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.

%8 03/13/2019 %G eng %U https://arxiv.org/abs/1903.05453 %0 Journal Article %D 2019 %T Photon pair condensation by engineered dissipation %A Ze-Pei Cian %A Guanyu Zhu %A Su-Kuan Chu %A Alireza Seif %A Wade DeGottardi %A Liang Jiang %A Mohammad Hafezi %XDissipation 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.

%8 04/02/2019 %G eng %U https://arxiv.org/abs/1904.00016 %0 Journal Article %D 2019 %T Polynomial Time Algorithms for Estimating Spectra of Adiabatic Hamiltonians %A Jacob Bringewatt %A William Dorland %A Stephen P. Jordan %XMuch research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians with Hamming symmetric potentials, such as the well studied "spike" example. Due to the large amount of symmetry in these potentials such problems are readily open to analysis both analytically and computationally. However, more realistic potentials do not have such a high degree of symmetry and may have many local minima. Here we present a somewhat more realistic class of problems consisting of many individually Hamming symmetric potential wells. For two or three such wells we demonstrate that such a problem can be solved exactly in time polynomial in the number of qubits and wells. For greater than three wells, we present a tight binding approach with which to efficiently analyze the performance of such Hamiltonians in an adiabatic computation. We provide several basic examples designed to highlight the usefulness of this toy model and to give insight into using the tight binding approach to examining it, including: (1) adiabatic unstructured search with a transverse field driver and a prior guess to the marked item and (2) a scheme for adiabatically simulating the ground states of small collections of strongly interacting spins, with an explicit demonstration for an Ising model Hamiltonian.

%8 05/25/2019 %G eng %U https://arxiv.org/abs/1905.07461 %0 Journal Article %J Phys. Rev. A %D 2019 %T Quantum Algorithm for Simulating the Wave Equation %A Pedro C.S. Costa %A Stephen P. Jordan %A Aaron Ostrander %XWe 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's equations.

%B Phys. Rev. A %V 99 %8 03/24/2019 %G eng %U https://arxiv.org/abs/1711.05394 %N 012323 %R https://doi.org/10.1103/PhysRevA.99.012323 %0 Journal Article %D 2019 %T Quantum Approximate Optimization with a Trapped-Ion Quantum Simulator %A G. Pagano %A A. Bapat %A P. Becker %A K. S. Collins %A A. De %A P. W. Hess %A H. B. Kaplan %A A. Kyprianidis %A W. L. Tan %A C. Baldwin %A L. T. Brady %A A. Deshpande %A F. Liu %A S. Jordan %A A. V. Gorshkov %A C. Monroe %XQuantum 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.

%8 06/06/2019 %G eng %U https://arxiv.org/abs/1906.02700 %0 Journal Article %J New J. Phys. %D 2019 %T Quantum repeaters based on two species trapped ions %A Siddhartha Santra %A Sreraman Muralidharan %A Martin Lichtman %A Liang Jiang %A Christopher Monroe %A Vladimir S. Malinovsky %XWe examine the viability of quantum repeaters based on two-species trapped ion modules for long distance quantum key distribution. Repeater nodes comprised of ion-trap modules of co-trapped ions of distinct species are considered. The species used for communication qubits has excellent optical properties while the other longer lived species serves as a memory qubit in the modules. Each module interacts with the network only via single photons emitted by the communication ions. Coherent Coulomb interaction between ions is utilized to transfer quantum information between the communication and memory ions and to achieve entanglement swapping between two memory ions. We describe simple modular quantum repeater architectures realizable with the ion-trap modules and numerically study the dependence of the quantum key distribution rate on various experimental parameters, including coupling efficiency, gate infidelity, operation time and length of the elementary links. Our analysis suggests crucial improvements necessary in a physical implementation for co-trapped two-species ions to be a competitive platform in long-distance quantum communication.

%B New J. Phys. %V 21 %8 05/02/2019 %G eng %U https://arxiv.org/abs/1811.10723 %N 073002 %R https://doi.org/10.1088/1367-2630/ab2a45 %0 Journal Article %D 2018 %T Bang-bang control as a design principle for classical and quantum optimization algorithms %A Aniruddha Bapat %A Stephen Jordan %XPhysically motivated classical heuristic optimization algorithms such as simulated annealing (SA) treat the objective function as an energy landscape, and allow walkers to escape local minima. It has been argued that quantum properties such as tunneling may give quantum algorithms advantage in finding ground states of vast, rugged cost landscapes. Indeed, the Quantum Adiabatic Algorithm (QAO) and the recent Quantum Approximate Optimization Algorithm (QAOA) have shown promising results on various problem instances that are considered classically hard. Here, we argue that the type of control strategy used by the optimization algorithm may be crucial to its success. Along with SA, QAO and QAOA, we define a new, bang-bang version of simulated annealing, BBSA, and study the performance of these algorithms on two well-studied problem instances from the literature. Both classically and quantumly, the successful control strategy is found to be bang-bang, exponentially outperforming the quasistatic analogues on the same instances. Lastly, we construct O(1)-depth QAOA protocols for a class of symmetric cost functions, and provide an accompanying physical picture.

%G eng %U https://arxiv.org/abs/1812.02746 %0 Journal Article %J Quantum %D 2018 %T BQP-completeness of Scattering in Scalar Quantum Field Theory %A Stephen P. Jordan %A Hari Krovi %A Keith S. M. Lee %A John Preskill %XRecent work has shown that quantum computers can compute scattering probabilities in massive quantum field theories, with a run time that is polynomial in the number of particles, their energy, and the desired precision. Here we study a closely related quantum field-theoretical problem: estimating the vacuum-to-vacuum transition amplitude, in the presence of spacetime-dependent classical sources, for a massive scalar field theory in (1+1) dimensions. We show that this problem is BQP-hard; in other words, its solution enables one to solve any problem that is solvable in polynomial time by a quantum computer. Hence, the vacuum-to-vacuum amplitude cannot be accurately estimated by any efficient classical algorithm, even if the field theory is very weakly coupled, unless BQP=BPP. Furthermore, the corresponding decision problem can be solved by a quantum computer in a time scaling polynomially with the number of bits needed to specify the classical source fields, and this problem is therefore BQP-complete. Our construction can be regarded as an idealized architecture for a universal quantum computer in a laboratory system described by massive phi^4 theory coupled to classical spacetime-dependent sources.

%B Quantum %V 2 %P 44 %8 2018/01/08 %G eng %U https://quantum-journal.org/papers/q-2018-01-08-44/ %R 10.22331/q-2018-01-08-44 %0 Journal Article %D 2018 %T Coherent optical nano-tweezers for ultra-cold atoms %A P. Bienias %A S. Subhankar %A Y. Wang %A T-C Tsui %A F. Jendrzejewski %A T. Tiecke %A G. Juzeliūnas %A L. Jiang %A S. L. Rolston %A J. V. Porto %A Alexey V. Gorshkov %XThere has been a recent surge of interest and progress in creating subwavelength free-space optical potentials for ultra-cold atoms. A key open question is whether geometric potentials, which are repulsive and ubiquitous in the creation of subwavelength free-space potentials, forbid the creation of narrow traps with long lifetimes. Here, we show that it is possible to create such traps. We propose two schemes for realizing subwavelength traps and demonstrate their superiority over existing proposals. We analyze the lifetime of atoms in such traps and show that long-lived bound states are possible. This work opens a new frontier for the subwavelength control and manipulation of ultracold matter, with applications in quantum chemistry and quantum simulation.

