extending and unifying the work of Ref. [1]. Specifically, we derive exact expressions for closed-time-path ordered correlation functions, and use these to study experimentally relevant observables, e.g. Bloch vector and spin-squeezing dynamics. In the second part, these correlation functions are then used to derive closed-form expressions for the dynamics of arbitrary spin-spin correlation functions in the presence of both T_1 (spontaneous spin relaxation/excitation) and T_2 (dephasing) type decoherence processes. Even though the decoherence is local, our solution reveals that the competition between Ising dynamics and T_1 decoherence gives rise to an emergent non-local dephasing effect, thereby drastically amplifying the degradation of quantum correlations. In addition to identifying the mechanism of this deleterious effect, our solution points toward a scheme to eliminate it via measurement-based coherent feedback. }, doi = {10.1088/1367-2630/15/11/113008}, url = {http://arxiv.org/abs/1306.0172v1}, author = {Michael Foss-Feig and Kaden R A Hazzard and John J Bollinger and Ana Maria Rey and Charles W Clark} } @article {1245, title = {Easy and hard functions for the Boolean hidden shift problem}, journal = {Proceedings of TQC 2013}, volume = {22}, year = {2013}, month = {2013/04/16}, pages = {50-79}, abstract = { We study the quantum query complexity of the Boolean hidden shift problem. Given oracle access to f(x+s) for a known Boolean function f, the task is to determine the n-bit string s. The quantum query complexity of this problem depends strongly on f. We demonstrate that the easiest instances of this problem correspond to bent functions, in the sense that an exact one-query algorithm exists if and only if the function is bent. We partially characterize the hardest instances, which include delta functions. Moreover, we show that the problem is easy for random functions, since two queries suffice. Our algorithm for random functions is based on performing the pretty good measurement on several copies of a certain state; its analysis relies on the Fourier transform. We also use this approach to improve the quantum rejection sampling approach to the Boolean hidden shift problem. }, doi = {10.4230/LIPIcs.TQC.2013.50}, url = {http://arxiv.org/abs/1304.4642v1}, author = {Andrew M. Childs and Robin Kothari and Maris Ozols and Martin Roetteler} } @article {1244, title = {A framework for bounding nonlocality of state discrimination}, journal = {Communications in Mathematical Physics}, volume = {323}, year = {2013}, month = {2013/9/4}, pages = {1121 - 1153}, abstract = { We consider the class of protocols that can be implemented by local quantum operations and classical communication (LOCC) between two parties. In particular, we focus on the task of discriminating a known set of quantum states by LOCC. Building on the work in the paper "Quantum nonlocality without entanglement" [BDF+99], we provide a framework for bounding the amount of nonlocality in a given set of bipartite quantum states in terms of a lower bound on the probability of error in any LOCC discrimination protocol. We apply our framework to an orthonormal product basis known as the domino states and obtain an alternative and simplified proof that quantifies its nonlocality. We generalize this result for similar bases in larger dimensions, as well as the "rotated" domino states, resolving a long-standing open question [BDF+99]. }, doi = {10.1007/s00220-013-1784-0}, url = {http://arxiv.org/abs/1206.5822v1}, author = {Andrew M. Childs and Debbie Leung and Laura Mancinska and Maris Ozols} } @article {1246, title = {Interpolatability distinguishes LOCC from separable von Neumann measurements}, journal = {Journal of Mathematical Physics}, volume = {54}, year = {2013}, month = {2013/06/25}, pages = {112204}, abstract = { Local operations with classical communication (LOCC) and separable operations are two classes of quantum operations that play key roles in the study of quantum entanglement. Separable operations are strictly more powerful than LOCC, but no simple explanation of this phenomenon is known. We show that, in the case of von Neumann measurements, the ability to interpolate measurements is an operational principle that sets apart LOCC and separable operations. }, doi = {10.1063/1.4830335}, url = {http://arxiv.org/abs/1306.5992v1}, author = {Andrew M. Childs and Debbie Leung and Laura Mancinska and Maris Ozols} } @article {1587, title = {Multilingual Summarization: Dimensionality Reduction and a Step Towards Optimal Term Coverage}, journal = {MultiLing (Workshop on Multilingual Multi-document Summarization)}, year = {2013}, month = {2013/08/09}, pages = {55-63}, abstract = {In this paper we present three term weighting approaches for multi-lingual document summarization and give results on the DUC 2002 data as well as on the 2013 Multilingual Wikipedia feature articles data set. We introduce a new intervalbounded nonnegative matrix factorization. We use this new method, latent semantic analysis (LSA), and latent Dirichlet allocation (LDA) to give three term-weighting methods for multi-document multi-lingual summarization. Results on DUC and TAC data, as well as on the MultiLing 2013 data, demonstrate that these methods are very promising, since they achieve oracle coverage scores in the range of humans for 6 of the 10 test languages. Finally, we present three term weighting approaches for the MultiLing13 single document summarization task on the Wikipedia featured articles. Our submissions signifi- cantly outperformed the baseline in 19 out of 41 languages. }, url = {http://aclweb.org/anthology/W/W13/W13-3108.pdf}, author = {John M. Conroy and Sashka T. Davis and Jeff Kubina and Yi-Kai Liu and Dianne P. O{\textquoteright}Leary and Judith D. Schlesinger} } @article {1229, title = {Product Formulas for Exponentials of Commutators}, journal = {Journal of Mathematical Physics}, volume = {54}, year = {2013}, month = {2013/02/07}, pages = {062202}, abstract = { We provide a recursive method for constructing product formula approximations to exponentials of commutators, giving the first approximations that are accurate to arbitrarily high order. Using these formulas, we show how to approximate unitary exponentials of (possibly nested) commutators using exponentials of the elementary operators, and we upper bound the number of elementary exponentials needed to implement the desired operation within a given error tolerance. By presenting an algorithm for quantum search using evolution according to a commutator, we show that the scaling of the number of exponentials in our product formulas with the evolution time is nearly optimal. Finally, we discuss applications of our product formulas to quantum control and to implementing anticommutators, providing new methods for simulating many-body interaction Hamiltonians. }, doi = {10.1063/1.4811386}, url = {http://arxiv.org/abs/1211.4945v2}, author = {Andrew M. Childs and Nathan Wiebe} } @article {1270, title = {Quantum Catalysis of Magnetic Phase Transitions in a Quantum Simulator}, journal = {Physical Review Letters}, volume = {111}, year = {2013}, month = {2013/9/5}, abstract = { We control quantum fluctuations to create the ground state magnetic phases of a classical Ising model with a tunable longitudinal magnetic field using a system of 6 to 10 atomic ion spins. Due to the long-range Ising interactions, the various ground state spin configurations are separated by multiple first-order phase transitions, which in our zero temperature system cannot be driven by thermal fluctuations. We instead use a transverse magnetic field as a quantum catalyst to observe the first steps of the complete fractal devil{\textquoteright}s staircase, which emerges in the thermodynamic limit and can be mapped to a large number of many-body and energy-optimization problems. }, doi = {10.1103/PhysRevLett.111.100506}, url = {http://arxiv.org/abs/1303.6983v2}, author = {Philip Richerme and Crystal Senko and Simcha Korenblit and Jacob Smith and Aaron Lee and Rajibul Islam and Wesley C. Campbell and Christopher Monroe} } @article {1504, title = {Single-photon nonlinear optics with graphene plasmons}, journal = {Physical Review Letters}, volume = {111}, year = {2013}, month = {2013/12/11}, abstract = { We show that it is possible to realize significant nonlinear optical interactions at the few photon level in graphene nanostructures. Our approach takes advantage of the electric field enhancement associated with the strong confinement of graphene plasmons and the large intrinsic nonlinearity of graphene. Such a system could provide a powerful platform for quantum nonlinear optical control of light. As an example, we consider an integrated optical device that exploits this large nonlinearity to realize a single photon switch. }, doi = {10.1103/PhysRevLett.111.247401}, url = {http://arxiv.org/abs/1309.2651v3}, author = {Michael Gullans and D. E. Chang and F. H. L. Koppens and F. J. Garc{\'\i}a de Abajo and M. D. Lukin} } @article {1460, title = {Symmetries of Codeword Stabilized Quantum Codes}, journal = {8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)}, volume = {22}, year = {2013}, month = {2013/03/28}, pages = {192-206}, abstract = { Symmetry is at the heart of coding theory. Codes with symmetry, especially cyclic codes, play an essential role in both theory and practical applications of classical error-correcting codes. Here we examine symmetry properties for codeword stabilized (CWS) quantum codes, which is the most general framework for constructing quantum error-correcting codes known to date. A CWS code Q can be represented by a self-dual additive code S and a classical code C, i.,e., Q=(S,C), however this representation is in general not unique. We show that for any CWS code Q with certain permutation symmetry, one can always find a self-dual additive code S with the same permutation symmetry as Q such that Q=(S,C). As many good CWS codes have been found by starting from a chosen S, this ensures that when trying to find CWS codes with certain permutation symmetry, the choice of S with the same symmetry will suffice. A key step for this result is a new canonical representation for CWS codes, which is given in terms of a unique decomposition as union stabilizer codes. For CWS codes, so far mainly the standard form (G,C) has been considered, where G is a graph state. We analyze the symmetry of the corresponding graph of G, which in general cannot possess the same permutation symmetry as Q. We show that it is indeed the case for the toric code on a square lattice with translational symmetry, even if its encoding graph can be chosen to be translational invariant. }, doi = {10.4230/LIPIcs.TQC.2013.192}, url = {http://arxiv.org/abs/1303.7020v2}, author = {Salman Beigi and Jianxin Chen and Markus Grassl and Zhengfeng Ji and Qiang Wang and Bei Zeng} } @article {1258, title = {A Time-Efficient Quantum Walk for 3-Distinctness Using Nested Updates}, year = {2013}, month = {2013/02/28}, abstract = { We present an extension to the quantum walk search framework that facilitates quantum walks with nested updates. We apply it to give a quantum walk algorithm for 3-Distinctness with query complexity ~O(n^{5/7}), matching the best known upper bound (obtained via learning graphs) up to log factors. Furthermore, our algorithm has time complexity ~O(n^{5/7}), improving the previous ~O(n^{3/4}). }, url = {http://arxiv.org/abs/1302.7316v1}, author = {Andrew M. Childs and Stacey Jeffery and Robin Kothari and Frederic Magniez} } @article {1197, title = {Topologically Protected Quantum State Transfer in a Chiral Spin Liquid}, journal = {Nature Communications}, volume = {4}, year = {2013}, month = {2013/3/12}, pages = {1585}, abstract = { Topology plays a central role in ensuring the robustness of a wide variety of physical phenomena. Notable examples range from the robust current carrying edge states associated with the quantum Hall and the quantum spin Hall effects to proposals involving topologically protected quantum memory and quantum logic operations. Here, we propose and analyze a topologically protected channel for the transfer of quantum states between remote quantum nodes. In our approach, state transfer is mediated by the edge mode of a chiral spin liquid. We demonstrate that the proposed method is intrinsically robust to realistic imperfections associated with disorder and decoherence. Possible experimental implementations and applications to the detection and characterization of spin liquid phases are discussed. }, doi = {10.1038/ncomms2531}, url = {http://arxiv.org/abs/1110.3788v1}, author = {Norman Y. Yao and Chris R. Laumann and Alexey V. Gorshkov and Hendrik Weimer and Liang Jiang and J. Ignacio Cirac and Peter Zoller and Mikhail D. Lukin} } @article {1459, title = {Uniqueness of Quantum States Compatible with Given Measurement Results}, journal = {Physical Review A}, volume = {88}, year = {2013}, month = {2013/7/11}, abstract = { We discuss the uniqueness of quantum states compatible with given results for measuring a set of observables. For a given pure state, we consider two different types of uniqueness: (1) no other pure state is compatible with the same measurement results and (2) no other state, pure or mixed, is compatible with the same measurement results. For case (1), it is known that for a d-dimensional Hilbert space, there exists a set of 4d-5 observables that uniquely determines any pure state. We show that for case (2), 5d-7 observables suffice to uniquely determine any pure state. Thus there is a gap between the results for (1) and (2), and we give some examples to illustrate this. The case of observables corresponding to reduced density matrices (RDMs) of a multipartite system is also discussed, where we improve known bounds on local dimensions for case (2) in which almost all pure states are uniquely determined by their RDMs. We further discuss circumstances where (1) can imply (2). We use convexity of the numerical range of operators to show that when only two observables are measured, (1) always implies (2). More generally, if there is a compact group of symmetries of the state space which has the span of the observables measured as the set of fixed points, then (1) implies (2). We analyze the possible dimensions for the span of such observables. Our results extend naturally to the case of low rank quantum states. }, doi = {10.1103/PhysRevA.88.012109}, url = {http://arxiv.org/abs/1212.3503v2}, author = {Jianxin Chen and Hillary Dawkins and Zhengfeng Ji and Nathaniel Johnston and David Kribs and Frederic Shultz and Bei Zeng} } @article {1221, title = {Universal computation by multi-particle quantum walk}, journal = {Science}, volume = {339}, year = {2013}, month = {2013/02/14}, pages = {791 - 794}, abstract = { A quantum walk is a time-homogeneous quantum-mechanical process on a graph defined by analogy to classical random walk. The quantum walker is a particle that moves from a given vertex to adjacent vertices in quantum superposition. Here we consider a generalization of quantum walk to systems with more than one walker. A continuous-time multi-particle quantum walk is generated by a time-independent Hamiltonian with a term corresponding to a single-particle quantum walk for each particle, along with an interaction term. Multi-particle quantum walk includes a broad class of interacting many-body systems such as the Bose-Hubbard model and systems of fermions or distinguishable particles with nearest-neighbor interactions. We show that multi-particle quantum walk is capable of universal quantum computation. Since it is also possible to efficiently simulate a multi-particle quantum walk of the type we consider using a universal quantum computer, this model exactly captures the power of quantum computation. In principle our construction could be used as an architecture for building a scalable quantum computer with no need for time-dependent control. }, doi = {10.1126/science.1229957}, url = {http://arxiv.org/abs/1205.3782v2}, author = {Andrew M. Childs and David Gosset and Zak Webb} } @article {1444, title = {Universal Entanglers for Bosonic and Fermionic Systems}, year = {2013}, month = {2013/05/31}, abstract = { A universal entangler (UE) is a unitary operation which maps all pure product states to entangled states. It is known that for a bipartite system of particles $1,2$ with a Hilbert space $\mathbb{C}^{d_1}\otimes\mathbb{C}^{d_2}$, a UE exists when $\min{(d_1,d_2)}\geq 3$ and $(d_1,d_2)\neq (3,3)$. It is also known that whenever a UE exists, almost all unitaries are UEs; however to verify whether a given unitary is a UE is very difficult since solving a quadratic system of equations is NP-hard in general. This work examines the existence and construction of UEs of bipartite bosonic/fermionic systems whose wave functions sit in the symmetric/antisymmetric subspace of $\mathbb{C}^{d}\otimes\mathbb{C}^{d}$. The development of a theory of UEs for these types of systems needs considerably different approaches from that used for UEs of distinguishable systems. This is because the general entanglement of identical particle systems cannot be discussed in the usual way due to the effect of (anti)-symmetrization which introduces "pseudo entanglement" that is inaccessible in practice. We show that, unlike the distinguishable particle case, UEs exist for bosonic/fermionic systems with Hilbert spaces which are symmetric (resp. antisymmetric) subspaces of $\mathbb{C}^{d}\otimes\mathbb{C}^{d}$ if and only if $d\geq 3$ (resp. $d\geq 8$). To prove this we employ algebraic geometry to reason about the different algebraic structures of the bosonic/fermionic systems. Additionally, due to the relatively simple coherent state form of unentangled bosonic states, we are able to give the explicit constructions of two bosonic UEs. Our investigation provides insight into the entanglement properties of systems of indisitinguishable particles, and in particular underscores the difference between the entanglement structures of bosonic, fermionic and distinguishable particle systems. }, url = {http://arxiv.org/abs/1305.7489v1}, author = {Joel Klassen and Jianxin Chen and Bei Zeng} } @article {1844, title = {Cavity QED with atomic mirrors}, journal = {New J. Phys.}, volume = {14}, year = {2012}, pages = {063003}, url = {http://iopscience.iop.org/1367-2630/14/6/063003/}, author = {D E Chang and Jiang, L and Alexey V. Gorshkov and H J Kimble} } @article {1458, title = {Comment on some results of Erdahl and the convex structure of reduced density matrices}, journal = {Journal of Mathematical Physics}, volume = {53}, year = {2012}, month = {2012/05/16}, pages = {072203}, abstract = { In J. Math. Phys. 13, 1608-1621 (1972), Erdahl considered the convex structure of the set of $N$-representable 2-body reduced density matrices in the case of fermions. Some of these results have a straightforward extension to the $m$-body setting and to the more general quantum marginal problem. We describe these extensions, but can not resolve a problem in the proof of Erdahl{\textquoteright}s claim that every extreme point is exposed in finite dimensions. Nevertheless, we can show that when $2m \geq N$ every extreme point of the set of $N$-representable $m$-body reduced density matrices has a unique pre-image in both the symmetric and anti-symmetric setting. Moreover, this extends to the quantum marginal setting for a pair of complementary $m$-body and $(N-m)$-body reduced density matrices. }, doi = {10.1063/1.4736842}, url = {http://arxiv.org/abs/1205.3682v1}, author = {Jianxin Chen and Zhengfeng Ji and Mary Beth Ruskai and Bei Zeng and Duan-Lu Zhou} } @article {1443, title = {Correlations in excited states of local Hamiltonians}, journal = {Physical Review A}, volume = {85}, year = {2012}, month = {2012/4/9}, abstract = { Physical properties of the ground and excited states of a $k$-local Hamiltonian are largely determined by the $k$-particle reduced density matrices ($k$-RDMs), or simply the $k$-matrix for fermionic systems---they are at least enough for the calculation of the ground state and excited state energies. Moreover, for a non-degenerate ground state of a $k$-local Hamiltonian, even the state itself is completely determined by its $k$-RDMs, and therefore contains no genuine ${>}k$-particle correlations, as they can be inferred from $k$-particle correlation functions. It is natural to ask whether a similar result holds for non-degenerate excited states. In fact, for fermionic systems, it has been conjectured that any non-degenerate excited state of a 2-local Hamiltonian is simultaneously a unique ground state of another 2-local Hamiltonian, hence is uniquely determined by its 2-matrix. And a weaker version of this conjecture states that any non-degenerate excited state of a 2-local Hamiltonian is uniquely determined by its 2-matrix among all the pure $n$-particle states. We construct explicit counterexamples to show that both conjectures are false. It means that correlations in excited states of local Hamiltonians could be dramatically different from those in ground states. We further show that any non-degenerate excited state of a $k$-local Hamiltonian is a unique ground state of another $2k$-local Hamiltonian, hence is uniquely determined by its $2k$-RDMs (or $2k$-matrix). }, doi = {10.1103/PhysRevA.85.040303}, url = {http://arxiv.org/abs/1106.1373v2}, author = {Jianxin Chen and Zhengfeng Ji and Zhaohui Wei and Bei Zeng} } @article {1448, title = {From Ground States to Local Hamiltonians}, journal = {Physical Review A}, volume = {86}, year = {2012}, month = {2012/8/30}, abstract = { Traditional quantum physics solves ground states for a given Hamiltonian, while quantum information science asks for the existence and construction of certain Hamiltonians for given ground states. In practical situations, one would be mainly interested in local Hamiltonians with certain interaction patterns, such as nearest neighbour interactions on some type of lattices. A necessary condition for a space $V$ to be the ground-state space of some local Hamiltonian with a given interaction pattern, is that the maximally mixed state supported on $V$ is uniquely determined by its reduced density matrices associated with the given pattern, based on the principle of maximum entropy. However, it is unclear whether this condition is in general also sufficient. We examine the situations for the existence of such a local Hamiltonian to have $V$ satisfying the necessary condition mentioned above as its ground-state space, by linking to faces of the convex body of the local reduced states. We further discuss some methods for constructing the corresponding local Hamiltonians with given interaction patterns, mainly from physical points of view, including constructions related to perturbation methods, local frustration-free Hamiltonians, as well as thermodynamical ensembles. }, doi = {10.1103/PhysRevA.86.022339}, url = {http://arxiv.org/abs/1110.6583v4}, author = {Jianxin Chen and Zhengfeng Ji and Bei Zeng and D. L. Zhou} } @article {1454, title = {Ground-State Spaces of Frustration-Free Hamiltonians}, journal = {Journal of Mathematical Physics}, volume = {53}, year = {2012}, month = {2012/01/01}, pages = {102201}, abstract = { We study the ground-state space properties for frustration-free Hamiltonians. We introduce a concept of {\textquoteleft}reduced spaces{\textquoteright} to characterize local structures of ground-state spaces. For a many-body system, we characterize mathematical structures for the set $\Theta_k$ of all the $k$-particle reduced spaces, which with a binary operation called join forms a semilattice that can be interpreted as an abstract convex structure. The smallest nonzero elements in $\Theta_k$, called atoms, are analogs of extreme points. We study the properties of atoms in $\Theta_k$ and discuss its relationship with ground states of $k$-local frustration-free Hamiltonians. For spin-1/2 systems, we show that all the atoms in $\Theta_2$ are unique ground states of some 2-local frustration-free Hamiltonians. Moreover, we show that the elements in $\Theta_k$ may not be the join of atoms, indicating a richer structure for $\Theta_k$ beyond the convex structure. Our study of $\Theta_k$ deepens the understanding of ground-state space properties for frustration-free Hamiltonians, from a new angle of reduced spaces. }, doi = {10.1063/1.4748527}, url = {http://arxiv.org/abs/1112.0762v1}, author = {Jianxin Chen and Zhengfeng Ji and David Kribs and Zhaohui Wei and Bei Zeng} } @article {1227, title = {Hamiltonian Simulation Using Linear Combinations of Unitary Operations}, journal = {Quantum Information and Computation}, volume = {12}, year = {2012}, month = {2012/11/01}, pages = {901-924}, abstract = { We present a new approach to simulating Hamiltonian dynamics based on implementing linear combinations of unitary operations rather than products of unitary operations. The resulting algorithm has superior performance to existing simulation algorithms based on product formulas and, most notably, scales better with the simulation error than any known Hamiltonian simulation technique. Our main tool is a general method to nearly deterministically implement linear combinations of nearby unitary operations, which we show is optimal among a large class of methods. }, url = {http://arxiv.org/abs/1202.5822v1}, author = {Andrew M. Childs and Nathan Wiebe} } @article {1228, title = {Levinson{\textquoteright}s theorem for graphs II}, journal = {Journal of Mathematical Physics}, volume = {53}, year = {2012}, month = {2012/11/21}, pages = {102207}, abstract = { We prove Levinson{\textquoteright}s theorem for scattering on an (m+n)-vertex graph with n semi-infinite paths each attached to a different vertex, generalizing a previous result for the case n=1. This theorem counts the number of bound states in terms of the winding of the determinant of the S-matrix. We also provide a proof that the bound states and incoming scattering states of the Hamiltonian together form a complete basis for the Hilbert space, generalizing another result for the case n=1. }, doi = {10.1063/1.4757665}, url = {http://arxiv.org/abs/1203.6557v2}, author = {Andrew M. Childs and David Gosset} } @article {1476, title = {Long-lived dipolar molecules and Feshbach molecules in a 3D optical lattice }, journal = {Physical Review Letters}, volume = {108}, year = {2012}, month = {2012/2/23}, abstract = { We have realized long-lived ground-state polar molecules in a 3D optical lattice, with a lifetime of up to 25 s, which is limited only by off-resonant scattering of the trapping light. Starting from a 2D optical lattice, we observe that the lifetime increases dramatically as a small lattice potential is added along the tube-shaped lattice traps. The 3D optical lattice also dramatically increases the lifetime for weakly bound Feshbach molecules. For a pure gas of Feshbach molecules, we observe a lifetime of >20 s in a 3D optical lattice; this represents a 100-fold improvement over previous results. This lifetime is also limited by off-resonant scattering, the rate of which is related to the size of the Feshbach molecule. Individually trapped Feshbach molecules in the 3D lattice can be converted to pairs of K and Rb atoms and back with nearly 100\% efficiency. }, doi = {10.1103/PhysRevLett.108.080405}, url = {http://arxiv.org/abs/1110.4420v1}, author = {Amodsen Chotia and Brian Neyenhuis and Steven A. Moses and Bo Yan and Jacob P. Covey and Michael Foss-Feig and Ana Maria Rey and Deborah S. Jin and Jun Ye} } @article {1449, title = {Minimum Entangling Power is Close to Its Maximum}, year = {2012}, month = {2012/10/04}, abstract = { Given a quantum gate $U$ acting on a bipartite quantum system, its maximum (average, minimum) entangling power is the maximum (average, minimum) entanglement generation with respect to certain entanglement measure when the inputs are restricted to be product states. In this paper, we mainly focus on the {\textquoteright}weakest{\textquoteright} one, i.e., the minimum entangling power, among all these entangling powers. We show that, by choosing von Neumann entropy of reduced density operator or Schmidt rank as entanglement measure, even the {\textquoteright}weakest{\textquoteright} entangling power is generically very close to its maximal possible entanglement generation. In other words, maximum, average and minimum entangling powers are generically close. We then study minimum entangling power with respect to other Lipschitiz-continuous entanglement measures and generalize our results to multipartite quantum systems. As a straightforward application, a random quantum gate will almost surely be an intrinsically fault-tolerant entangling device that will always transform every low-entangled state to near-maximally entangled state. }, url = {http://arxiv.org/abs/1210.1296v1}, author = {Jianxin Chen and Zhengfeng Ji and David W Kribs and Bei Zeng} } @article {1503, title = {Nanoplasmonic Lattices for Ultracold atoms}, journal = {Physical Review Letters}, volume = {109}, year = {2012}, month = {2012/12/6}, abstract = { We propose to use sub-wavelength confinement of light associated with the near field of plasmonic systems to create nanoscale optical lattices for ultracold atoms. Our approach combines the unique coherence properties of isolated atoms with the sub-wavelength manipulation and strong light-matter interaction associated with nano-plasmonic systems. It allows one to considerably increase the energy scales in the realization of Hubbard models and to engineer effective long-range interactions in coherent and dissipative many-body dynamics. Realistic imperfections and potential applications are discussed. }, doi = {10.1103/PhysRevLett.109.235309}, url = {http://arxiv.org/abs/1208.6293v3}, author = {Michael Gullans and T. Tiecke and D. E. Chang and J. Feist and J. D. Thompson and J. I. Cirac and P. Zoller and M. D. Lukin} } @article {1439, title = {Non-Additivity of the Entanglement of Purification (Beyond Reasonable Doubt) }, year = {2012}, month = {2012/06/06}, abstract = { We demonstrate the convexity of the difference between the regularized entanglement of purification and the entropy, as a function of the state. This is proved by means of a new asymptotic protocol to prepare a state from pre-shared entanglement and by local operations only. We go on to employ this convexity property in an investigation of the additivity of the (single-copy) entanglement of purification: using numerical results for two-qubit Werner states we find strong evidence that the entanglement of purification is different from its regularization, hence that entanglement of purification is not additive. }, url = {http://arxiv.org/abs/1206.1307v1}, author = {Jianxin Chen and Andreas Winter} } @article {1493, title = {Photonic quantum simulation of ground state configurations of Heisenberg square and checkerboard lattice spin systems }, year = {2012}, month = {2012/05/12}, abstract = { Photonic quantum simulators are promising candidates for providing insight into other small- to medium-sized quantum systems. The available photonic quantum technology is reaching the state where significant advantages arise for the quantum simulation of interesting questions in Heisenberg spin systems. Here we experimentally simulate such spin systems with single photons and linear optics. The effective Heisenberg-type interactions among individual single photons are realized by quantum interference at the tunable direction coupler followed by the measurement process. The effective interactions are characterized by comparing the entanglement dynamics using pairwise concurrence of a four-photon quantum system. We further show that photonic quantum simulations of generalized Heisenberg interactions on a four-site square lattice and a six-site checkerboard lattice are in reach of current technology. }, url = {http://arxiv.org/abs/1205.2801v1}, author = {Xiao-song Ma and Borivoje Dakic and Sebastian Kropatsche and William Naylor and Yang-hao Chan and Zhe-Xuan Gong and Lu-ming Duan and Anton Zeilinger and Philip Walther} } @article {1222, title = {The quantum query complexity of read-many formulas}, journal = {Lecture Notes in Computer Science}, volume = {7501}, year = {2012}, month = {2012/09/10}, pages = {337-348}, abstract = { The quantum query complexity of evaluating any read-once formula with n black-box input bits is Theta(sqrt(n)). However, the corresponding problem for read-many formulas (i.e., formulas in which the inputs have fanout) is not well understood. Although the optimal read-once formula evaluation algorithm can be applied to any formula, it can be suboptimal if the inputs have large fanout. We give an algorithm for evaluating any formula with n inputs, size S, and G gates using O(min{n, sqrt{S}, n^{1/2} G^{1/4}}) quantum queries. Furthermore, we show that this algorithm is optimal, since for any n,S,G there exists a formula with n inputs, size at most S, and at most G gates that requires