%G eng %U https://arxiv.org/abs/1808.02487 %0 Journal Article %J Physical Review A %D 2018 %T Diffusion Monte Carlo Versus Adiabatic Computation for Local Hamiltonians %A Jacob Bringewatt %A William Dorland %A Stephen P. Jordan %A Alan Mink %XMost research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real, nonnegative amplitudes. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX-k-SAT problems, use k-local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved n-body interactions. Here we present a new 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.

%B Physical Review A %V 97 %P 022323 %8 2018/02/15 %G eng %U https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.022323 %N 2 %R 10.1103/PhysRevA.97.022323 %0 Journal Article %J Phys. Rev. Lett. 121, 043604 %D 2018 %T Distributed Quantum Metrology and the Entangling Power of Linear Networks %A Wenchao Ge %A Kurt Jacobs %A Zachary Eldredge %A Alexey V. Gorshkov %A Michael Foss-Feig %XWe derive a bound on the ability of a linear optical network to estimate a linear combination of independent phase shifts by using an arbitrary non-classical but unentangled input state, thereby elucidating the quantum resources required to obtain the Heisenberg limit with a multi-port interferometer. Our bound reveals that while linear networks can generate highly entangled states, they cannot effectively combine quantum resources that are well distributed across multiple modes for the purposes of metrology: in this sense linear networks endowed with well-distributed quantum resources behave classically. Conversely, our bound shows that linear networks can achieve the Heisenberg limit for distributed metrology when the input photons are hoarded in a small number of input modes, and we present an explicit scheme for doing so. Our results also have implications for measures of non-classicality.

%B Phys. Rev. Lett. 121, 043604 %8 2018/07/25 %G eng %U https://arxiv.org/abs/1707.06655 %R https://doi.org/10.1103/PhysRevLett.121.043604 %0 Journal Article %D 2018 %T Distributed Quantum Metrology and the Entangling Power of Linear Networks %A Wenchao Ge %A Kurt Jacobs %A Zachary Eldredge %A Alexey V. Gorshkov %A Michael Foss-Feig %XWe derive a bound on the ability of a linear optical network to estimate a linear combination of independent phase shifts by using an arbitrary non-classical but unentangled input state, thereby elucidating the quantum resources required to obtain the Heisenberg limit with a multi-port interferometer. Our bound reveals that while linear networks can generate highly entangled states, they cannot effectively combine quantum resources that are well distributed across multiple modes for the purposes of metrology: in this sense linear networks endowed with well-distributed quantum resources behave classically. Conversely, our bound shows that linear networks can achieve the Heisenberg limit for distributed metrology when the input photons are hoarded in a small number of input modes, and we present an explicit scheme for doing so. Our results also have implications for measures of non-classicality.

%8 2018/07/25 %G eng %U https://arxiv.org/abs/1707.06655 %R https://doi.org/10.1103/PhysRevLett.121.043604 %0 Journal Article %J Nature %D 2018 %T Experimentally Generated Randomness Certified by the Impossibility of Superluminal Signals %A Peter Bierhorst %A Emanuel Knill %A Scott Glancy %A Yanbao Zhang %A Alan Mink %A Stephen Jordan %A Andrea Rommal %A Yi-Kai Liu %A Bradley Christensen %A Sae Woo Nam %A Martin J. Stevens %A Lynden K. Shalm %XFrom 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.

%B Nature %V 556 %P 223-226 %8 2018/04/11 %G eng %U https://arxiv.org/abs/1803.06219 %R https://doi.org/10.1038/s41586-018-0019-0 %0 Journal Article %J Phys. Rev. A 98, 012332 (2018) %D 2018 %T Faster Quantum Algorithm to simulate Fermionic Quantum Field Theory %A Moosavian, Ali Hamed %A Stephen Jordan %XIn quantum algorithms discovered so far for simulating scattering processes in quantum field theories, state preparation is the slowest step. We present a new algorithm for preparing particle states to use in simulation of Fermionic Quantum Field Theory (QFT) on a quantum computer, which is based on the matrix product state ansatz. We apply this to the massive Gross-Neveu model in one spatial dimension to illustrate the algorithm, but we believe the same algorithm with slight modifications can be used to simulate any one-dimensional massive Fermionic QFT. In the case where the number of particle species is one, our algorithm can prepare particle states using O(ε−3.23…) gates, which is much faster than previous known results, namely O(ε−8−o(1)). Furthermore, unlike previous methods which were based on adiabatic state preparation, the method given here should be able to simulate quantum phases unconnected to the free theory.

%B Phys. Rev. A 98, 012332 (2018) %V A %P 012332 %8 2018/05/04 %G eng %U https://arxiv.org/abs/1711.04006 %N 98 %R https://doi.org/10.1103/PhysRevA.98.012332 %0 Journal Article %D 2018 %T On non-adaptive quantum chosen-ciphertext attacks and Learning with Errors %A Gorjan Alagic %A Stacey Jeffery %A Maris Ozols %A Alexander Poremba %XLarge-scale quantum computing is a significant threat to classical public-key cryptography. In strong "quantum access" security models, numerous symmetric-key cryptosystems are also vulnerable. We consider classical encryption in a model which grants the adversary quantum oracle access to encryption and decryption, but where the latter is restricted to non-adaptive (i.e., pre-challenge) queries only. We define this model formally using appropriate notions of ciphertext indistinguishability and semantic security (which are equivalent by standard arguments) and call it QCCA1 in analogy to the classical CCA1 security model. Using a bound on quantum random-access codes, we show that the standard PRF- and PRP-based encryption schemes are QCCA1-secure when instantiated with quantum-secure primitives. We then revisit standard IND-CPA-secure Learning with Errors (LWE) encryption and show that leaking just one quantum decryption query (and no other queries or leakage of any kind) allows the adversary to recover the full secret key with constant success probability. In the classical setting, by contrast, recovering the key uses a linear number of decryption queries, and this is optimal. The algorithm at the core of our attack is a (large-modulus version of) the well-known Bernstein-Vazirani algorithm. We emphasize that our results should *not* be interpreted as a weakness of these cryptosystems in their stated security setting (i.e., post-quantum chosen-plaintext secrecy). Rather, our results mean that, if these cryptosystems are exposed to chosen-ciphertext attacks (e.g., as a result of deployment in an inappropriate real-world setting) then quantum attacks are even more devastating than classical ones.

%G eng %U https://arxiv.org/abs/1808.09655 %0 Journal Article %J Phys. Rev. Lett. %D 2018 %T Optimal Pure-State Qubit Tomography via Sequential Weak Measurements %A Ezad Shojaee %A Christopher S. Jackson %A Carlos A. Riofrio %A Amir Kalev %A Ivan H. Deutsch %XThe spin-coherent-state positive-operator-valued-measure (POVM) is a fundamental measurement in quantum science, with applications including tomography, metrology, teleportation, benchmarking, and measurement of Husimi phase space probabilities. We prove that this POVM is achieved by collectively measuring the spin projection of an ensemble of qubits weakly and isotropically. We apply this in the context of optimal tomography of pure qubits. We show numerically that through a sequence of weak measurements of random directions of the collective spin component, sampled discretely or in a continuous measurement with random controls, one can approach the optimal bound.

%B Phys. Rev. Lett. %V 121 %G eng %U https://arxiv.org/abs/1805.01012 %N 130404 %R https://doi.org/10.1103/PhysRevLett.121.130404 %0 Journal Article %J In: Shacham H., Boldyreva A. (eds) Advances in Cryptology – CRYPTO 2018. CRYPTO 2018. Lecture Notes in Computer Science. %D 2018 %T Pseudorandom States, Non-Cloning Theorems and Quantum Money %A Zhengfeng Ji %A Yi-Kai Liu %A Fang Song %XWe propose the concept of pseudorandom states and study their constructions, properties, and applications. Under the assumption that quantum-secure one-way functions exist, we present concrete and efficient constructions of pseudorandom states. The non-cloning theorem plays a central role in our study—it motivates the proper definition and characterizes one of the important properties of pseudorandom quantum states. Namely, there is no efficient quantum algorithm that can create more copies of the state from a given number of pseudorandom states. As the main application, we prove that any family of pseudorandom states naturally gives rise to a private-key quantum money scheme.

%B In: Shacham H., Boldyreva A. (eds) Advances in Cryptology – CRYPTO 2018. CRYPTO 2018. Lecture Notes in Computer Science. %V 10993 %8 2017/11/01 %G eng %U https://arxiv.org/abs/1711.00385 %R https://doi.org/10.1007/978-3-319-96878-0_5 %0 Journal Article %D 2018 %T Quantum adiabatic optimization without heuristics %A Michael Jarret %A Brad Lackey %A Aike Liu %A Kianna Wan %XQuantum adiabatic optimization (QAO) is performed using a time-dependent Hamiltonian H(s) with spectral gap γ(s). Assuming the existence of an oracle Γ such that γ(s)=Θ(Γ(s)), we provide an algorithm that reliably performs QAO in time Oγ−1minlog(γ−1min) with Olog(γ−1min) oracle queries, where γmin=minsγ(s). Our strategy is not heuristic and does not require guessing time parameters or annealing paths. Rather, our algorithm naturally produces an annealing path such that dH/ds≈γ(s) and chooses its own runtime T to be as close as possible to optimal while promising convergence to the ground state. We then demonstrate the feasibility of this approach in practice by explicitly constructing a gap oracle Γ for the problem of finding a vertex m=argminuW(u) of the cost function W:V⟶[0,1], restricting ourselves to computational basis measurements and driving Hamiltonian H(0)=I−V−1∑u,v∈V|u⟩⟨v|, with V=|V|. Requiring only that W have a constant lower bound on its spectral gap and upper bound κ on its spectral ratio, our QAO algorithm returns m using Γ with probability (1−ε)(1−e−1/ε) in time O˜(ε−1[V−−√+(κ−1)2/3V2/3]). This achieves a quantum advantage for all κ, and when κ≈1, recovers Grover scaling up to logarithmic factors. We implement the algorithm as a subroutine in an optimization procedure that produces m with exponentially small failure probability and expected runtime O˜(ε−1[V−−√+(κ−1)2/3V2/3]), even when κ is not known beforehand.

%G eng %U https://arxiv.org/abs/1810.04686 %0 Journal Article %J IEEE Security & Privacy %D 2018 %T Quantum Cryptanalysis: Shor, Grover, and Beyond %A Stephen P. Jordan %A Yi-Kai Liu %B IEEE Security & Privacy %V 16 %P 14-21 %8 2018/09 %G eng %N 5 %R 10.1109/MSP.2018.3761719 %0 Journal Article %J Physical Review Letters %D 2017 %T Efimov States of Strongly Interacting Photons %A M. J. Gullans %A S. Diehl %A S. T. Rittenhouse %A B. P. Ruzic %A J. P. D'Incao %A P. Julienne %A Alexey V. Gorshkov %A J. M. Taylor %XWe demonstrate the emergence of universal Efimov physics for interacting photons in cold gases of Rydberg atoms. We consider the behavior of three photons injected into the gas in their propagating frame, where a paraxial approximation allows us to consider them as massive particles. In contrast to atoms and nuclei, the photons have a large anisotropy between their longitudinal mass, arising from dispersion, and their transverse mass, arising from diffraction. Nevertheless, we show that in suitably rescaled coordinates the effective interactions become dominated by s-wave scattering near threshold and, as a result, give rise to an Efimov effect near unitarity, but with spatially anisotropic wavefunctions in the original coordinates. We show that the three-body loss of these Efimov trimers can be strongly suppressed and determine conditions under which these states are observable in current experiments. These effects can be naturally extended to probe few-body universality beyond three bodies, as well as the role of Efimov physics in the non-equilbrium, many-body regime.

%B Physical Review Letters %V 119 %P 233601 %8 2017/12/04 %G eng %U https://arxiv.org/abs/1709.01955 %N 23 %R 10.1103/PhysRevLett.119.233601 %0 Journal Article %J Physical Review Letters %D 2017 %T Experimental Study of Optimal Measurements for Quantum State Tomography %A Sosa-Martinez, H. %A Lysne, N. K. %A Baldwin, C. H. %A Kalev, A. %A Deutsch, I. H. %A Jessen, P. S. %XQuantum tomography is a critically important tool to evaluate quantum hardware, making it essential to develop optimized measurement strategies that are both accurate and efficient. We compare a variety of strategies using nearly pure test states. Those that are informationally complete for all states are found to be accurate and reliable even in the presence of errors in the measurements themselves, while those designed to be complete only for pure states are far more efficient but highly sensitive to such errors. Our results highlight the unavoidable trade-offs inherent in quantum tomography.

%B Physical Review Letters %V 119 %P 150401 %8 2017/10/13 %G eng %U https://link.aps.org/doi/10.1103/PhysRevLett.119.150401 %N 15 %R 10.1103/PhysRevLett.119.150401 %0 Journal Article %D 2017 %T Experimentally Generated Random Numbers Certified by the Impossibility of Superluminal Signaling %A Peter Bierhorst %A Emanuel Knill %A Scott Glancy %A Alan Mink %A Stephen P. Jordan %A Andrea Rommal %A Yi-Kai Liu %A Bradley Christensen %A Sae Woo Nam %A Lynden K. Shalm %XRandom 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.

%8 2017/02/16 %G eng %U https://arxiv.org/abs/1702.05178# %0 Journal Article %J Physical Review D %D 2017 %T Fast optimization algorithms and the cosmological constant %A Ning Bao %A Raphael Bousso %A Stephen P. Jordan %A Brad Lackey %XDenef and Douglas have observed that in certain landscape models the problem of finding small values of the cosmological constant is a large instance of an NP-hard problem. The number of elementary operations (quantum gates) needed to solve this problem by brute force search exceeds the estimated computational capacity of the observable universe. Here we describe a way out of this puzzling circumstance: despite being NP-hard, the problem of finding a small cosmological constant can be attacked by more sophisticated algorithms whose performance vastly exceeds brute force search. In fact, in some parameter regimes the average-case complexity is polynomial. We demonstrate this by explicitly finding a cosmological constant of order 10−120 in a randomly generated 109 -dimensional ADK landscape.