Omega(min{n, sqrt{S}, n^{1/2} G^{1/4}}) queries. We also show that the algorithm remains nearly optimal for circuits of any particular depth k >= 3, and we give a linear-size circuit of depth 2 that requires Omega (n^{5/9}) queries. Applications of these results include a Omega (n^{19/18}) lower bound for Boolean matrix product verification, a nearly tight characterization of the quantum query complexity of evaluating constant-depth circuits with bounded fanout, new formula gate count lower bounds for several functions including PARITY, and a construction of an AC^0 circuit of linear size that can only be evaluated by a formula with Omega(n^{2-epsilon}) gates. }, doi = {10.1007/978-3-642-33090-2_30}, url = {http://arxiv.org/abs/1112.0548v1}, author = {Andrew M. Childs and Shelby Kimmel and Robin Kothari} } @article {1492, title = {Quantum Simulation of Spin Models on an Arbitrary Lattice with Trapped Ions }, journal = {New Journal of Physics}, volume = {14}, year = {2012}, month = {2012/09/27}, pages = {095024}, abstract = { A collection of trapped atomic ions represents one of the most attractive platforms for the quantum simulation of interacting spin networks and quantum magnetism. Spin-dependent optical dipole forces applied to an ion crystal create long-range effective spin-spin interactions and allow the simulation of spin Hamiltonians that possess nontrivial phases and dynamics. Here we show how appropriate design of laser fields can provide for arbitrary multidimensional spin-spin interaction graphs even for the case of a linear spatial array of ions. This scheme uses currently existing trap technology and is scalable to levels where classical methods of simulation are intractable. }, doi = {10.1088/1367-2630/14/9/095024}, url = {http://arxiv.org/abs/1201.0776v1}, author = {Simcha Korenblit and Dvir Kafri and Wess C. Campbell and Rajibul Islam and Emily E. Edwards and Zhe-Xuan Gong and Guin-Dar Lin and Luming Duan and Jungsang Kim and Kihwan Kim and Christopher Monroe} } @article {1456, title = {Rank Reduction for the Local Consistency Problem}, journal = {Journal of Mathematical Physics}, volume = {53}, year = {2012}, month = {2012/02/09}, pages = {022202}, abstract = { We address the problem of how simple a solution can be for a given quantum local consistency instance. More specifically, we investigate how small the rank of the global density operator can be if the local constraints are known to be compatible. We prove that any compatible local density operators can be satisfied by a low rank global density operator. Then we study both fermionic and bosonic versions of the N-representability problem as applications. After applying the channel-state duality, we prove that any compatible local channels can be obtained through a global quantum channel with small Kraus rank. }, doi = {10.1063/1.3685644}, url = {http://arxiv.org/abs/1106.3235v2}, author = {Jianxin Chen and Zhengfeng Ji and Alexander Klyachko and David W. Kribs and Bei Zeng} } @article {1200, title = {Scalable Architecture for a Room Temperature Solid-State Quantum Information Processor }, journal = {Nature Communications}, volume = {3}, year = {2012}, month = {2012/4/24}, pages = {800}, abstract = { The realization of a scalable quantum information processor has emerged over the past decade as one of the central challenges at the interface of fundamental science and engineering. Much progress has been made towards this goal. Indeed, quantum operations have been demonstrated on several trapped ion qubits, and other solid-state systems are approaching similar levels of control. Extending these techniques to achieve fault-tolerant operations in larger systems with more qubits remains an extremely challenging goal, in part, due to the substantial technical complexity of current implementations. Here, we propose and analyze an architecture for a scalable, solid-state quantum information processor capable of operating at or near room temperature. The architecture is applicable to realistic conditions, which include disorder and relevant decoherence mechanisms, and includes a hierarchy of control at successive length scales. Our approach is based upon recent experimental advances involving Nitrogen-Vacancy color centers in diamond and will provide fundamental insights into the physics of non-equilibrium many-body quantum systems. Additionally, the proposed architecture may greatly alleviate the stringent constraints, currently limiting the realization of scalable quantum processors. }, doi = {10.1038/ncomms1788}, url = {http://arxiv.org/abs/1012.2864v1}, author = {Norman Y. Yao and Liang Jiang and Alexey V. Gorshkov and Peter C. Maurer and Geza Giedke and J. Ignacio Cirac and Mikhail D. Lukin} } @article {1866, title = {Deciding Unitary Equivalence Between Matrix Polynomials and Sets of Bipartite Quantum States}, journal = {Quantum Information and Computation}, volume = {11}, year = {2011}, month = {2001/09/01}, pages = {813{\textendash}819}, abstract = {

In this brief report, we consider the equivalence between two sets of\ m\ + 1 bipartite quantum states under local unitary transformations. For pure states, this problem corresponds to the matrix algebra question of whether two degree m matrix polynomials are unitarily equivalent; i.e.\ UAiV\† =\ Bi\ for 0 \≤\ i\ \≤\ m\ where\ U\ and\ V\ are unitary and (Ai, Bi) are arbitrary pairs of rectangular matrices. We present a randomized polynomial-time algorithm that solves this problem with an arbitrarily high success probability and outputs transforming matrices\ U\ and\ V.

}, keywords = {matrix polynomials, Schwartz-Zippel lemma, unitary transformations}, issn = {1533-7146}, url = {http://dl.acm.org/citation.cfm?id=2230936.2230942}, author = {Chitambar, Eric and Carl Miller and Shi, Yaoyun} } @article {1303, title = {Detecting paired and counterflow superfluidity via dipole oscillations}, journal = {Physical Review A}, volume = {84}, year = {2011}, month = {2011/10/27}, abstract = { We suggest an experimentally feasible procedure to observe paired and counterflow superfluidity in ultra-cold atom systems. We study the time evolution of one-dimensional mixtures of bosonic atoms in an optical lattice following an abrupt displacement of an additional weak confining potential. We find that the dynamic responses of the paired superfluid phase for attractive inter-species interactions and the counterflow superfluid phase for repulsive interactions are qualitatively distinct and reflect the quasi long-range order that characterizes these states. These findings suggest a clear experimental procedure to detect these phases, and give an intuitive insight into their dynamics. }, doi = {10.1103/PhysRevA.84.041609}, url = {http://arxiv.org/abs/1103.3513v3}, author = {Anzi Hu and L. Mathey and Eite Tiesinga and Ippei Danshita and Carl J. Williams and Charles W. Clark} } @article {1457, title = {Entanglement can completely defeat quantum noise}, journal = {Physical Review Letters}, volume = {107}, year = {2011}, month = {2011/12/15}, abstract = { We describe two quantum channels that individually cannot send any information, even classical, without some chance of decoding error. But together a single use of each channel can send quantum information perfectly reliably. This proves that the zero-error classical capacity exhibits superactivation, the extreme form of the superadditivity phenomenon in which entangled inputs allow communication over zero capacity channels. But our result is stronger still, as it even allows zero-error quantum communication when the two channels are combined. Thus our result shows a new remarkable way in which entanglement across two systems can be used to resist noise, in this case perfectly. We also show a new form of superactivation by entanglement shared between sender and receiver. }, doi = {10.1103/PhysRevLett.107.250504}, url = {http://arxiv.org/abs/1109.0540v1}, author = {Jianxin Chen and Toby S. Cubitt and Aram W. Harrow and Graeme Smith} } @article {1351, title = {Fast and robust quantum computation with ionic Wigner crystals}, journal = {Physical Review A}, volume = {83}, year = {2011}, month = {2011/4/15}, abstract = {We present a detailed analysis of the modulated-carrier quantum phase gate implemented with Wigner crystals of ions confined in Penning traps. We elaborate on a recent scheme, proposed by two of the authors, to engineer two-body interactions between ions in such crystals. We analyze for the first time the situation in which the cyclotron (w_c) and the crystal rotation (w_r) frequencies do not fulfill the condition w_c=2w_r. It is shown that even in the presence of the magnetic field in the rotating frame the many-body (classical) Hamiltonian describing small oscillations from the ion equilibrium positions can be recast in canonical form. As a consequence, we are able to demonstrate that fast and robust two-qubit gates are achievable within the current experimental limitations. Moreover, we describe a realization of the state-dependent sign-changing dipole forces needed to realize the investigated quantum computing scheme. }, doi = {10.1103/PhysRevA.83.042319}, url = {http://arxiv.org/abs/1011.5616v2}, author = {J. D. Baltrusch and A. Negretti and J. M. Taylor and T. Calarco} } @article {1225, title = {Levinson{\textquoteright}s theorem for graphs}, journal = {Journal of Mathematical Physics}, volume = {52}, year = {2011}, month = {2011/06/30}, pages = {082102}, abstract = { We prove an analog of Levinson{\textquoteright}s theorem for scattering on a weighted (m+1)-vertex graph with a semi-infinite path attached to one of its vertices. In particular, we show that the number of bound states in such a scattering problem is equal to m minus half the winding number of the phase of the reflection coefficient (where each so-called half-bound state is counted as half a bound state). }, doi = {10.1063/1.3622608}, url = {http://arxiv.org/abs/1103.5077v2}, author = {Andrew M. Childs and DJ Strouse} } @article {1447, title = {No-go Theorem for One-way Quantum Computing on Naturally Occurring Two-level Systems }, journal = {Physical Review A}, volume = {83}, year = {2011}, month = {2011/5/9}, abstract = { One-way quantum computing achieves the full power of quantum computation by performing single particle measurements on some many-body entangled state, known as the resource state. As single particle measurements are relatively easy to implement, the preparation of the resource state becomes a crucial task. An appealing approach is simply to cool a strongly correlated quantum many-body system to its ground state. In addition to requiring the ground state of the system to be universal for one-way quantum computing, we also want the Hamiltonian to have non-degenerate ground state protected by a fixed energy gap, to involve only two-body interactions, and to be frustration-free so that measurements in the course of the computation leave the remaining particles in the ground space. Recently, significant efforts have been made to the search of resource states that appear naturally as ground states in spin lattice systems. The approach is proved to be successful in spin-5/2 and spin-3/2 systems. Yet, it remains an open question whether there could be such a natural resource state in a spin-1/2, i.e., qubit system. Here, we give a negative answer to this question by proving that it is impossible for a genuinely entangled qubit states to be a non-degenerate ground state of any two-body frustration-free Hamiltonian. What is more, we prove that every spin-1/2 frustration-free Hamiltonian with two-body interaction always has a ground state that is a product of single- or two-qubit states, a stronger result that is interesting independent of the context of one-way quantum computing. }, doi = {10.1103/PhysRevA.83.050301}, url = {http://arxiv.org/abs/1004.3787v1}, author = {Jianxin Chen and Xie Chen and Runyao Duan and Zhengfeng Ji and Bei Zeng} } @article {1181, title = {Quantum Magnetism with Polar Alkali Dimers}, journal = {Physical Review A}, volume = {84}, year = {2011}, month = {2011/9/15}, abstract = { We show that dipolar interactions between ultracold polar alkali dimers in optical lattices can be used to realize a highly tunable generalization of the t-J model, which we refer to as the t-J-V-W model. The model features long-range spin-spin interactions J_z and J_perp of XXZ type, long-range density-density interaction V, and long-range density-spin interaction W, all of which can be controlled in both magnitude and sign independently of each other and of the tunneling t. The "spin" is encoded in the rotational degree of freedom of the molecules, while the interactions are controlled by applied static electric and continuous-wave microwave fields. Furthermore, we show that nuclear spins of the molecules can be used to implement an additional (orbital) degree of freedom that is coupled to the original rotational degree of freedom in a tunable way. The presented system is expected to exhibit exotic physics and to provide insights into strongly correlated phenomena in condensed matter systems. Realistic experimental imperfections are discussed. }, doi = {10.1103/PhysRevA.84.033619}, url = {http://arxiv.org/abs/1106.1655v1}, author = {Alexey V. Gorshkov and Salvatore R. Manmana and Gang Chen and Eugene Demler and Mikhail D. Lukin and Ana Maria Rey} } @article {1846, title = {Quantum magnetism with polar alkali-metal dimers}, journal = {Phys. Rev. A}, volume = {84}, year = {2011}, pages = {033619}, url = {http://link.aps.org/abstract/PRA/v84/e033619/}, author = {Alexey V. Gorshkov and Manmana, S R and Chen, G and Demler, E and Lukin, M D and Rey, A M} } @article {1224, title = {Quantum query complexity of minor-closed graph properties}, journal = {Proc. 28th Symposium on Theoretical Aspects of Computer Science (STACS 2011), Leibniz International Proceedings in Informatics}, volume = {9}, year = {2011}, month = {2011/01/01}, pages = {661-672}, abstract = { We study the quantum query complexity of minor-closed graph properties, which include such problems as determining whether an $n$-vertex graph is planar, is a forest, or does not contain a path of a given length. We show that most minor-closed properties---those that cannot be characterized by a finite set of forbidden subgraphs---have quantum query complexity \Theta(n^{3/2}). To establish this, we prove an adversary lower bound using a detailed analysis of the structure of minor-closed properties with respect to forbidden topological minors and forbidden subgraphs. On the other hand, we show that minor-closed properties (and more generally, sparse graph properties) that can be characterized by finitely many forbidden subgraphs can be solved strictly faster, in o(n^{3/2}) queries. Our algorithms are a novel application of the quantum walk search framework and give improved upper bounds for several subgraph-finding problems. }, doi = {10.4230/LIPIcs.STACS.2011.661}, url = {http://arxiv.org/abs/1011.1443v2}, author = {Andrew M. Childs and Robin Kothari} } @article {1446, title = {Superactivation of the Asymptotic Zero-Error Classical Capacity of a Quantum Channel}, journal = {IEEE Transactions on Information Theory}, volume = {57}, year = {2011}, month = {2011/12/01}, pages = {8114 - 8126}, abstract = { The zero-error classical capacity of a quantum channel is the asymptotic rate at which it can be used to send classical bits perfectly, so that they can be decoded with zero probability of error. We show that there exist pairs of quantum channels, neither of which individually have any zero-error capacity whatsoever (even if arbitrarily many uses of the channels are available), but such that access to even a single copy of both channels allows classical information to be sent perfectly reliably. In other words, we prove that the zero-error classical capacity can be superactivated. This result is the first example of superactivation of a classical capacity of a quantum channel. }, doi = {10.1109/TIT.2011.2169109}, url = {http://arxiv.org/abs/0906.2547v3}, author = {Toby S. Cubitt and Jianxin Chen and Aram W. Harrow} } @article {1198, title = {Tunable Superfluidity and Quantum Magnetism with Ultracold Polar Molecules }, journal = {Physical Review Letters}, volume = {107}, year = {2011}, month = {2011/9/8}, abstract = { By selecting two dressed rotational states of ultracold polar molecules in an optical lattice, we obtain a highly tunable generalization of the t-J model, which we refer to as the t-J-V-W model. In addition to XXZ spin exchange, the model features density-density interactions and novel density-spin interactions; all interactions are dipolar. We show that full control of all interaction parameters in both magnitude and sign can be achieved independently of each other and of the tunneling. As a first step towards demonstrating the potential of the system, we apply the density matrix renormalization group method (DMRG) to obtain the 1D phase diagram of the simplest experimentally realizable case. Specifically, we show that the tunability and the long-range nature of the interactions in the t-J-V-W model enable enhanced superfluidity. Finally, we show that Bloch oscillations in a tilted lattice can be used to probe the phase diagram experimentally. }, doi = {10.1103/PhysRevLett.107.115301}, url = {http://arxiv.org/abs/1106.1644v1}, author = {Alexey V. Gorshkov and Salvatore R. Manmana and Gang Chen and Jun Ye and Eugene Demler and Mikhail D. Lukin and Ana Maria Rey} } @article {1242, title = {Characterization of universal two-qubit Hamiltonians}, year = {2010}, month = {2010/04/09}, abstract = { Suppose we can apply a given 2-qubit Hamiltonian H to any (ordered) pair of qubits. We say H is n-universal if it can be used to approximate any unitary operation on n qubits. While it is well known that almost any 2-qubit Hamiltonian is 2-universal (Deutsch, Barenco, Ekert 1995; Lloyd 1995), an explicit characterization of the set of non-universal 2-qubit Hamiltonians has been elusive. Our main result is a complete characterization of 2-non-universal 2-qubit Hamiltonians. In particular, there are three ways that a 2-qubit Hamiltonian H can fail to be universal: (1) H shares an eigenvector with the gate that swaps two qubits, (2) H acts on the two qubits independently (in any of a certain family of bases), or (3) H has zero trace. A 2-non-universal 2-qubit Hamiltonian can still be n-universal for some n >= 3. We give some partial results on 3-universality. Finally, we also show how our characterization of 2-universal Hamiltonians implies the well-known result that almost any 2-qubit unitary is universal. }, url = {http://arxiv.org/abs/1004.1645v2}, author = {Andrew M. Childs and Debbie Leung and Laura Mancinska and Maris Ozols} } @article {1436, title = {Efficient quantum state tomography}, journal = {Nature Communications}, volume = {1}, year = {2010}, month = {2010/12/21}, pages = {149}, abstract = { Quantum state tomography, the ability to deduce the state of a quantum system from measured data, is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger systems it becomes infeasible because the number of quantum measurements and the amount of computation required to process them grows exponentially in the system size. Here we show that we can do exponentially better than direct state tomography for a wide range of quantum states, in particular those that are well approximated by a matrix product state ansatz. We present two schemes for tomography in 1-D quantum systems and touch on generalizations. One scheme requires unitary operations on a constant number of subsystems, while the other requires only local measurements together with more elaborate post-processing. Both schemes rely only on a linear number of experimental operations and classical postprocessing that is polynomial in the system size. A further strength of the methods is that the accuracy of the reconstructed states can be rigorously certified without any a priori assumptions. }, doi = {10.1038/ncomms1147}, url = {http://arxiv.org/abs/1101.4366v1}, author = {Marcus Cramer and Martin B. Plenio and Steven T. Flammia and David Gross and Stephen D. Bartlett and Rolando Somma and Olivier Landon-Cardinal and Yi-Kai Liu and David Poulin} } @article {1284, title = {Feshbach Resonances in Ultracold Gases}, journal = {Reviews of Modern Physics}, volume = {82}, year = {2010}, month = {2010/4/29}, pages = {1225 - 1286}, abstract = { Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This Review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules. }, doi = {10.1103/RevModPhys.82.1225}, url = {http://arxiv.org/abs/0812.1496v2}, author = {Cheng Chin and Rudolf Grimm and Paul Julienne and Eite Tiesinga} } @article {1868, title = {Matrix pencils and entanglement classification}, journal = {Journal of Mathematical Physics}, volume = {51}, year = {2010}, month = {2010/01/01}, pages = {072205}, abstract = {

Quantum entanglement plays a central role in quantum information processing. A main objective of the theory is to classify different types of entanglement according to their interconvertibility through manipulations that do not require additional entanglement to perform. While bipartite entanglement is well understood in this framework, the classification of entanglements among three or more subsystems is inherently much more difficult. In this paper, we study pure state entanglement in systems of dimension\ 2\⊗m\⊗n. Two states are considered equivalent if they can be reversibly converted from one to the other with a nonzero probability using only local quantum resources and classical communication (SLOCC). We introduce a connection between entanglement manipulations in these systems and the well-studied theory of matrix pencils. All previous attempts to study general SLOCC equivalence in such systems have relied on somewhat contrived techniques which fail to reveal the elegant structure of the problem that can be seen from the matrix pencil approach. Based on this method, we report the first polynomial-time algorithm for deciding when two2\⊗m\⊗n\ states are SLOCC equivalent. We then proceed to present a canonical form for all\ 2\⊗m\⊗n\ states based on the matrix pencil construction such that two states are equivalent if and only if they have the same canonical form. Besides recovering the previously known 26 distinct SLOCC equivalence classes in\ 2\⊗3\⊗n\ systems, we also determine the hierarchy between these classes.

}, issn = {00222488}, doi = {10.1063/1.3459069}, url = {http://scitation.aip.org/content/aip/journal/jmp/51/7/10.1063/1.3459069}, author = {Chitambar, Eric and Carl Miller and Shi, Yaoyun} } @article {1413, title = {Noise correlations of one-dimensional Bose mixtures in optical lattices}, journal = {Physical Review A}, volume = {81}, year = {2010}, month = {2010/6/2}, abstract = { We study the noise correlations of one-dimensional binary Bose mixtures, as a probe of their quantum phases. In previous work, we found a rich structure of many-body phases in such mixtures, such as paired and counterflow superfluidity. Here we investigate the signature of these phases in the noise correlations of the atomic cloud after time-of-flight expansion, using both Luttinger liquid theory and the time-evolving block decimation (TEBD) method. We find that paired and counterflow superfluidity exhibit distinctive features in the noise spectra. We treat both extended and inhomogeneous systems, and our numerical work shows that the essential physics of the extended systems is present in the trapped-atom systems of current experimental interest. For paired and counterflow superfluid phases, we suggest methods for extracting Luttinger parameters from noise correlation spectroscopy. }, doi = {10.1103/PhysRevA.81.063602}, url = {http://arxiv.org/abs/1002.4918v2}, author = {Anzi Hu and L. Mathey and Carl J. Williams and Charles W. Clark} } @article {1442, title = {Optimal Perfect Distinguishability between Unitaries and Quantum Operations }, year = {2010}, month = {2010/10/12}, abstract = { We study optimal perfect distinguishability between a unitary and a general quantum operation. In 2-dimensional case we provide a simple sufficient and necessary condition for sequential perfect distinguishability and an analytical formula of optimal query time. We extend the sequential condition to general d-dimensional case. Meanwhile, we provide an upper bound and a lower bound for optimal sequential query time. In the process a new iterative method is given, the most notable innovation of which is its independence to auxiliary systems or entanglement. Following the idea, we further obtain an upper bound and a lower bound of (entanglement-assisted) q-maximal fidelities between a unitary and a quantum operation. Thus by the recursion in [1] an upper bound and a lower bound for optimal general perfect discrimination are achieved. Finally our lower bound result can be extended to the case of arbitrary two quantum operations. }, url = {http://arxiv.org/abs/1010.2298v1}, author = {Cheng Lu and Jianxin Chen and Runyao Duan} } @article {1455, title = {Principle of Maximum Entropy and Ground Spaces of Local Hamiltonians}, year = {2010}, month = {2010/10/13}, abstract = { The structure of the ground spaces of quantum systems consisting of local interactions is of fundamental importance to different areas of physics. In this Letter, we present a necessary and sufficient condition for a subspace to be the ground space of a k-local Hamiltonian. Our analysis are motivated by the concept of irreducible correlations studied by [Linden et al., PRL 89, 277906] and [Zhou, PRL 101, 180505], which is in turn based on the principle of maximum entropy. It establishes a better understanding of the ground spaces of local Hamiltonians and builds an intimate link of ground spaces to the correlations of quantum states. }, url = {http://arxiv.org/abs/1010.2739v4}, author = {Jianxin Chen and Zhengfeng Ji and Mary Beth Ruskai and Bei Zeng and Duanlu Zhou} } @article {1218, title = {Quantum algorithms for algebraic problems}, journal = {Reviews of Modern Physics}, volume = {82}, year = {2010}, month = {2010/1/15}, pages = {1 - 52}, abstract = { Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for classical computers. Understanding what other computational problems can be solved significantly faster using quantum algorithms is one of the major challenges in the theory of quantum computation, and such algorithms motivate the formidable task of building a large-scale quantum computer. This article reviews the current state of quantum algorithms, focusing on algorithms with superpolynomial speedup over classical computation, and in particular, on problems with an algebraic flavor. }, doi = {10.1103/RevModPhys.82.1}, url = {http://arxiv.org/abs/0812.0380v1}, author = {Andrew M. Childs and Wim van Dam} } @article {1243, title = {Quantum property testing for bounded-degree graphs}, journal = {Proc. RANDOM}, year = {2010}, month = {2010/12/14}, pages = {365-376}, abstract = { We study quantum algorithms for testing bipartiteness and expansion of bounded-degree graphs. We give quantum algorithms that solve these problems in time O(N^(1/3)), beating the Omega(sqrt(N)) classical lower bound. For testing expansion, we also prove an Omega(N^(1/4)) quantum query lower bound, thus ruling out the possibility of an exponential quantum speedup. Our quantum algorithms follow from a combination of classical property testing techniques due to Goldreich and Ron, derandomization, and the quantum algorithm for element distinctness. The quantum lower bound is obtained by the polynomial method, using novel algebraic techniques and combinatorial analysis to accommodate the graph structure. }, doi = {10.1007/978-3-642-22935-0_31}, url = {http://arxiv.org/abs/1012.3174v3}, author = {Andris Ambainis and Andrew M. Childs and Yi-Kai Liu} } @article {1206, title = {On the relationship between continuous- and discrete-time quantum walk}, journal = {Communications in Mathematical Physics}, volume = {294}, year = {2010}, month = {2009/10/10}, pages = {581 - 603}, abstract = { Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or discrete time. But whereas a continuous-time random walk can be obtained as the limit of a sequence of discrete-time random walks, the two types of quantum walk appear fundamentally different, owing to the need for extra degrees of freedom in the discrete-time case. In this article, I describe a precise correspondence between continuous- and discrete-time quantum walks on arbitrary graphs. Using this correspondence, I show that continuous-time quantum walk can be obtained as an appropriate limit of discrete-time quantum walks. The correspondence also leads to a new technique for simulating Hamiltonian dynamics, giving efficient simulations even in cases where the Hamiltonian is not sparse. The complexity of the simulation is linear in the total evolution time, an improvement over simulations based on high-order approximations of the Lie product formula. As applications, I describe a continuous-time quantum walk algorithm for element distinctness and show how to optimally simulate continuous-time query algorithms of a certain form in the conventional quantum query model. Finally, I discuss limitations of the method for simulating Hamiltonians with negative matrix elements, and present two problems that motivate attempting to circumvent these limitations. }, doi = {10.1007/s00220-009-0930-1}, url = {http://arxiv.org/abs/0810.0312v3}, author = {Andrew M. Childs} } @article {1223, title = {Simulating sparse Hamiltonians with star decompositions}, year = {2010}, month = {2010/03/18}, abstract = { We present an efficient algorithm for simulating the time evolution due to a sparse Hamiltonian. In terms of the maximum degree d and dimension N of the space on which the Hamiltonian H acts for time t, this algorithm uses (d^2(d+log* N)||Ht||)^{1+o(1)} queries. This improves the complexity of the sparse Hamiltonian simulation algorithm of Berry, Ahokas, Cleve, and Sanders, which scales like (d^4(log* N)||Ht||)^{1+o(1)}. To achieve this, we decompose a general sparse Hamiltonian into a small sum of Hamiltonians whose graphs of non-zero entries have the property that every connected component is a star, and efficiently simulate each of these pieces. }, doi = {10.1007/978-3-642-18073-6_8}, url = {http://arxiv.org/abs/1003.3683v2}, author = {Andrew M. Childs and Robin Kothari} } @article {1220, title = {Black-box Hamiltonian simulation and unitary implementation}, year = {2009}, month = {2009/10/22}, abstract = { We present general methods for simulating black-box Hamiltonians using quantum walks. These techniques have two main applications: simulating sparse Hamiltonians and implementing black-box unitary operations. In particular, we give the best known simulation of sparse Hamiltonians with constant precision. Our method has complexity linear in both the sparseness D (the maximum number of nonzero elements in a column) and the evolution time t, whereas previous methods had complexity scaling as D^4 and were superlinear in t. We also consider the task of implementing an arbitrary unitary operation given a black-box description of its matrix elements. Whereas standard methods for performing an explicitly specified N x N unitary operation use O(N^2) elementary gates, we show that a black-box unitary can be performed with bounded error using O(N^{2/3} (log log N)^{4/3}) queries to its matrix elements. In fact, except for pathological cases, it appears that most unitaries can be performed with only O(sqrt{N}) queries, which is optimal. }, url = {http://arxiv.org/abs/0910.4157v4}, author = {Dominic W. Berry and Andrew M. Childs} } @article {1293, title = {Collisional cooling of ultra-cold atom ensembles using Feshbach resonances }, journal = {Physical Review A}, volume = {80}, year = {2009}, month = {2009/9/8}, abstract = { We propose a new type of cooling mechanism for ultra-cold fermionic atom ensembles, which capitalizes on the energy dependence of inelastic collisions in the presence of a Feshbach resonance. We first discuss the case of a single magnetic resonance, and find that the final temperature and the cooling rate is limited by the width of the resonance. A concrete example, based on a p-wave resonance of $^{40}$K, is given. We then improve upon this setup by using both a very sharp optical or radio-frequency induced resonance and a very broad magnetic resonance and show that one can improve upon temperatures reached with current technologies. }, doi = {10.1103/PhysRevA.80.030702}, url = {http://arxiv.org/abs/0903.2568v1}, author = {L. Mathey and Eite Tiesinga and Paul S. Julienne and Charles W. Clark} } @article {1299, title = {Counterflow and paired superfluidity in one-dimensional Bose mixtures in optical lattices }, journal = {Physical Review A}, volume = {80}, year = {2009}, month = {2009/8/24}, abstract = { We study the quantum phases of mixtures of ultra-cold bosonic atoms held in an optical lattice that confines motion