%B Physical Review D %V 96 %P 103512 %8 2017/11/13 %G eng %U https://arxiv.org/abs/1706.08503 %N 10 %R 10.1103/PhysRevD.96.103512 %0 Journal Article %J Physical Review A %D 2017 %T Fast quantum computation at arbitrarily low energy %A Stephen P. Jordan %XOne version of the energy-time uncertainty principle states that the minimum time T⊥ for a quantum system to evolve from a given state to any orthogonal state is h/(4ΔE), where ΔE is the energy uncertainty. A related bound called the Margolus-Levitin theorem states that T⊥≥h/(2⟨E⟩), where ⟨E⟩ is the expectation value of energy and the ground energy is taken to be zero. Many subsequent works have interpreted T⊥ as defining a minimal time for an elementary computational operation and correspondingly a fundamental limit on clock speed determined by a system's energy. Here we present local time-independent Hamiltonians in which computational clock speed becomes arbitrarily large relative to ⟨E⟩ and ΔE as the number of computational steps goes to infinity. We argue that energy considerations alone are not sufficient to obtain an upper bound on computational speed, and that additional physical assumptions such as limits to information density and information transmission speed are necessary to obtain such a bound.

%B Physical Review A %V 95 %P 032305 %8 2017/03/06 %G eng %U http://link.aps.org/doi/10.1103/PhysRevA.95.032305 %R 10.1103/PhysRevA.95.032305 %0 Journal Article %J Journal of Mathematical Analysis and Applications %D 2017 %T Modulus of continuity eigenvalue bounds for homogeneous graphs and convex subgraphs with applications to quantum Hamiltonians %A Michael Jarret %A Stephen P. Jordan %XWe adapt modulus of continuity estimates to the study of spectra of combinatorial graph Laplacians, as well as the Dirichlet spectra of certain weighted Laplacians. The latter case is equivalent to stoquastic Hamiltonians and is of current interest in both condensed matter physics and quantum computing. In particular, we introduce a new technique which bounds the spectral gap of such Laplacians (Hamiltonians) by studying the limiting behavior of the oscillations of their eigenvectors when introduced into the heat equation. Our approach is based on recent advances in the PDE literature, which include a proof of the fundamental gap theorem by Andrews and Clutterbuck.

%B Journal of Mathematical Analysis and Applications %V 452 %P 1269-1290 %8 2017/03/03 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022247X1730272X %N 2 %R 10.1016/j.jmaa.2017.03.030 %0 Journal Article %D 2017 %T Parallel Device-Independent Quantum Key Distribution %A Rahul Jain %A Carl Miller %A Yaoyun Shi %XA prominent application of quantum cryptography is the distribution of cryptographic keys with unconditional security. Recently, such security was extended by Vazirani and Vidick (Physical Review Letters, 113, 140501, 2014) to the device-independent (DI) scenario, where the users do not need to trust the integrity of the underlying quantum devices. The protocols analyzed by them and by subsequent authors all require a sequential execution of N multiplayer games, where N is the security parameter. In this work, we prove unconditional security of a protocol where all games are executed in parallel. Our result further reduces the requirements for QKD (allowing for arbitrary information leakage within each players' lab) and opens the door to more efficient implementation. To the best of our knowledge, this is the first parallel security proof for a fully device-independent QKD protocol. Our protocol tolerates a constant level of device imprecision and achieves a linear key rate.

%8 2017/03/15 %G eng %U https://arxiv.org/abs/1703.05426 %0 Journal Article %D 2017 %T Quantum Algorithms for Graph Connectivity and Formula Evaluation %A Stacey Jeffery %A Shelby Kimmel %XWe give a new upper bound on the quantum query complexity of deciding st-connectivity on certain classes of planar graphs, and show the bound is sometimes exponentially better than previous results. We then show Boolean formula evaluation reduces to deciding connectivity on just such a class of graphs. Applying the algorithm for st-connectivity to Boolean formula evaluation problems, we match the O( √ N) bound on the quantum query complexity of evaluating formulas on N variables, give a quadratic speed-up over the classical query complexity of a certain class of promise Boolean formulas, and show this approach can yield superpolynomial quantum/classical separations. These results indicate that this st-connectivity-based approach may be the “right” way of looking at quantum algorithms for formula evaluation.

%8 2017/04/03 %G eng %U https://arxiv.org/abs/1704.00765 %0 Journal Article %J Physical Review Letters %D 2017 %T Quantum state tomography via reduced density matrices %A Tao Xin %A Dawei Lu %A Joel Klassen %A Nengkun Yu %A Zhengfeng Ji %A Jianxin Chen %A Xian Ma %A Guilu Long %A Bei Zeng %A Raymond Laflamme %XQuantum 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.

%B Physical Review Letters %V 118 %P 020401 %8 2017/01/09 %G eng %U http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.020401 %R 10.1103/PhysRevLett.118.020401 %0 Journal Article %D 2017 %T Substochastic Monte Carlo Algorithms %A Michael Jarret %A Brad Lackey %XIn this paper we introduce and formalize Substochastic Monte Carlo (SSMC) algorithms. These algorithms, originally intended to be a better classical foil to quantum annealing than simulated annealing, prove to be worthy optimization algorithms in their own right. In SSMC, a population of walkers is initialized according to a known distribution on an arbitrary search space and varied into the solution of some optimization problem of interest. The first argument of this paper shows how an existing classical algorithm, "Go-With-The-Winners" (GWW), is a limiting case of SSMC when restricted to binary search and particular driving dynamics.

Although limiting to GWW, SSMC is more general. We show that (1) GWW can be efficiently simulated within the SSMC framework, (2) SSMC can be exponentially faster than GWW, (3) by naturally incorporating structural information, SSMC can exponentially outperform the quantum algorithm that first inspired it, and (4) SSMC exhibits desirable search features in general spaces. Our approach combines ideas from genetic algorithms (GWW), theoretical probability (Fleming-Viot processes), and quantum computing. Not only do we demonstrate that SSMC is often more efficient than competing algorithms, but we also hope that our results connecting these disciplines will impact each independently. An implemented version of SSMC has previously enjoyed some success as a competitive optimization algorithm for Max-

Most experimental and theoretical studies of adiabatic optimization use stoquastic Hamiltonians, whose ground states are expressible using only real nonnegative amplitudes. This raises a question as to whether classical Monte Carlo methods can simulate stoquastic adiabatic algorithms with polynomial overhead. Here, we analyze diffusion Monte Carlo algorithms. We argue that, based on differences between L1 and L2 normalized states, these algorithms suffer from certain obstructions preventing them from efficiently simulating stoquastic adiabatic evolution in generality. In practice however, we obtain good performance by introducing a method that we call Substochastic Monte Carlo. In fact, our simulations are good classical optimization algorithms in their own right, competitive with the best previously known heuristic solvers for MAX-k-SAT at k=2,3,4.

%B Physical Review A %V 94 %P 042318 %8 2016/07/12 %G eng %U https://arxiv.org/abs/1607.03389 %0 Journal Article %J XRDS %D 2016 %T Black Holes, Quantum Mechanics, and the Limits of Polynomial-time Computability %A Stephen P. Jordan %XWhich computational problems can be solved in polynomial-time and which cannot? Though seemingly technical, this question has wide-ranging implications and brings us to the heart of both theoretical computer science and modern physics.

%B XRDS %V 23 %P 30–33 %8 2016/09/20 %G eng %U http://doi.acm.org/10.1145/2983539 %R 10.1145/2983539 %0 Conference Paper %B Computational Security of Quantum Encryption. In: Nascimento A., Barreto P. (eds) Information Theoretic Security. %D 2016 %T Computational Security of Quantum Encryption %A Gorjan Alagic %A Anne Broadbent %A Bill Fefferman %A Tommaso Gagliardoni %A Christian Schaffner %A Michael St. Jules %XQuantum-mechanical devices have the potential to transform cryptography. Most research in this area has focused either on the information-theoretic advantages of quantum protocols or on the security of classical cryptographic schemes against quantum attacks. In this work, we initiate the study of another relevant topic: the encryption of quantum data in the computational setting. In this direction, we establish quantum versions of several fundamental classical results. First, we develop natural definitions for private-key and public-key encryption schemes for quantum data. We then define notions of semantic security and indistinguishability, and, in analogy with the classical work of Goldwasser and Micali, show that these notions are equivalent. Finally, we construct secure quantum encryption schemes from basic primitives. In particular, we show that quantum-secure one-way functions imply IND-CCA1-secure symmetric-key quantum encryption, and that quantum-secure trapdoor one-way permutations imply semantically-secure public-key quantum encryption.