or hopping to one spatial dimension. The phases are found by using Tomonaga-Luttinger liquid theory as well as the numerical method of time evolving block decimation (TEBD). We consider a binary mixture with repulsive intra-species interactions, and either repulsive or attractive inter-species interaction. For a homogeneous system, we find paired- and counterflow-superfluid phases at different filling and hopping energies. We also predict parameter regions in which these types of superfluid order coexist with charge density wave order. We show that the Tomonaga-Luttinger liquid theory and TEBD qualitatively agree on the location of the phase boundary to superfluidity. We then describe how these phases are modified and can be detected when an additional harmonic trap is present. In particular, we show how experimentally measurable quantities, such as time-of-flight images and the structure factor, can be used to distinguish the quantum phases. Finally, we suggest applying a Feshbach ramp to detect the paired superfluid state, and a $\pi/2$ pulse followed by Bragg spectroscopy to detect the counterflow superfluid phase. }, doi = {10.1103/PhysRevA.80.023619}, url = {http://arxiv.org/abs/0906.2150v1}, author = {Anzi Hu and L. Mathey and Ippei Danshita and Eite Tiesinga and Carl J. Williams and Charles W. Clark} } @article {1254, title = {Discrete-query quantum algorithm for NAND trees}, journal = {Theory of Computing}, volume = {5}, year = {2009}, month = {2009/07/01}, pages = {119 - 123}, abstract = { Recently, Farhi, Goldstone, and Gutmann gave a quantum algorithm for evaluating NAND trees that runs in time O(sqrt(N log N)) in the Hamiltonian query model. In this note, we point out that their algorithm can be converted into an algorithm using O(N^{1/2 + epsilon}) queries in the conventional quantum query model, for any fixed epsilon > 0. }, doi = {10.4086/toc.2009.v005a005}, url = {http://arxiv.org/abs/quant-ph/0702160v1}, author = {Andrew M. Childs and Richard Cleve and Stephen P. Jordan and David Yeung} } @article {1219, title = {Limitations on the simulation of non-sparse Hamiltonians}, year = {2009}, month = {2009/08/31}, abstract = { The problem of simulating sparse Hamiltonians on quantum computers is well studied. The evolution of a sparse N x N Hamiltonian H for time t can be simulated using O(||Ht||poly(log N)) operations, which is essentially optimal due to a no--fast-forwarding theorem. Here, we consider non-sparse Hamiltonians and show significant limitations on their simulation. We generalize the no--fast-forwarding theorem to dense Hamiltonians, ruling out generic simulations taking time o(||Ht||), even though ||H|| is not a unique measure of the size of a dense Hamiltonian $H$. We also present a stronger limitation ruling out the possibility of generic simulations taking time poly(||Ht||,log N), showing that known simulations based on discrete-time quantum walk cannot be dramatically improved in general. On the positive side, we show that some non-sparse Hamiltonians can be simulated efficiently, such as those with graphs of small arboricity. }, url = {http://arxiv.org/abs/0908.4398v2}, author = {Andrew M. Childs and Robin Kothari} } @article {1256, title = {The quantum query complexity of certification}, year = {2009}, month = {2009/03/06}, abstract = { We study the quantum query complexity of finding a certificate for a d-regular, k-level balanced NAND formula. Up to logarithmic factors, we show that the query complexity is Theta(d^{(k+1)/2}) for 0-certificates, and Theta(d^{k/2}) for 1-certificates. In particular, this shows that the zero-error quantum query complexity of evaluating such formulas is O(d^{(k+1)/2}) (again neglecting a logarithmic factor). Our lower bound relies on the fact that the quantum adversary method obeys a direct sum theorem. }, url = {http://arxiv.org/abs/0903.1291v2}, author = {Andris Ambainis and Andrew M. Childs and Fran{\c c}ois Le Gall and Seiichiro Tani} } @article {1205, title = {Universal computation by quantum walk}, journal = {Physical Review Letters}, volume = {102}, year = {2009}, month = {2009/5/4}, abstract = { In some of the earliest work on quantum mechanical computers, Feynman showed how to implement universal quantum computation by the dynamics of a time-independent Hamiltonian. I show that this remains possible even if the Hamiltonian is restricted to be a sparse matrix with all entries equal to 0 or 1, i.e., the adjacency matrix of a low-degree graph. Thus quantum walk can be regarded as a universal computational primitive, with any desired quantum computation encoded entirely in some underlying graph. The main idea of the construction is to implement quantum gates by scattering processes. }, doi = {10.1103/PhysRevLett.102.180501}, url = {http://arxiv.org/abs/0806.1972v1}, author = {Andrew M. Childs} } @article {1438, title = {Ancilla-Assisted Discrimination of Quantum Gates}, year = {2008}, month = {2008/09/02}, abstract = { The intrinsic idea of superdense coding is to find as many gates as possible such that they can be perfectly discriminated. In this paper, we consider a new scheme of discrimination of quantum gates, called ancilla-assisted discrimination, in which a set of quantum gates on a $d-$dimensional system are perfectly discriminated with assistance from an $r-$dimensional ancilla system. The main contribution of the present paper is two-fold: (1) The number of quantum gates that can be discriminated in this scheme is evaluated. We prove that any $rd+1$ quantum gates cannot be perfectly discriminated with assistance from the ancilla, and there exist $rd$ quantum gates which can be perfectly discriminated with assistance from the ancilla. (2) The dimensionality of the minimal ancilla system is estimated. We prove that there exists a constant positive number $c$ such that for any $k\leq cr$ quantum gates, if they are $d$-assisted discriminable, then they are also $r$-assisted discriminable, and there are $c^{\prime}r\textrm{}(c^{\prime}>c)$ different quantum gates which can be discriminated with a $d-$dimensional ancilla, but they cannot be discriminated if the ancilla is reduced to an $r-$dimensional system. Thus, the order $O(r)$ of the number of quantum gates that can be discriminated with assistance from an $r-$dimensional ancilla is optimal. The results reported in this paper represent a preliminary step toward understanding the role ancilla system plays in discrimination of quantum gates as well as the power and limit of superdense coding. }, url = {http://arxiv.org/abs/0809.0336v1}, author = {Jianxin Chen and Mingsheng Ying} } @article {1355, title = {Coherence of an optically illuminated single nuclear spin qubit}, journal = {Physical Review Letters}, volume = {100}, year = {2008}, month = {2008/2/19}, abstract = {We investigate the coherence properties of individual nuclear spin quantum bits in diamond [Dutt et al., Science, 316, 1312 (2007)] when a proximal electronic spin associated with a nitrogen-vacancy (NV) center is being interrogated by optical radiation. The resulting nuclear spin dynamics are governed by time-dependent hyperfine interaction associated with rapid electronic transitions, which can be described by a spin-fluctuator model. We show that due to a process analogous to motional averaging in nuclear magnetic resonance, the nuclear spin coherence can be preserved after a large number of optical excitation cycles. Our theoretical analysis is in good agreement with experimental results. It indicates a novel approach that could potentially isolate the nuclear spin system completely from the electronic environment. }, doi = {10.1103/PhysRevLett.100.073001}, url = {http://arxiv.org/abs/0707.1341v2}, author = {Liang Jiang and M. V. Gurudev Dutt and Emre Togan and Lily Childress and Paola Cappellaro and J. M. Taylor and Mikhail D. Lukin} } @article {1453, title = {Existence of Universal Entangler}, journal = {Journal of Mathematical Physics}, volume = {49}, year = {2008}, month = {2008/01/01}, pages = {012103}, abstract = { A gate is called entangler if it transforms some (pure) product states to entangled states. A universal entangler is a gate which transforms all product states to entangled states. In practice, a universal entangler is a very powerful device for generating entanglements, and thus provides important physical resources for accomplishing many tasks in quantum computing and quantum information. This Letter demonstrates that a universal entangler always exists except for a degenerated case. Nevertheless, the problem how to find a universal entangler remains open. }, doi = {10.1063/1.2829895}, url = {http://arxiv.org/abs/0704.1473v2}, author = {Jianxin Chen and Runyao Duan and Zhengfeng Ji and Mingsheng Ying and Jun Yu} } @article {1354, title = {High-sensitivity diamond magnetometer with nanoscale resolution}, journal = {Nature Physics}, volume = {4}, year = {2008}, month = {2008/9/14}, pages = {810 - 816}, abstract = {We present a novel approach to the detection of weak magnetic fields that takes advantage of recently developed techniques for the coherent control of solid-state electron spin quantum bits. Specifically, we investigate a magnetic sensor based on Nitrogen-Vacancy centers in room-temperature diamond. We discuss two important applications of this technique: a nanoscale magnetometer that could potentially detect precession of single nuclear spins and an optical magnetic field imager combining spatial resolution ranging from micrometers to millimeters with a sensitivity approaching few femtotesla/Hz$^{1/2}$. }, doi = {10.1038/nphys1075}, url = {http://arxiv.org/abs/0805.1367v1}, author = {J. M. Taylor and P. Cappellaro and L. Childress and L. Jiang and D. Budker and P. R. Hemmer and A. Yacoby and R. Walsworth and M. D. Lukin} } @article {1169, title = {Photon storage in Lambda-type optically dense atomic media. IV. Optimal control using gradient ascent }, journal = {Physical Review A}, volume = {77}, year = {2008}, month = {2008/4/4}, abstract = { We use the numerical gradient ascent method from optimal control theory to extend efficient photon storage in Lambda-type media to previously inaccessible regimes and to provide simple intuitive explanations for our optimization techniques. In particular, by using gradient ascent to shape classical control pulses used to mediate photon storage, we open up the possibility of high efficiency photon storage in the non-adiabatic limit, in which analytical solutions to the equations of motion do not exist. This control shaping technique enables an order-of-magnitude increase in the bandwidth of the memory. We also demonstrate that the often discussed connection between time reversal and optimality in photon storage follows naturally from gradient ascent. Finally, we discuss the optimization of controlled reversible inhomogeneous broadening. }, doi = {10.1103/PhysRevA.77.043806}, url = {http://arxiv.org/abs/0710.2698v2}, author = {Alexey V. Gorshkov and Tommaso Calarco and Mikhail D. Lukin and Anders S. Sorensen} } @article {1292, title = {Tunneling phase gate for neutral atoms in a double-well lattice}, journal = {Physical Review A}, volume = {77}, year = {2008}, month = {2008/5/12}, abstract = { We propose a new two--qubit phase gate for ultra--cold atoms confined in an experimentally realized tilted double--well optical lattice [Sebby--Strabley et al., Phys. Rev. A {\bf 73} 033605 (2006)]. Such a lattice is capable of confining pairs of atoms in a two--dimensional array of double--well potentials where control can be exercised over the barrier height and the energy difference of the minima of the two wells (known as the {\textquoteleft}{\textquoteleft}tilt{\textquoteright}{\textquoteright}). The four lowest single--particle motional states consist of two pairs of motional states in which each pair is localized on one side of the central barrier, allowing for two atoms confined in such a lattice to be spatially separated qubits. We present a time--dependent scheme to manipulate the tilt to induce tunneling oscillations which produce a collisional phase gate. Numerical simulations demonstrate that this gate can be performed with high fidelity. }, doi = {10.1103/PhysRevA.77.050304}, url = {http://arxiv.org/abs/0712.1856v1}, author = {Frederick W. Strauch and Mark Edwards and Eite Tiesinga and Carl J. Williams and Charles W. Clark} } @article {1357, title = {Wigner crystals of ions as quantum hard drives}, journal = {Physical Review A}, volume = {78}, year = {2008}, month = {2008/12/18}, abstract = {Atomic systems in regular lattices are intriguing systems for implementing ideas in quantum simulation and information processing. Focusing on laser cooled ions forming Wigner crystals in Penning traps, we find a robust and simple approach to engineering non-trivial 2-body interactions sufficient for universal quantum computation. We then consider extensions of our approach to the fast generation of large cluster states, and a non-local architecture using an asymmetric entanglement generation procedure between a Penning trap system and well-established linear Paul trap designs. }, doi = {10.1103/PhysRevA.78.062331}, url = {http://arxiv.org/abs/0706.1951v1}, author = {J. M. Taylor and T. Calarco} } @article {1255, title = {Every NAND formula of size N can be evaluated in time N^{1/2+o(1)} on a quantum computer }, year = {2007}, month = {2007/03/02}, abstract = { For every NAND formula of size N, there is a bounded-error N^{1/2+o(1)}-time quantum algorithm, based on a coined quantum walk, that evaluates this formula on a black-box input. Balanced, or {\textquoteleft}{\textquoteleft}approximately balanced,{\textquoteright}{\textquoteright} NAND formulas can be evaluated in O(sqrt{N}) queries, which is optimal. It follows that the (2-o(1))-th power of the quantum query complexity is a lower bound on the formula size, almost solving in the positive an open problem posed by Laplante, Lee and Szegedy. }, url = {http://arxiv.org/abs/quant-ph/0703015v3}, author = {Andrew M. Childs and Ben W. Reichardt and Robert Spalek and Shengyu Zhang} } @article {1253, title = {Improved quantum algorithms for the ordered search problem via semidefinite programming }, journal = {Physical Review A}, volume = {75}, year = {2007}, month = {2007/3/26}, abstract = { One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem using a constant factor fewer queries. However, the precise value of this constant is unknown. By characterizing a class of quantum query algorithms for ordered search in terms of a semidefinite program, we find new quantum algorithms for small instances of the ordered search problem. Extending these algorithms to arbitrarily large instances using recursion, we show that there is an exact quantum ordered search algorithm using 4 log_{605} N \approx 0.433 log_2 N queries, which improves upon the previously best known exact algorithm. }, doi = {10.1103/PhysRevA.75.032335}, url = {http://arxiv.org/abs/quant-ph/0608161v1}, author = {Andrew M. Childs and Andrew J. Landahl and Pablo A. Parrilo} } @article {1214, title = {The limitations of nice mutually unbiased bases}, journal = {Journal of Algebraic Combinatorics}, volume = {25}, year = {2007}, month = {2006/7/11}, pages = {111 - 123}, abstract = { Mutually unbiased bases of a Hilbert space can be constructed by partitioning a unitary error basis. We consider this construction when the unitary error basis is a nice error basis. We show that the number of resulting mutually unbiased bases can be at most one plus the smallest prime power contained in the dimension, and therefore that this construction cannot improve upon previous approaches. We prove this by establishing a correspondence between nice mutually unbiased bases and abelian subgroups of the index group of a nice error basis and then bounding the number of such subgroups. This bound also has implications for the construction of certain combinatorial objects called nets. }, doi = {10.1007/s10801-006-0002-y}, url = {http://arxiv.org/abs/quant-ph/0412066v1}, author = {Michael Aschbacher and Andrew M. Childs and Pawel Wocjan} } @article {1441, title = {The LU-LC conjecture is false}, year = {2007}, month = {2007/09/09}, abstract = { The LU-LC conjecture is an important open problem concerning the structure of entanglement of states described in the stabilizer formalism. It states that two local unitary equivalent stabilizer states are also local Clifford equivalent. If this conjecture were true, the local equivalence of stabilizer states would be extremely easy to characterize. Unfortunately, however, based on the recent progress made by Gross and Van den Nest, we find that the conjecture is false. }, url = {http://arxiv.org/abs/0709.1266v2}, author = {Zhengfeng Ji and Jianxin Chen and Zhaohui Wei and Mingsheng Ying} } @article {1588, title = {N-representability is QMA-complete}, journal = {Phys. Rev. Lett.