%B Computational Security of Quantum Encryption. In: Nascimento A., Barreto P. (eds) Information Theoretic Security. %8 2016/11/10 %G eng %U https://link.springer.com/chapter/10.1007%2F978-3-319-49175-2_3 %0 Journal Article %J Physical Review A %D 2016 %T Detecting Consistency of Overlapping Quantum Marginals by Separability %A Jianxin Chen %A Zhengfeng Ji %A Nengkun Yu %A Bei Zeng %X 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. %B Physical Review A %V 93 %P 032105 %8 2016/03/03 %G eng %U http://arxiv.org/abs/1509.06591 %N 3 %R 10.1103/PhysRevA.93.032105 %0 Journal Article %J Physical Review Letters %D 2016 %T Grover search and the no-signaling principle %A Ning Bao %A Adam Bouland %A Stephen P. Jordan %XFrom an information processing point of view, two of the key properties of quantum physics are the no-signaling principle and the Grover search lower bound. That is, despite admitting stronger-than-classical correlations, quantum mechanics does not imply superluminal signaling, and despite a form of exponential parallelism, quantum mechanics does not imply polynomial-time brute force solution of NP-complete problems. Here, we investigate the degree to which these two properties are connected. We examine four classes of deviations from quantum mechanics, for which we draw inspiration from the literature on the black hole information paradox: nonunitary dynamics, non-Born-rule measurement, cloning, and postselection. We find that each model admits superluminal signaling if and only if it admits a query complexity speedup over Grover's algorithm. Furthermore, we show that the physical resources required to send a superluminal signal scale polynomially with the resources needed to speed up Grover's algorithm. Hence, one can perform a physically reasonable experiment demonstrating superluminal signaling if and only if one can perform a reasonable experiment inducing a speedup over Grover's algorithm.

%B Physical Review Letters %V 117 %P 120501 %8 2016/09/14 %G eng %U http://arxiv.org/abs/1511.00657 %0 Journal Article %J Nature Photonics %D 2016 %T High resolution adaptive imaging of a single atom %A J. D. Wong-Campos %A K. G. Johnson %A Brian Neyenhuis %A J. Mizrahi %A Chris Monroe %XWe report the optical imaging of a single atom with nanometer resolution using an adaptive optical alignment technique that is applicable to general optical microscopy. By decomposing the image of a single laser-cooled atom, we identify and correct optical aberrations in the system and realize an atomic position sensitivity of ≈ 0.5 nm/Hz−−−√ with a minimum uncertainty of 1.7 nm, allowing the direct imaging of atomic motion. This is the highest position sensitivity ever measured for an isolated atom, and opens up the possibility of performing out-of-focus 3D particle tracking, imaging of atoms in 3D optical lattices or sensing forces at the yoctonewton (10−24 N) scale.

%B Nature Photonics %P 606-610 %8 2016/07/18 %G eng %U https://www.nature.com/nphoton/journal/v10/n9/full/nphoton.2016.136.html %N 10 %R 10.1038/nphoton.2016.136 %0 Journal Article %J Physical Review A %D 2016 %T A Hubbard model for ultracold bosonic atoms interacting via zero-point-energy induced three-body interactions %A Saurabh Paul %A P. R. Johnson %A Eite Tiesinga %XWe show that for ultra-cold neutral bosonic atoms held in a three-dimensional periodic potential or optical lattice, a Hubbard model with dominant, attractive three-body interactions can be generated. In fact, we derive that the effect of pair-wise interactions can be made small or zero starting from the realization that collisions occur at the zero-point energy of an optical lattice site and the strength of the interactions is energy dependent from effective-range contributions. We determine the strength of the two- and three-body interactions for scattering from van-der-Waals potentials and near Fano-Feshbach resonances. For van-der-Waals potentials, which for example describe scattering of alkaline-earth atoms, we find that the pair-wise interaction can only be turned off for species with a small negative scattering length, leaving the 88Sr isotope a possible candidate. Interestingly, for collisional magnetic Feshbach resonances this restriction does not apply and there often exist magnetic fields where the two-body interaction is small. We illustrate this result for several known narrow resonances between alkali-metal atoms as well as chromium atoms. Finally, we compare the size of the three-body interaction with hopping rates and describe limits due to three-body recombination.

%B Physical Review A %V 93 %P 043616 %8 2016/04/19 %G eng %U http://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.043616 %N 4 %R 10.1103/PhysRevA.93.043616 %0 Journal Article %D 2016 %T Joint product numerical range and geometry of reduced density matrices %A Jianxin Chen %A Cheng Guo %A Zhengfeng Ji %A Yiu-Tung Poon %A Nengkun Yu %A Bei Zeng %A Jie Zhou %X 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'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. %8 2016/06/23 %G eng %U http://arxiv.org/abs/1606.07422 %0 Journal Article %J Physical Review A %D 2016 %T Optimized tomography of continuous variable systems using excitation counting %A Shen, Chao %A Heeres, Reinier W. %A Reinhold, Philip %A Jiang, Luyao %A Yi-Kai Liu %A Schoelkopf, Robert J. %A Jiang, Liang %XWe propose a systematic procedure to optimize quantum state tomography protocols for continuous variable systems based on excitation counting preceded by a displacement operation. Compared with conventional tomography based on Husimi or Wigner function measurement, the excitation counting approach can significantly reduce the number of measurement settings. We investigate both informational completeness and robustness, and provide a bound of reconstruction error involving the condition number of the sensing map. We also identify the measurement settings that optimize this error bound, and demonstrate that the improved reconstruction robustness can lead to an order-of-magnitude reduction of estimation error with given resources. This optimization procedure is general and can incorporate prior information of the unknown state to further simplify the protocol.

%B Physical Review A %V 94 %P 052327 %8 2016/11/21 %G eng %U http://link.aps.org/doi/10.1103/PhysRevA.94.052327 %R 10.1103/PhysRevA.94.052327 %0 Journal Article %J Physical Review A %D 2016 %T Photoassociation of spin polarized Chromium %A Jahn Rührig %A Tobias Bäuerle %A Paul S. Julienne %A Eite Tiesinga %A Tilman Pfau %X We report the homonuclear photoassociation (PA) of ultracold 52Cr atoms in an optical dipole trap. This constitutes the first measurement of PA in an element with total electron spin S~>1. Although Cr, with its 7S3 ground and 7P4,3,2 excited states, is expected to have a complicated PA spectrum we show that a spin polarized cloud exhibits a remarkably simple PA spectrum when circularly polarized light is applied. Over a scan range of 20 GHz below the 7P3 asymptote we observe two distinct vibrational series each following a LeRoy-Bernstein law for a C3/R3 potential with excellent agreement. We determine the C3 coefficients of the Hund's case c) relativistic adiabatic potentials to be -1.83±0.02 a.u. and -1.46±0.01a.u.. Theoretical non-rotating Movre-Pichler calculations enable a first assignment of the series to Ω=6u and 5g potential energy curves. In a different set of experiments we disturb the selection rules by a transverse magnetic field which leads to additional PA series. %B Physical Review A %V 93 %P 021406 %8 2016/02/29 %G eng %U http://arxiv.org/abs/1512.04378 %N 2 %R 10.1103/PhysRevA.93.021406 %0 Journal Article %J Physical Review A %D 2016 %T Pure-state tomography with the expectation value of Pauli operators %A Xian Ma %A Tyler Jackson %A Hui Zhou %A Jianxin Chen %A Dawei Lu %A Michael D. Mazurek %A Kent A.G. Fisher %A Xinhua Peng %A David Kribs %A Kevin J. Resch %A Zhengfeng Ji %A Bei Zeng %A Raymond Laflamme %XWe 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.

%B Physical Review A %V 93 %P 032140 %8 2016/03/31 %G eng %U http://arxiv.org/abs/1601.05379 %N 3 %R http://dx.doi.org/10.1103/PhysRevA.93.032140 %0 Journal Article %J Physical Review A %D 2016 %T Quantifying the coherence of pure quantum states %A Jianxin Chen %A Nathaniel Johnston %A Chi-Kwong Li %A Sarah Plosker %XIn 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.

%B Physical Review A %V 94 %P 042313 %8 2016/10/07 %G eng %U https://doi.org/10.1103/PhysRevA.94.042313 %N 4 %R 10.1103/PhysRevA.94.042313 %0 Journal Article %J Physical Review A %D 2016 %T Subwavelength-width optical tunnel junctions for ultracold atoms %A Jendrzejewski, F. %A Eckel, S. %A Tiecke, T. G. %A G. Juzeliūnas %A Campbell, G. K. %A Jiang, Liang %A Alexey V. Gorshkov %XWe 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.

%B Physical Review A %V 94 %P 063422 %8 2016/12/27 %G eng %U http://link.aps.org/doi/10.1103/PhysRevA.94.063422 %N 6 %R 10.1103/PhysRevA.94.063422 %0 Journal Article %J Physical Review Letters %D 2016 %T Tomography is necessary for universal entanglement detection with single-copy observables %A Dawei Lu %A Tao Xin %A Nengkun Yu %A Zhengfeng Ji %A Jianxin Chen %A Guilu Long %A Jonathan Baugh %A Xinhua Peng %A Bei Zeng %A Raymond Laflamme %X 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. %B Physical Review Letters %V 116 %P 230501 %8 2016/06/07 %G eng %U http://arxiv.org/abs/1511.00581 %N 23 %R 10.1103/PhysRevLett.116.230501 %0 Journal Article %J Journal of Physics A %D 2016 %T Yang-Baxter operators need quantum entanglement to distinguish knots %A Gorjan Alagic %A Michael Jarret %A Stephen P. Jordan %X Any solution to the Yang-Baxter equation yields a family of representations of braid groups. Under certain conditions, identified by Turaev, the appropriately normalized trace of these representations yields a link invariant. Any Yang-Baxter solution can be interpreted as a two-qudit quantum gate. Here we show that if this gate is non-entangling, then the resulting invariant of knots is trivial. We thus obtain a general connection between topological entanglement and quantum entanglement, as suggested by Kauffman et al. %B Journal of Physics A %V 49 %P 075203 %8 2016/01/12 %G eng %U http://arxiv.org/abs/1507.05979 %N 7 %R 10.1088/1751-8113/49/7/075203 %0 Journal Article %J Quantum Information and Computation %D 2015 %T Adiabatic optimization without local minima %A Michael Jarret %A Stephen P. Jordan %X Several previous works have investigated the circumstances under which quantum adiabatic optimization algorithms can tunnel out of local energy minima that trap simulated annealing or other classical local search algorithms. Here we investigate the even more basic question of whether adiabatic optimization algorithms always succeed in polynomial time for trivial optimization problems in which there are no local energy minima other than the global minimum. Surprisingly, we find a counterexample in which the potential is a single basin on a graph, but the eigenvalue gap is exponentially small as a function of the number of vertices. In this counterexample, the ground state wavefunction consists of two "lobes" separated by a region of exponentially small amplitude. Conversely, we prove if the ground state wavefunction is single-peaked then the eigenvalue gap scales at worst as one over the square of the number of vertices. %B Quantum Information and Computation %V 15 %P 181-199 %8 2015/05/01 %G eng %U http://arxiv.org/abs/1405.7552 %N 3-4 %! Quantum Information and Computation %0 Journal Article %J New Journal of Physics %D 2015 %T Demonstration of Robust Quantum Gate Tomography via Randomized Benchmarking %A Blake R. Johnson %A Marcus P. da Silva %A Colm A. Ryan %A Shelby Kimmel %A Jerry M. Chow %A Thomas A. Ohki %X 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 `atomic' 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. %B New Journal of Physics %V 17 %P 113019 %8 2015/11/05 %G eng %U http://arxiv.org/abs/1505.06686 %N 11 %R 10.1088/1367-2630/17/11/113019 %0 Journal Article %J New Journal of Physics %D 2015 %T Discontinuity of Maximum Entropy Inference and Quantum Phase Transitions %A Jianxin Chen %A Zhengfeng Ji %A Chi-Kwong Li %A Yiu-Tung Poon %A Yi Shen %A Nengkun Yu %A Bei Zeng %A Duanlu Zhou %X 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. %B New Journal of Physics %V 17 %P 083019 %8 2015/08/10 %G eng %U http://arxiv.org/abs/1406.5046v2 %N 8 %! New J. Phys. %R 10.1088/1367-2630/17/8/083019 %0 Journal Article %J Communications in Mathematical Physics %D 2015 %T The Minimum Size of Unextendible Product Bases in the Bipartite Case (and Some Multipartite Cases) %A Jianxin Chen %A Nathaniel Johnston %X 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. %B Communications in Mathematical Physics %V 333 %P 351 - 365 %8 2014/10/10 %G eng %U http://arxiv.org/abs/1301.1406v1 %N 1 %! Commun. Math. Phys. %R 10.1007/s00220-014-2186-7 %0 Journal Article %J Physical Review A %D 2015 %T Self-heterodyne detection of the \it in-situ phase of an atomic-SQUID %A Ranchu Mathew %A Avinash Kumar %A Stephen Eckel %A Fred Jendrzejewski %A Gretchen K. Campbell %A Mark Edwards %A Eite Tiesinga %X 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. %B Physical Review A %V 92 %P 033602 %8 2015/09/03 %G eng %U http://arxiv.org/abs/1506.09149v2 %N 3 %! Phys. Rev. A %R 10.1103/PhysRevA.92.033602 %0 Journal Article %J 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014) %D 2014 %T Classical simulation of Yang-Baxter gates %A Gorjan Alagic %A Aniruddha Bapat %A Stephen P. Jordan %X A unitary operator that satisfies the constant Yang-Baxter equation immediately yields a unitary representation of the braid group B n for every $n \ge 2$. If we view such an operator as a quantum-computational gate, then topological braiding corresponds to a quantum circuit. A basic question is when such a representation affords universal quantum computation. In this work, we show how to classically simulate these circuits when the gate in question belongs to certain families of solutions to the Yang-Baxter equation. These include all of the qubit (i.e., $d = 2$) solutions, and some simple families that include solutions for arbitrary $d \ge 2$. Our main tool is a probabilistic classical algorithm for efficient simulation of a more general class of quantum circuits. This algorithm may be of use outside the present setting. %B 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014) %V 27 %P 161-175 %8 2014/07/05 %G eng %U http://arxiv.org/abs/1407.1361v1 %! 9th Conference on the Theory of Quantum Computation %R 10.4230/LIPIcs.TQC.2014.161 %0 Journal Article %J Journal of Mathematical Cryptology %D 2014 %T Constructing elliptic curve isogenies in quantum subexponential time %A Andrew M. Childs %A David Jao %A Vladimir Soukharev %X 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'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. %B Journal of Mathematical Cryptology %V 8 %P 1 - 29 %8 2014/01/01 %G eng %U http://arxiv.org/abs/1012.4019v2 %N 1 %! J. Math. Cryptol. %R 10.1515/jmc-2012-0016 %0 Journal Article %J Journal of Mathematical Physics %D 2014 %T The Fundamental Gap for a Class of Schrödinger Operators on Path and Hypercube Graphs %A Michael Jarret %A Stephen P. Jordan %X We consider the difference between the two lowest eigenvalues (the fundamental gap) of a Schr\"{o}dinger operator acting on a class of graphs. In particular, we derive tight bounds for the gap of Schr\"{o}dinger operators with convex potentials acting on the path graph. Additionally, for the hypercube graph, we derive a tight bound for the gap of Schr\"{o}dinger operators with convex potentials dependent only upon vertex Hamming weight. Our proof makes use of tools from the literature of the fundamental gap theorem as proved in the continuum combined with techniques unique to the discrete case. We prove the tight bound for the hypercube graph as a corollary to our path graph results. %B Journal of Mathematical Physics %V 55 %P 052104 %8 2014/03/06 %G eng %U http://arxiv.org/abs/1403.1473v1 %N 5 %! J. Math. Phys. %R 10.1063/1.4878120 %0 Journal Article %J Physical Review Letters %D 2014 %T Many-body dynamics of dipolar molecules in an optical lattice %A Kaden R. A. Hazzard %A Bryce Gadway %A Michael Foss-Feig %A Bo Yan %A Steven A. Moses %A Jacob P. Covey %A Norman Y. Yao %A Mikhail D. Lukin %A Jun Ye %A Deborah S. Jin %A Ana Maria Rey %X 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. %B Physical Review Letters %V 113 %8 2014/11/7 %G eng %U http://arxiv.org/abs/1402.2354v1 %N 19 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.113.195302 %0 Journal Article %J Physical Review A %D 2014 %T Nonequilibrium quantum fluctuations of a dispersive medium: Spontaneous emission, photon statistics, entropy generation, and stochastic motion %A Mohammad F. Maghrebi %A Robert L. Jaffe %A Mehran Kardar %X We study the implications of quantum fluctuations of a dispersive medium, under steady rotation, either in or out of thermal equilibrium with its environment. A rotating object exhibits a quantum instability by dissipating its mechanical motion via spontaneous emission of photons, as well as internal heat generation. Universal relations are derived for the radiated energy and angular momentum as trace formulas involving the object's scattering matrix. We also compute the quantum noise by deriving the full statistics of the radiated photons out of thermal and/or dynamic equilibrium. The (entanglement) entropy generation is quantified, and the total entropy is shown to be always increasing. Furthermore, we derive a Fokker-Planck equation governing the stochastic angular motion resulting from the fluctuating back-reaction frictional torque. As a result, we find a quantum limit on the uncertainty of the object's angular velocity in steady rotation. Finally, we show in some detail that a rotating object drags nearby objects, making them spin parallel to its axis of rotation. A scalar toy model is introduced in the first part to simplify the technicalities and ease the conceptual complexities; a detailed discussion of quantum electrodynamics is presented in the second part. %B Physical Review A %V 90 %8 2014/7/16 %G eng %U http://arxiv.org/abs/1401.0701v1 %N 1 %! Phys. Rev. A %R 10.1103/PhysRevA.90.012515 %0 Conference Proceedings %B In Proceedings of the Sixth Conference on Theory of Quantum Computation, Communication and Cryptography (TQC14) %D 2014 %T Partial-indistinguishability obfuscation using braids %A Gorjan Alagic %A Stacey Jeffery %A Stephen P. Jordan %XAn obfuscator is an algorithm that translates circuits into functionally-equivalent similarly-sized circuits that are hard to understand. Efficient obfuscators would have many applications in cryptography. Until recently, theoretical progress has mainly been limited to no-go results. Recent works have proposed the first efficient obfuscation algorithms for classical logic circuits, based on a notion of indistinguishability against polynomial-time adversaries. In this work, we propose a new notion of obfuscation, which we call partial-indistinguishability. This notion is based on computationally universal groups with efficiently computable normal forms, and appears to be incomparable with existing definitions. We describe universal gate sets for both classical and quantum computation, in which our definition of obfuscation can be met by polynomial-time algorithms. We also discuss some potential applications to testing quantum computers. We stress that the cryptographic security of these obfuscators, especially when composed with translation from other gate sets, remains an open question.