}, volume = {98}, year = {2007}, month = {2007/03/16}, abstract = {We study the computational complexity of the N-representability problem in quantum chemistry. We show that this problem is quantum Merlin-Arthur complete, which is the quantum generalization of nondeterministic polynomial time complete. Our proof uses a simple mapping from spin systems to fermionic systems, as well as a convex optimization technique that reduces the problem of finding ground states to N representability.}, doi = {10.1103/PhysRevLett.98.110503}, url = {http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.98.110503}, author = {Yi-Kai Liu and Matthias Christandl and F. Verstraete} } @article {1217, title = {Optimal quantum adversary lower bounds for ordered search}, year = {2007}, month = {2007/08/24}, abstract = { The goal of the ordered search problem is to find a particular item in an ordered list of n items. Using the adversary method, Hoyer, Neerbek, and Shi proved a quantum lower bound for this problem of (1/pi) ln n + Theta(1). Here, we find the exact value of the best possible quantum adversary lower bound for a symmetrized version of ordered search (whose query complexity differs from that of the original problem by at most 1). Thus we show that the best lower bound for ordered search that can be proved by the adversary method is (1/pi) ln n + O(1). Furthermore, we show that this remains true for the generalized adversary method allowing negative weights. }, doi = {10.1007/978-3-540-70575-8_71}, url = {http://arxiv.org/abs/0708.3396v1}, author = {Andrew M. Childs and Troy Lee} } @article {1257, title = {Quantum algorithms for hidden nonlinear structures}, year = {2007}, month = {2007/05/21}, abstract = { Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central problem solved by Shor{\textquoteright}s factoring algorithm. We suggest an alternative generalization, namely to problems of finding hidden nonlinear structures over finite fields. We give examples of two such problems that can be solved efficiently by a quantum computer, but not by a classical computer. We also give some positive results on the quantum query complexity of finding hidden nonlinear structures. }, doi = {10.1109/FOCS.2007.18}, url = {http://arxiv.org/abs/0705.2784v1}, author = {Andrew M. Childs and Leonard J. Schulman and Umesh V. Vazirani} } @article {1194, title = {Signatures of incoherence in a quantum information processor}, year = {2007}, month = {2007/05/24}, abstract = { Incoherent noise is manifest in measurements of expectation values when the underlying ensemble evolves under a classical distribution of unitary processes. While many incoherent processes appear decoherent, there are important differences. The distribution functions underlying incoherent processes are either static or slowly varying with respect to control operations and so the errors introduced by these distributions are refocusable. The observation and control of incoherence in small Hilbert spaces is well known. Here we explore incoherence during an entangling operation, such as is relevant in quantum information processing. As expected, it is more difficult to separate incoherence and decoherence over such processes. However, by studying the fidelity decay under a cyclic entangling map we are able to identify distinctive experimental signatures of incoherence. This result is demonstrated both through numerical simulations and experimentally in a three qubit nuclear magnetic resonance implementation. }, url = {http://arxiv.org/abs/0705.3666v2}, author = {Michael K. Henry and Alexey V. Gorshkov and Yaakov S. Weinstein and Paola Cappellaro and Joseph Emerson and Nicolas Boulant and Jonathan S. Hodges and Chandrasekhar Ramanathan and Timothy F. Havel and Rudy Martinez and David G. Cory} } @article {1364, title = {Fault-tolerant Quantum Communication with Minimal Physical Requirements}, journal = {Physical Review Letters}, volume = {96}, year = {2006}, month = {2006/2/23}, abstract = {We describe a novel protocol for a quantum repeater which enables long distance quantum communication through realistic, lossy photonic channels. Contrary to previous proposals, our protocol incorporates active purification of arbitrary errors at each step of the protocol using only two qubits at each repeater station. Because of these minimal physical requirements, the present protocol can be realized in simple physical systems such as solid-state single photon emitters. As an example, we show how nitrogen vacancy color centers in diamond can be used to implement the protocol, using the nuclear and electronic spin to form the two qubits. }, doi = {10.1103/PhysRevLett.96.070504}, url = {http://arxiv.org/abs/quant-ph/0410123v3}, author = {L. Childress and J. M. Taylor and A. S. Sorensen and M. D. Lukin} } @article {1416, title = {Mean-field treatment of the damping of the oscillations of a 1D Bose gas in an optical lattice }, journal = {Physical Review A}, volume = {73}, year = {2006}, month = {2006/1/9}, abstract = { We present a theoretical treatment of the surprisingly large damping observed recently in one-dimensional Bose-Einstein atomic condensates in optical lattices. We show that time-dependent Hartree-Fock-Bogoliubov (HFB) calculations can describe qualitatively the main features of the damping observed over a range of lattice depths. We also derive a formula of the fluctuation-dissipation type for the damping, based on a picture in which the coherent motion of the condensate atoms is disrupted as they try to flow through the random local potential created by the irregular motion of noncondensate atoms. We expect this irregular motion to result from the well-known dynamical instability exhibited by the mean-field theory for these systems. When parameters for the characteristic strength and correlation times of the fluctuations, obtained from the HFB calculations, are substituted in the damping formula, we find very good agreement with the experimentally-observed damping, as long as the lattice is shallow enough for the fraction of atoms in the Mott insulator phase to be negligible. We also include, for completeness, the results of other calculations based on the Gutzwiller ansatz, which appear to work better for the deeper lattices. }, doi = {10.1103/PhysRevA.73.013605}, url = {http://arxiv.org/abs/cond-mat/0410677v4}, author = {Julio Gea-Banacloche and Ana Maria Rey and Guido Pupillo and Carl J. Williams and Charles W. Clark} } @article {1410, title = {Pseudo-fermionization of 1-D bosons in optical lattices}, journal = {New Journal of Physics}, volume = {8}, year = {2006}, month = {2006/08/30}, pages = {161 - 161}, abstract = { We present a model that generalizes the Bose-Fermi mapping for strongly correlated 1D bosons in an optical lattice, to cases in which the average number of atoms per site is larger than one. This model gives an accurate account of equilibrium properties of such systems, in parameter regimes relevant to current experiments. The application of this model to non-equilibrium phenomena is explored by a study of the dynamics of an atom cloud subject to a sudden displacement of the confining potential. Good agreement is found with results of recent experiments. The simplicity and intuitive appeal of this model make it attractive as a general tool for understanding bosonic systems in the strongly correlated regime. }, doi = {10.1088/1367-2630/8/8/161}, url = {http://arxiv.org/abs/cond-mat/0505325v2}, author = {Guido Pupillo and Ana Maria Rey and Carl J. Williams and Charles W. Clark} } @article {1252, title = {Two-way quantum communication channels}, journal = {International Journal of Quantum Information}, volume = {04}, year = {2006}, month = {2006/02/01}, pages = {63 - 83}, abstract = { We consider communication between two parties using a bipartite quantum operation, which constitutes the most general quantum mechanical model of two-party communication. We primarily focus on the simultaneous forward and backward communication of classical messages. For the case in which the two parties share unlimited prior entanglement, we give inner and outer bounds on the achievable rate region that generalize classical results due to Shannon. In particular, using a protocol of Bennett, Harrow, Leung, and Smolin, we give a one-shot expression in terms of the Holevo information for the entanglement-assisted one-way capacity of a two-way quantum channel. As applications, we rederive two known additivity results for one-way channel capacities: the entanglement-assisted capacity of a general one-way channel, and the unassisted capacity of an entanglement-breaking one-way channel. }, doi = {10.1142/S0219749906001621}, url = {http://arxiv.org/abs/quant-ph/0506039v1}, author = {Andrew M. Childs and Debbie W. Leung and Hoi-Kwong Lo} } @article {1241, title = {Weak Fourier-Schur sampling, the hidden subgroup problem, and the quantum collision problem }, year = {2006}, month = {2006/09/14}, abstract = { Schur duality decomposes many copies of a quantum state into subspaces labeled by partitions, a decomposition with applications throughout quantum information theory. Here we consider applying Schur duality to the problem of distinguishing coset states in the standard approach to the hidden subgroup problem. We observe that simply measuring the partition (a procedure we call weak Schur sampling) provides very little information about the hidden subgroup. Furthermore, we show that under quite general assumptions, even a combination of weak Fourier sampling and weak Schur sampling fails to identify the hidden subgroup. We also prove tight bounds on how many coset states are required to solve the hidden subgroup problem by weak Schur sampling, and we relate this question to a quantum version of the collision problem. }, doi = {10.1007/978-3-540-70918-3_51}, url = {http://arxiv.org/abs/quant-ph/0609110v1}, author = {Andrew M. Childs and Aram W. Harrow and Pawel Wocjan} } @article {1415, title = {Bragg Spectroscopy of ultracold atoms loaded in an optical lattice}, journal = {Physical Review A}, volume = {72}, year = {2005}, month = {2005/8/12}, abstract = { We study Bragg spectroscopy of ultra-cold atoms in one-dimensional optical lattices as a method for probing the excitation spectrum in the Mott insulator phase, in particular the one particle-hole excitation band. Within the framework of perturbation theory we obtain an analytical expression for the dynamic structure factor $S(q,\omega)$ and use it to calculate the imparted energy which has shown to be a relevant observable in recent experiments. We test the accuracy of our approximations by comparing them with numerically exact solutions of the Bose-Hubbard model in restricted cases and establish the limits of validity of our linear response analysis. Finally we show that when the system is deep in the Mott insulator regime, its response to the Bragg perturbation is temperature dependent. We suggest that this dependence might be used as a tool to probe temperatures of order of the Mott gap. }, doi = {10.1103/PhysRevA.72.023407}, url = {http://arxiv.org/abs/cond-mat/0406552v2}, author = {Ana Maria Rey and P. Blair Blakie and Guido Pupillo and Carl J. Williams and Charles W. Clark} } @article {1363, title = {Fault-tolerant quantum repeaters with minimal physical resources, and implementations based on single photon emitters}, journal = {Physical Review A}, volume = {72}, year = {2005}, month = {2005/11/28}, abstract = {We analyze a novel method that uses fixed, minimal physical resources to achieve generation and nested purification of quantum entanglement for quantum communication over arbitrarily long distances, and discuss its implementation using realistic photon emitters and photonic channels. In this method, we use single photon emitters with two internal degrees of freedom formed by an electron spin and a nuclear spin to build intermediate nodes in a quantum channel. State-selective fluorescence is used for probabilistic entanglement generation between electron spins in adjacent nodes. We analyze in detail several approaches which are applicable to realistic, homogeneously broadened single photon emitters. Furthermore, the coupled electron and nuclear spins can be used to efficiently implement entanglement swapping and purification. We show that these techniques can be combined to generate high-fidelity entanglement over arbitrarily long distances. We present a specific protocol that functions in polynomial time and tolerates percent-level errors in entanglement fidelity and local operations. The scheme has the lowest requirements on physical resources of any current scheme for fully fault-tolerant quantum repeaters. }, doi = {10.1103/PhysRevA.72.052330}, url = {http://arxiv.org/abs/quant-ph/0502112v1}, author = {L. I. Childress and J. M. Taylor and A. S. Sorensen and M. D. Lukin} } @article {1240, title = {From optimal measurement to efficient quantum algorithms for the hidden subgroup problem over semidirect product groups }, year = {2005}, month = {2005/04/11}, abstract = { We approach the hidden subgroup problem by performing the so-called pretty good measurement on hidden subgroup states. For various groups that can be expressed as the semidirect product of an abelian group and a cyclic group, we show that the pretty good measurement is optimal and that its probability of success and unitary implementation are closely related to an average-case algebraic problem. By solving this problem, we find efficient quantum algorithms for a number of nonabelian hidden subgroup problems, including some for which no efficient algorithm was previously known: certain metacyclic groups as well as all groups of the form (Z_p)^r X| Z_p for fixed r (including the Heisenberg group, r=2). In particular, our results show that entangled measurements across multiple copies of hidden subgroup states can be useful for efficiently solving the nonabelian HSP. }, doi = {10.1109/SFCS.2005.38}, url = {http://arxiv.org/abs/quant-ph/0504083v2}, author = {Dave Bacon and Andrew M. Childs and Wim van Dam} } @article {1239, title = {Optimal measurements for the dihedral hidden subgroup problem}, year = {2005}, month = {2005/01/10}, abstract = { We consider the dihedral hidden subgroup problem as the problem of distinguishing hidden subgroup states. We show that the optimal measurement for solving this problem is the so-called pretty good measurement. We then prove that the success probability of this measurement exhibits a sharp threshold as a function of the density nu=k/log N, where k is the number of copies of the hidden subgroup state and 2N is the order of the dihedral group. In particular, for nu<1 the optimal measurement (and hence any measurement) identifies the hidden subgroup with a probability that is exponentially small in log N, while for nu>1 the optimal measurement identifies the hidden subgroup with a probability of order unity. Thus the dihedral group provides an example of a group G for which Omega(log|G|) hidden subgroup states are necessary to solve the hidden subgroup problem. We also consider the optimal measurement for determining a single bit of the answer, and show that it exhibits the same threshold. Finally, we consider implementing the optimal measurement by a quantum circuit, and thereby establish further connections between the dihedral hidden subgroup problem and average case subset sum problems. In particular, we show that an efficient quantum algorithm for a restricted version of the optimal measurement would imply an efficient quantum algorithm for the subset sum problem, and conversely, that the ability to quantum sample from subset sum solutions allows one to implement the optimal measurement. }, url = {http://arxiv.org/abs/quant-ph/0501044v2}, author = {Dave Bacon and Andrew M. Childs and Wim van Dam} } @article {1215, title = {Quantum algorithm for a generalized hidden shift problem}, year = {2005}, month = {2005/07/19}, abstract = { Consider the following generalized hidden shift problem: given a function f on {0,...,M-1} x Z_N satisfying f(b,x)=f(b+1,x+s) for b=0,1,...,M-2, find the unknown shift s in Z_N. For M=N, this problem is an instance of the abelian