%B In Proceedings of the Sixth Conference on Theory of Quantum Computation, Communication and Cryptography (TQC14) %8 2014/08/21 %G eng %U http://arxiv.org/abs/1212.6358 %0 Journal Article %D 2014 %T Quantum Algorithms for Fermionic Quantum Field Theories %A Stephen P. Jordan %A Keith S. M. Lee %A John Preskill %X Extending previous work on scalar field theories, we develop a quantum algorithm to compute relativistic scattering amplitudes in fermionic field theories, exemplified by the massive Gross-Neveu model, a theory in two spacetime dimensions with quartic interactions. The algorithm introduces new techniques to meet the additional challenges posed by the characteristics of fermionic fields, and its run time is polynomial in the desired precision and the energy. Thus, it constitutes further progress towards an efficient quantum algorithm for simulating the Standard Model of particle physics. %8 2014/04/28 %G eng %U http://arxiv.org/abs/1404.7115v1 %0 Journal Article %J Quantum Information and Computation %D 2014 %T Quantum Computation of Scattering in Scalar Quantum Field Theories %A Stephen P. Jordan %A Keith S. M. Lee %A John Preskill %X Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally, and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great computational complexity and can generally be performed only when the interaction strength is weak. A full understanding of the foundations and rich consequences of quantum field theory remains an outstanding challenge. We develop a quantum algorithm to compute relativistic scattering amplitudes in massive phi-fourth theory in spacetime of four and fewer dimensions. The algorithm runs in a time that is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. Thus, it offers exponential speedup over existing classical methods at high precision or strong coupling. %B Quantum Information and Computation %V 14 %P 1014-1080 %8 2014/09/01 %G eng %U http://arxiv.org/abs/1112.4833v1 %N 11-12 %! Quantum Information and Computation 14 %0 Journal Article %J Physical Review X %D 2014 %T Robust Extraction of Tomographic Information via Randomized Benchmarking %A Shelby Kimmel %A Marcus P. da Silva %A Colm A. Ryan %A Blake R. Johnson %A Thomas Ohki %X We describe how randomized benchmarking can be used to reconstruct the unital part of any trace-preserving quantum map, which in turn is sufficient for the full characterization of any unitary evolution, or more generally, any unital trace-preserving evolution. This approach inherits randomized benchmarking's robustness to preparation and measurement imperfections, therefore avoiding systematic errors caused by these imperfections. We also extend these techniques to efficiently estimate the average fidelity of a quantum map to unitary maps outside of the Clifford group. The unitaries we consider include operations commonly used to achieve universal quantum computation in a fault-tolerant setting. In addition, we rigorously bound the time and sampling complexities of randomized benchmarking procedures. %B Physical Review X %V 4 %8 2014/3/25 %G eng %U http://arxiv.org/abs/1306.2348v1 %N 1 %! Phys. Rev. X %R 10.1103/PhysRevX.4.011050 %0 Journal Article %J Physical Review A %D 2014 %T Spin-orbit-coupled topological Fulde-Ferrell states of fermions in a harmonic trap %A Lei Jiang %A Eite Tiesinga %A Xia-Ji Liu %A Hui Hu %A Han Pu %X Motivated by recent experimental breakthroughs in generating spin-orbit coupling in ultracold Fermi gases using Raman laser beams, we present a systematic study of spin-orbit-coupled Fermi gases confined in a quasi-one-dimensional trap in the presence of an in-plane Zeeman field (which can be realized using a finite two-photon Raman detuning). We find that a topological Fulde-Ferrell state will emerge, featuring finite-momentum Cooper pairing and zero-energy Majorana excitations localized near the edge of the trap based on the self-consistent Bogoliubov-de Genes (BdG) equations. We find analytically the wavefunctions of the Majorana modes. Finally using the time-dependent BdG we show how the finite-momentum pairing field manifests itself in the expansion dynamics of the atomic cloud. %B Physical Review A %V 90 %8 2014/11/7 %G eng %U http://arxiv.org/abs/1404.6211v1 %N 5 %! Phys. Rev. A %R 10.1103/PhysRevA.90.053606 %0 Journal Article %J Quantum Information Computation %D 2014 %T Strong Equivalence of Reversible Circuits is coNP-complete %A Stephen P. Jordan %K complexity %K reversible circuits %XIt is well-known that deciding equivalence of logic circuits is a coNP-complete problem. As a corollary, the problem of deciding weak equivalence of reversible circuits, i.e. allowing initialized ancilla bits in the input and ignoring "garbage" ancilla bits in the output, is also coNP-complete. The complexity of deciding strong equivalence, including the ancilla bits, is less obvious and may depend on gate set. Here we use Barrington's theorem to show that deciding strong equivalence of reversible circuits built from the Fredkin gate is coNP-complete. This implies coNP-completeness of deciding strong equivalence for other commonly used universal reversible gate sets, including any gate set that includes the Toffoli or Fredkin gate.