hidden subgroup problem, which can be solved efficiently on a quantum computer, whereas for M=2, it is equivalent to the dihedral hidden subgroup problem, for which no efficient algorithm is known. For any fixed positive epsilon, we give an efficient (i.e., poly(log N)) quantum algorithm for this problem provided M > N^epsilon. The algorithm is based on the "pretty good measurement" and uses H. Lenstra{\textquoteright}s (classical) algorithm for integer programming as a subroutine. }, url = {http://arxiv.org/abs/quant-ph/0507190v1}, author = {Andrew M. Childs and Wim van Dam} } @article {1216, title = {On the quantum hardness of solving isomorphism problems as nonabelian hidden shift problems }, year = {2005}, month = {2005/10/25}, abstract = { We consider an approach to deciding isomorphism of rigid n-vertex graphs (and related isomorphism problems) by solving a nonabelian hidden shift problem on a quantum computer using the standard method. Such an approach is arguably more natural than viewing the problem as a hidden subgroup problem. We prove that the hidden shift approach to rigid graph isomorphism is hard in two senses. First, we prove that Omega(n) copies of the hidden shift states are necessary to solve the problem (whereas O(n log n) copies are sufficient). Second, we prove that if one is restricted to single-register measurements, an exponential number of hidden shift states are required. }, url = {http://arxiv.org/abs/quant-ph/0510185v1}, author = {Andrew M. Childs and Pawel Wocjan} } @article {1418, title = {Scalable register initialization for quantum computing in an optical lattice }, journal = {Journal of Physics B: Atomic, Molecular and Optical Physics}, volume = {38}, year = {2005}, month = {2005/06/14}, pages = {1687 - 1694}, abstract = { The Mott insulator state created by loading an atomic Bose-Einstein condensate (BEC) into an optical lattice may be used as a means to prepare a register of atomic qubits in a quantum computer. Such architecture requires a lattice commensurately filled with atoms, which corresponds to the insulator state only in the limit of zero inter-well tunneling. We show that a lattice with spatial inhomogeneity created by a quadratic magnetic trapping potential can be used to isolate a subspace in the center which is impervious to hole-hoping. Components of the wavefunction with more than one atom in any well can be projected out by selective measurement on a molecular photo-associative transition. Maintaining the molecular coupling induces a quantum Zeno effect that can sustain a commensurately filled register for the duration of a quantum computation. }, doi = {10.1088/0953-4075/38/11/010}, url = {http://arxiv.org/abs/quant-ph/0312069v1}, author = {Gavin K. Brennen and Guido Pupillo and Ana Maria Rey and Charles W. Clark and Carl J. Williams} } @article {1297, title = {Sodium Bose-Einstein Condensates in an Optical Lattice}, journal = {Physical Review A}, volume = {72}, year = {2005}, month = {2005/10/10}, abstract = { The phase transition from a superfluid to a Mott insulator has been observed in a $^{23}$Na Bose-Einstein condensate. A dye laser detuned $\approx 5$nm red of the Na $3^2$S$ \to 3^2$P$_{1/2}$ transition was used to form the three dimensional optical lattice. The heating effects of the small detuning as well as the three-body decay processes constrained the timescale of the experiment. Certain lattice detunings were found to induce a large loss of atoms. These loss features were shown to be due to photoassociation of atoms to vibrational levels in the Na$_2$ $(1) ^3\Sigma_g^+$ state. }, doi = {10.1103/PhysRevA.72.043604}, url = {http://arxiv.org/abs/cond-mat/0507288v1}, author = {K. Xu and Y. Liu and J. R. Abo-Shaeer and T. Mukaiyama and J. K. Chin and D. E. Miller and W. Ketterle and Kevin M. Jones and Eite Tiesinga} } @article {1409, title = {Ultracold atoms confined in an optical lattice plus parabolic potential: a closed-form approach }, journal = {Physical Review A}, volume = {72}, year = {2005}, month = {2005/9/22}, abstract = { We discuss interacting and non-interacting one dimensional atomic systems trapped in an optical lattice plus a parabolic potential. We show that, in the tight-binding approximation, the non-interacting problem is exactly solvable in terms of Mathieu functions. We use the analytic solutions to study the collective oscillations of ideal bosonic and fermionic ensembles induced by small displacements of the parabolic potential. We treat the interacting boson problem by numerical diagonalization of the Bose-Hubbard Hamiltonian. From analysis of the dependence upon lattice depth of the low-energy excitation spectrum of the interacting system, we consider the problems of "fermionization" of a Bose gas, and the superfluid-Mott insulator transition. The spectrum of the noninteracting system turns out to provide a useful guide to understanding the collective oscillations of the interacting system, throughout a large and experimentally relevant parameter regime. }, doi = {10.1103/PhysRevA.72.033616}, url = {http://arxiv.org/abs/cond-mat/0503477v2}, author = {Ana Maria Rey and Guido Pupillo and Charles W. Clark and Carl J. Williams} } @article {1251, title = {Unified derivations of measurement-based schemes for quantum computation}, journal = {Physical Review A}, volume = {71}, year = {2005}, month = {2005/3/17}, abstract = { We present unified, systematic derivations of schemes in the two known measurement-based models of quantum computation. The first model (introduced by Raussendorf and Briegel [Phys. Rev. Lett., 86, 5188 (2001)]) uses a fixed entangled state, adaptive measurements on single qubits, and feedforward of the measurement results. The second model (proposed by Nielsen [Phys. Lett. A, 308, 96 (2003)] and further simplified by Leung [Int. J. Quant. Inf., 2, 33 (2004)]) uses adaptive two-qubit measurements that can be applied to arbitrary pairs of qubits, and feedforward of the measurement results. The underlying principle of our derivations is a variant of teleportation introduced by Zhou, Leung, and Chuang [Phys. Rev. A, 62, 052316 (2000)]. Our derivations unify these two measurement-based models of quantum computation and provide significantly simpler schemes. }, doi = {10.1103/PhysRevA.71.032318}, url = {http://arxiv.org/abs/quant-ph/0404132v2}, author = {Andrew M. Childs and Debbie W. Leung and Michael A. Nielsen} } @article {1411, title = {Advantages of high-speed technique for quantum key distribution; reply to quant-ph/0407050 }, year = {2004}, month = {2004/07/18}, abstract = { We respond to a comment on our high-speed technique for the implementation of free-space quantum key distribution (QKD). The model used in the comment assigns inappropriately high link losses to the technique in question. We show that the use of reasonable loss parameters in the model invalidates the comment{\textquoteright}s main conclusion and highlights the benefits of increased transmission rates. }, url = {http://arxiv.org/abs/quant-ph/0407139v1}, author = {J. C. Bienfang and Charles W. Clark and Carl J. Williams and E. W. Hagley and Jesse Wen} } @article {1365, title = {Quantum information processing using localized ensembles of nuclear spins}, year = {2004}, month = {2004/07/23}, abstract = {We describe a technique for quantum information processing based on localized en sembles of nuclear spins. A qubit is identified as the presence or absence of a collective excitation of a mesoscopic ensemble of nuclear spins surrounding a single quantum dot. All single and two-qubit operations can be effected using hyperfine interactions and single-electron spin rotations, hence the proposed scheme avoids gate errors arising from entanglement between spin and orbital degrees of freedom. Ultra-long coherence times of nuclear spins suggest that this scheme could be particularly well suited for applications where long lived memory is essential. }, url = {http://arxiv.org/abs/cond-mat/0407640v2}, author = {J. M. Taylor and G. Giedke and H. Christ and B. Paredes and J. I. Cirac and P. Zoller and M. D. Lukin and A. Imamoglu} } @article {1420, title = {Quantum key distribution with 1.25 Gbps clock synchronization}, journal = {Optics Express}, volume = {12}, year = {2004}, month = {2004/05/17}, pages = {2011}, abstract = { We have demonstrated the exchange of sifted quantum cryptographic key over a 730 meter free-space link at rates of up to 1.0 Mbps, two orders of magnitude faster than previously reported results. A classical channel at 1550 nm operates in parallel with a quantum channel at 845 nm. Clock recovery techniques on the classical channel at 1.25 Gbps enable quantum transmission at up to the clock rate. System performance is currently limited by the timing resolution of our silicon avalanche photodiode detectors. With improved detector resolution, our technique will yield another order of magnitude increase in performance, with existing technology. }, doi = {10.1364/OPEX.12.002011}, url = {http://arxiv.org/abs/quant-ph/0405097v1}, author = {J. C. Bienfang and A. J. Gross and A. Mink and B. J. Hershman and A. Nakassis and X. Tang and R. Lu and D. H. Su and Charles W Clark and Carl J. Williams and E. W. Hagley and Jesse Wen} } @article {1406, title = {Relativistic many-body calculations of electric-dipole matrix elements, lifetimes and polarizabilities in rubidium }, journal = {Physical Review A}, volume = {69}, year = {2004}, month = {2004/2/27}, abstract = { Electric-dipole matrix elements for ns-n{\textquoteright}p, nd-n{\textquoteright}p, and 6d-4f transitions in Rb are calculated using a relativistic all-order method. A third-order calculation is also carried out for these matrix elements to evaluate the importance of the high-order many-body perturbation theory contributions. The all-order matrix elements are used to evaluate lifetimes of ns and np levels with n=6, 7, 8 and nd levels with n=4, 5, 6 for comparison with experiment and to provide benchmark values for these lifetimes. The dynamic polarizabilities are calculated for ns states of rubidium. The resulting lifetime and polarizability values are compared with available theory and experiment. }, doi = {10.1103/PhysRevA.69.022509}, url = {http://arxiv.org/abs/physics/0307057v1}, author = {M. S. Safronova and Carl J. Williams and Charles W. Clark} } @article {1238, title = {Reversible simulation of bipartite product Hamiltonians}, journal = {IEEE Transactions on Information Theory}, volume = {50}, year = {2004}, month = {2004/06/01}, pages = {1189 - 1197}, abstract = { Consider two quantum systems A and B interacting according to a product Hamiltonian H = H_A x H_B. We show that any two such Hamiltonians can be used to simulate each other reversibly (i.e., without efficiency losses) with the help of local unitary operations and local ancillas. Accordingly, all non-local features of a product Hamiltonian -- including the rate at which it can be used to produce entanglement, transmit classical or quantum information, or simulate other Hamiltonians -- depend only upon a single parameter. We identify this parameter and use it to obtain an explicit expression for the entanglement capacity of all product Hamiltonians. Finally, we show how the notion of simulation leads to a natural formulation of measures of the strength of a nonlocal Hamiltonian. }, doi = {10.1109/TIT.2004.828069}, url = {http://arxiv.org/abs/quant-ph/0303097v1}, author = {Andrew M. Childs and Debbie W. Leung and Guifre Vidal} } @article {1419, title = {Scalable quantum computation in systems with Bose-Hubbard dynamics}, journal = {Journal of Modern Optics}, volume = {51}, year = {2004}, month = {2004/02/15}, pages = {2395 - 2404}, abstract = { Several proposals for quantum computation utilize a lattice type architecture with qubits trapped by a periodic potential. For systems undergoing many body interactions described by the Bose-Hubbard Hamiltonian, the ground state of the system carries number fluctuations that scale with the number of qubits. This process degrades the initialization of the quantum computer register and can introduce errors during error correction. In an earlier manuscript we proposed a solution to this problem tailored to the loading of cold atoms into an optical lattice via the Mott Insulator phase transition. It was shown that by adding an inhomogeneity to the lattice and performing a continuous measurement, the unit filled state suitable for a quantum computer register can be maintained. Here, we give a more rigorous derivation of the register fidelity in homogeneous and inhomogeneous lattices and provide evidence that the protocol is effective in the finite temperature regime. }, doi = {10.1080/09500340408231798}, url = {http://arxiv.org/abs/quant-ph/0403052v2}, author = {Guido Pupillo and Ana Maria Rey and Gavin Brennen and Carl J. Williams and Charles W. Clark} } @article {1213, title = {Spatial search and the Dirac equation}, journal = {Physical Review A}, volume = {70}, year = {2004}, month = {2004/10/19}, abstract = { We consider the problem of searching a d-dimensional lattice of N sites for a single marked location. We present a Hamiltonian that solves this problem in time of order sqrt(N) for d>2 and of order sqrt(N) log(N) in the critical dimension d=2. This improves upon the performance of our previous quantum walk search algorithm (which has a critical dimension of d=4), and matches the performance of a corresponding discrete-time quantum walk algorithm. The improvement uses a lattice version of the Dirac Hamiltonian, and thus requires the introduction of spin (or coin) degrees of freedom. }, doi = {10.1103/PhysRevA.70.042312}, url = {http://arxiv.org/abs/quant-ph/0405120v1}, author = {Andrew M. Childs and Jeffrey Goldstone} } @article {1211, title = {Spatial search by quantum walk}, journal = {Physical Review A}, volume = {70}, year = {2004}, month = {2004/8/23}, abstract = { Grover{\textquoteright}s quantum search algorithm provides a way to speed up combinatorial search, but is not directly applicable to searching a physical database. Nevertheless, Aaronson and Ambainis showed that a database of N items laid out in d spatial dimensions can be searched in time of order sqrt(N) for d>2, and in time of order sqrt(N) poly(log N) for d=2. We consider an alternative search algorithm based on a continuous time quantum walk on a graph. The case of the complete graph gives the continuous time search algorithm of Farhi and Gutmann, and other previously known results can be used to show that sqrt(N) speedup can also be achieved on the hypercube. We show that full sqrt(N) speedup can be achieved on a d-dimensional periodic lattice for d>4. In d=4, the quantum walk search algorithm takes time of order sqrt(N) poly(log N), and in d<4, the algorithm does not provide substantial speedup. }, doi = {10.1103/PhysRevA.70.022314}, url = {http://arxiv.org/abs/quant-ph/0306054v2}, author = {Andrew M. Childs and Jeffrey Goldstone} } @article {1414, title = {Bogoliubov approach to superfluidity of atoms in an optical lattice}, journal = {Journal of Physics B: Atomic, Molecular and Optical Physics}, volume = {36}, year = {2003}, month = {2003/03/14}, pages = {825 - 841}, abstract = { We use the Bogoliubov theory of atoms in an optical lattice to study the approach to the Mott-insulator transition. We derive an explicit expression for the superfluid density based on the rigidity of the system under phase variations. This enables us to explore the connection between the quantum depletion of the condensate and the quasi-momentum distribution on the one hand and the superfluid fraction on the other. The approach to the insulator phase may be characterized through the filling of the band by quantum depletion, which should be directly observable via the matter wave interference patterns. We complement these findings by self-consistent Hartree-Fock-Bogoliubov-Popov calculations for one-dimensional lattices including the effects of a parabolic trapping potential. }, doi = {10.1088/0953-4075/36/5/304}, url = {http://arxiv.org/abs/cond-mat/0210550v2}, author = {Ana Maria Rey and Keith Burnett and Robert Roth and Mark Edwards and Carl J. Williams and Charles W. Clark} } @article {1250, title = {Lower bounds on the complexity of simulating quantum gates}, journal = {Physical Review A}, volume = {68}, year = {2003}, month = {2003/11/18}, abstract = { We give a simple proof of a formula for the minimal time required to simulate a two-qubit unitary operation using a fixed two-qubit Hamiltonian together with fast local unitaries. We also note that a related lower bound holds for arbitrary n-qubit gates. }, doi = {10.1103/PhysRevA.68.052311}, url = {http://arxiv.org/abs/quant-ph/0307190v1}, author = {Andrew M. Childs and Henry L. Haselgrove and Michael A. Nielsen} } @article {1407, title = {Optimizing the fast Rydberg quantum gate}, journal = {Physical Review A}, volume = {67}, year = {2003}, month = {2003/4/17}, abstract = { The fast phase gate scheme, in which the qubits are atoms confined in sites of an optical lattice, and gate operations are mediated by excitation of Rydberg states, was proposed by Jaksch et al. Phys. Rev. Lett. 85, 2208 (2000). A potential source of decoherence in this system derives from motional heating, which occurs if the ground and Rydberg states of the atom move in different optical lattice potentials. We propose to minimize this effect by choosing the lattice photon frequency \omega so that the ground and Rydberg states have the same frequency-dependent polarizability \alpha(omega). The results are presented for the case of Rb. }, doi = {10.1103/PhysRevA.67.040303}, url = {http://arxiv.org/abs/quant-ph/0212081v1}, author = {M. S. Safronova and Carl J. Williams and Charles W. Clark} } @article {1212, title = {Quantum algorithms for subset finding}, year = {2003}, month = {2003/11/06}, abstract = { Recently, Ambainis gave an O(N^(2/3))-query quantum walk algorithm for element distinctness, and more generally, an O(N^(L/(L+1)))-query algorithm for finding L equal numbers. We point out that this algorithm actually solves a much more general problem, the problem of finding a subset of size L that satisfies any given property. We review the algorithm and give a considerably simplified analysis of its query complexity. We present several applications, including two algorithms for the problem of finding an L-clique in an N-vertex graph. One of these algorithms uses O(N^(2L/(L+1))) edge queries, and the other uses \tilde{O}(N^((5L-2)/(2L+4))), which is an improvement for L <= 5. The latter algorithm generalizes a recent result of Magniez, Santha, and Szegedy, who considered the case L=3 (finding a triangle). We also pose two open problems regarding continuous time quantum walk and lower bounds. }, url = {http://arxiv.org/abs/quant-ph/0311038v2}, author = {Andrew M. Childs and Jason M. Eisenberg} } @article {1296, title = {Ultracold Cs$_2$ Feshbach Spectroscopy}, year = {2003}, month = {2003/12/23}, abstract = { We have observed and located more than 60 magnetic field-induced Feshbach resonances in ultracold collisions of ground-state $^{133}$Cs atoms. These resonances are associated with molecular states with up to four units of rotational angular momentum, and are detected through variations in the elastic, inelastic, and radiative collision cross sections. These observations allow us to greatly improve upon the interaction potentials between two cesium atoms and to reproduce the positions of most resonances to accuracies better than 0.5\%. Based on the relevant coupling scheme between the electron spin, nuclear spin, and orbital angular momenta of the nuclei, quantum numbers and energy structure of the molecular states beneath the dissociation continuum are revealed. Finally, we predict the relevant collision properties for cesium Bose-Einstein condensation experiments. }, url = {http://arxiv.org/abs/cond-mat/0312613v2}, author = {Cheng Chin and Vladan Vuletic and Andrew J. Kerman and Steven Chu and Eite Tiesinga and Paul J. Leo and Carl J. Williams} } @article {1210, title = {Asymptotic entanglement capacity of the Ising and anisotropic Heisenberg interactions }, year = {2002}, month = {2002/07/10}, abstract = { We compute the asymptotic entanglement capacity of the Ising interaction ZZ, the anisotropic Heisenberg interaction XX + YY, and more generally, any two-qubit Hamiltonian with canonical form K = a XX + b YY. We also describe an entanglement assisted classical communication protocol using the Hamiltonian K with rate equal to the asymptotic entanglement capacity. }, url = {http://arxiv.org/abs/quant-ph/0207052v2}, author = {Andrew M. Childs and D. W. Leung and F. Verstraete and G. Vidal} } @article {1328, title = {Characterizing quantum theory in terms of information-theoretic constraints}, journal = {Foundations of Physics}, volume = {33}, year = {2002}, month = {2003/11/01}, pages = {1561 - 1591}, abstract = { We show that three fundamental information-theoretic constraints--the impossibility of superluminal information transfer between two physical systems by performing measurements on one of them, the impossibility of broadcasting the information contained in an unknown physical state, and the impossibility of unconditionally secure bit commitment--suffice to entail that the observables and state space of a physical theory are quantum-mechanical. We demonstrate the converse derivation in part, and consider the implications of alternative answers to a remaining open question about nonlocality and bit commitment. }, doi = {10.1023/A:1026056716397}, url = {http://arxiv.org/abs/quant-ph/0211089v2}, author = {Rob Clifton and Jeffrey Bub and Hans Halvorson} } @article {1263, title = {Exponential algorithmic speedup by quantum walk}, year = {2002}, month = {2002/09/24}, abstract = { We construct an oracular (i.e., black box) problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on a continuous time quantum walk, and thus employs a different technique from previous quantum algorithms based on quantum Fourier transforms. We show how to implement the quantum walk efficiently in our oracular setting. We then show how this quantum walk can be used to solve our problem by rapidly traversing a graph. Finally, we prove that no classical algorithm can solve this problem with high probability in subexponential time. }, doi = {10.1145/780542.780552}, url = {http://arxiv.org/abs/quant-ph/0209131v2}, author = {Andrew M. Childs and Richard Cleve and Enrico Deotto and Edward Farhi and Sam Gutmann and Daniel A. Spielman} } @article {1262, title = {Quantum search by measurement}, journal = {Physical Review A}, volume = {66}, year = {2002}, month = {2002/9/23}, abstract = { We propose a quantum algorithm for solving combinatorial search problems that uses only a sequence of measurements. The algorithm is similar in spirit to quantum computation by adiabatic evolution, in that the goal is to remain in the ground state of a time-varying Hamiltonian. Indeed, we show that the running times of the two algorithms are closely related. We also show how to achieve the quadratic speedup for Grover{\textquoteright}s unstructured search problem with only two measurements. Finally, we discuss some similarities and differences between the adiabatic and measurement algorithms. }, doi = {10.1103/PhysRevA.66.032314}, url = {http://arxiv.org/abs/quant-ph/0204013v1}, author = {Andrew M. Childs and Enrico Deotto and Edward Farhi and Jeffrey Goldstone and Sam Gutmann and Andrew J. Landahl} } @article {1261, title = {Universal simulation of Hamiltonian dynamics for qudits}, journal = {Physical Review A}, volume = {66}, year = {2002}, month = {2002/8/30}, abstract = { What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd et al. (quant-ph/0106064) provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling N-qubit Hamiltonian, and local unitaries. We extend this result to the case where the component systems have D dimensions. As a consequence we explain how universal quantum computation can be performed with any fixed two-body entangling N-qudit Hamiltonian, and local unitaries. }, doi = {10.1103/PhysRevA.66.022317}, url = {http://arxiv.org/abs/quant-ph/0109064v2}, author = {Michael A. Nielsen and Michael J. Bremner and Jennifer L. Dodd and Andrew M. Childs and Christopher M. Dawson} } @article {1248, title = {Exact sampling from non-attractive distributions using summary states}, journal = {Physical Review E}, volume = {63}, year = {2001}, month = {2001/2/22}, abstract = { Propp and Wilson{\textquoteright}s method of coupling from the past allows one to efficiently generate exact samples from attractive statistical distributions (e.g., the ferromagnetic Ising model). This method may be generalized to non-attractive distributions by the use of summary states, as first described by Huber. Using this method, we present exact samples from a frustrated antiferromagnetic triangular Ising model and the antiferromagnetic q=3 Potts model. We discuss the advantages and limitations of the method of summary states for practical sampling, paying particular attention to the slowing down of the algorithm at low temperature. In particular, we show that such a slowing down can occur in the absence of a physical phase transition. }, doi = {10.1103/PhysRevE.63.036113}, url = {http://arxiv.org/abs/cond-mat/0005132v1}, author = {Andrew M. Childs and Ryan B. Patterson and David J. C. MacKay} } @article {1208, title = {An example of the difference between quantum and classical random walks}, journal = {Quantum Information Processing}, volume = {1}, year = {2001}, month = {2002/04/01}, pages = {35 - 43}, abstract = { In this note, we discuss a general definition of quantum random walks on graphs and illustrate with a simple graph the possibility of very different behavior between a classical random walk and its quantum analogue. In this graph, propagation between a particular pair of nodes is exponentially faster in the quantum case. }, doi = {10.1023/A:1019609420309}, url = {http://arxiv.org/abs/quant-ph/0103020v1}, author = {Andrew M. Childs and Edward Farhi and Sam Gutmann} } @article {1249, title = {Realization of quantum process tomography in NMR}, journal = {Physical Review A}, volume = {64}, year = {2001}, month = {2001/6/13}, abstract = { Quantum process tomography is a procedure by which the unknown dynamical evolution of an open quantum system can be fully experimentally characterized. We demonstrate explicitly how this procedure can be implemented with a nuclear magnetic resonance quantum computer. This allows us to measure the fidelity of a controlled-not logic gate and to experimentally investigate the error model for our computer. Based on the latter analysis, we test an important assumption underlying nearly all models of quantum error correction, the independence of errors on different qubits. }, doi = {10.1103/PhysRevA.64.012314}, url = {http://arxiv.org/abs/quant-ph/0012032v1}, author = {Andrew M. Childs and Isaac L. Chuang and Debbie W. Leung} } @article {1209, title = {Robustness of adiabatic quantum computation}, journal = {Physical Review A}, volume = {65}, year = {2001}, month = {2001/12/14}, abstract = { We study the fault tolerance of quantum computation by adiabatic evolution, a quantum algorithm for solving various combinatorial search problems. We describe an inherent robustness of adiabatic computation against two kinds of errors, unitary control errors and decoherence, and we study this robustness using numerical simulations of the algorithm. }, doi = {10.1103/PhysRevA.65.012322}, url = {http://arxiv.org/abs/quant-ph/0108048v1}, author = {Andrew M. Childs and Edward Farhi and John Preskill} } @article {1204, title = {Secure assisted quantum computation}, year = {2001}, month = {2001/11/07}, abstract = { Suppose Alice wants to perform some computation that could be done quickly on a quantum computer, but she cannot do universal quantum computation. Bob can do universal quantum computation and claims he is willing to help, but Alice wants to be sure that Bob cannot learn her input, the result of her calculation, or perhaps even the function she is trying to compute. We describe a simple, efficient protocol by which Bob can help Alice perform the computation, but there is no way for him to learn anything about it. We also discuss techniques for Alice to detect whether Bob is honestly helping her or if he is introducing errors. }, url = {http://arxiv.org/abs/quant-ph/0111046v2}, author = {Andrew M. Childs} } @article {1260, title = {Universal simulation of Markovian quantum dynamics}, journal = {Physical Review A}, volume = {64}, year = {2001}, month = {2001/11/9}, abstract = { Although the conditions for performing arbitrary unitary operations to simulate the dynamics of a closed quantum system are well understood, the same is not true of the more general class of quantum operations (also known as superoperators) corresponding to the dynamics of open quantum systems. We propose a framework for the generation of Markovian quantum dynamics and study the resources needed for universality. For the case of a single qubit, we show that a single nonunitary process is necessary and sufficient to generate all unital Markovian quantum dynamics, whereas a set of processes parametrized by one continuous parameter is needed in general. We also obtain preliminary results for the unital case in higher dimensions. }, doi = {10.1103/PhysRevA.64.062302}, url = {http://arxiv.org/abs/quant-ph/0008070v2}, author = {Dave Bacon and Andrew M. Childs and Isaac L. Chuang and Julia Kempe and Debbie W. Leung and Xinlan Zhou} } @article {1237, title = {Finding cliques by quantum adiabatic evolution}, year = {2000}, month = {2000/12/19}, abstract = { Quantum adiabatic evolution provides a general technique for the solution of combinatorial search problems on quantum computers. We present the results of a numerical study of a particular application of quantum adiabatic evolution, the problem of finding the largest clique in a random graph. An n-vertex random graph has each edge included with probability 1/2, and a clique is a completely connected subgraph. There is no known classical algorithm that finds the largest clique in a random graph with high probability and runs in a time polynomial in n. For the small graphs we are able to investigate (n <= 18), the quantum algorithm appears to require only a quadratic run time. }, url = {http://arxiv.org/abs/quant-ph/0012104v1}, author = {Andrew M. Childs and Edward Farhi and Jeffrey Goldstone and Sam Gutmann} } @article {1236, title = {Quantum information and precision measurement}, journal = {Journal of Modern Optics}, volume = {47}, year = {2000}, month = {1999/04/07}, pages = {155 - 176}, abstract = { We describe some applications of quantum information theory to the analysis of quantum limits on measurement sensitivity. A measurement of a weak force acting on a quantum system is a determination of a classical parameter appearing in the master equation that governs the evolution of the system; limitations on measurement accuracy arise because it is not possible to distinguish perfectly among the different possible values of this parameter. Tools developed in the study of quantum information and computation can be exploited to improve the precision of physics experiments; examples include superdense coding, fast database search, and the quantum Fourier transform. }, doi = {10.1080/09500340008244034}, url = {http://arxiv.org/abs/quant-ph/9904021v2}, author = {Andrew M. Childs and John Preskill and Joseph Renes} } @article {1207, title = {Universal quantum computation with two-level trapped ions}, journal = {Physical Review A}, volume = {63}, year = {2000}, month = {2000/12/11}, abstract = { Although the initial proposal for ion trap quantum computation made use of an auxiliary internal level to perform logic between ions, this resource is not necessary in principle. Instead, one may perform such operations directly using sideband laser pulses, operating with an arbitrary (sufficiently small) Lamb-Dicke parameter. We explore the potential of this technique, showing how to perform logical operations between the internal state of an ion and the collective motional state and giving explicit constructions for a controlled-not gate between ions. }, doi = {10.1103/PhysRevA.63.012306}, url = {http://arxiv.org/abs/quant-ph/0008065v1}, author = {Andrew M. Childs and Isaac L. Chuang} } @article {1327, title = {Revised Proof of the Uniqueness Theorem for {\textquoteright}No Collapse{\textquoteright} Interpretations of Quantum Mechanics }, year = {1999}, month = {1999/10/22}, abstract = { We show that the Bub-Clifton uniqueness theorem for {\textquoteright}no collapse{\textquoteright} interpretations of quantum mechanics (Studies in the History and Philosophy of Modern Physics 27, 181-219 (1996)) can be proved without the {\textquoteright}weak separability{\textquoteright} assumption. }, url = {http://arxiv.org/abs/quant-ph/9910097v1}, author = {Jeffrey Bub and Rob Clifton and Sheldon Goldstein} }