%B Quantum Information Computation %V 14 %P 1302–1307 %8 2014/11/01 %G eng %U http://dl.acm.org/citation.cfm?id=2685179.2685182 %0 Journal Article %J Physical Review Letters %D 2014 %T Suppressing the loss of ultracold molecules via the continuous quantum Zeno effect %A Bihui Zhu %A Bryce Gadway %A Michael Foss-Feig %A Johannes Schachenmayer %A Michael Wall %A Kaden R. A. Hazzard %A Bo Yan %A Steven A. Moses %A Jacob P. Covey %A Deborah S. Jin %A Jun Ye %A Murray Holland %A Ana Maria Rey %X 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. %B Physical Review Letters %V 112 %8 2014/2/20 %G eng %U http://arxiv.org/abs/1310.2221v2 %N 7 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.112.070404 %0 Journal Article %J Physical Review A %D 2014 %T Symmetric Extension of Two-Qubit States %A Jianxin Chen %A Zhengfeng Ji %A David Kribs %A Norbert Lütkenhaus %A Bei Zeng %X 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 $\rho_{ABB'}$, such that the $AB$ marginal state is identical to the $AB'$ marginal state, i.e. $\rho_{AB'}=\rho_{AB}$. 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. %B Physical Review A %V 90 %8 2014/9/17 %G eng %U http://arxiv.org/abs/1310.3530v2 %N 3 %! Phys. Rev. A %R 10.1103/PhysRevA.90.032318 %0 Journal Article %J Physical Review A %D 2013 %T Quadrature interferometry for nonequilibrium ultracold bosons in optical lattices %A Eite Tiesinga %A Philip R. Johnson %X We develop an interferometric technique for making time-resolved measurements of field-quadrature operators for nonequilibrium ultracold bosons in optical lattices. The technique exploits the internal state structure of magnetic atoms to create two subsystems of atoms in different spin states and lattice sites. A Feshbach resonance turns off atom-atom interactions in one spin subsystem, making it a well-characterized reference state, while atoms in the other subsystem undergo nonequilibrium dynamics for a variable hold time. Interfering the subsystems via a second beam-splitting operation, time-resolved quadrature measurements on the interacting atoms are obtained by detecting relative spin populations. The technique can provide quadrature measurements for a variety of Hamiltonians and lattice geometries (e.g., cubic, honeycomb, superlattices), including systems with tunneling, spin-orbit couplings using artificial gauge fields, and higher-band effects. Analyzing the special case of a deep lattice with negligible tunneling, we obtain the time evolution of both quadrature observables and their fluctuations. As a second application, we show that the interferometer can be used to measure atom-atom interaction strengths with super-Heisenberg scaling n^(-3/2) in the mean number of atoms per lattice site n, and standard quantum limit scaling M^(-1/2) in the number of lattice sites M. In our analysis, we require M >> 1 and for realistic systems n is small, and therefore the scaling in total atom number N = nM is below the Heisenberg limit; nevertheless, measurements testing the scaling behaviors for interaction-based quantum metrologies should be possible in this system. %B Physical Review A %V 87 %8 2013/1/22 %G eng %U http://arxiv.org/abs/1212.1193v2 %N 1 %! Phys. Rev. A %R 10.1103/PhysRevA.87.013423 %0 Journal Article %J Physical Review A %D 2013 %T Quantum Logic between Remote Quantum Registers %A Norman Y. Yao %A Zhe-Xuan Gong %A Chris R. Laumann %A Steven D. Bennett %A L. -M. Duan %A Mikhail D. Lukin %A Liang Jiang %A Alexey V. Gorshkov %X We analyze two approaches to quantum state transfer in solid-state spin systems. First, we consider unpolarized spin-chains and extend previous analysis to various experimentally relevant imperfections, including quenched disorder, dynamical decoherence, and uncompensated long range coupling. In finite-length chains, the interplay between disorder-induced localization and decoherence yields a natural optimal channel fidelity, which we calculate. Long-range dipolar couplings induce a finite intrinsic lifetime for the mediating eigenmode; extensive numerical simulations of dipolar chains of lengths up to L=12 show remarkably high fidelity despite these decay processes. We further consider the extension of the protocol to bosonic systems of coupled oscillators. Second, we introduce a quantum mirror based architecture for universal quantum computing which exploits all of the spins in the system as potential qubits. While this dramatically increases the number of qubits available, the composite operations required to manipulate "dark" spin qubits significantly raise the error threshold for robust operation. Finally, as an example, we demonstrate that eigenmode-mediated state transfer can enable robust long-range logic between spatially separated Nitrogen-Vacancy registers in diamond; numerical simulations confirm that high fidelity gates are achievable even in the presence of moderate disorder. %B Physical Review A %V 87 %8 2013/2/6 %G eng %U http://arxiv.org/abs/1206.0014v1 %N 2 %! Phys. Rev. A %R 10.1103/PhysRevA.87.022306 %0 Journal Article %J 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013) %D 2013 %T Symmetries of Codeword Stabilized Quantum Codes %A Salman Beigi %A Jianxin Chen %A Markus Grassl %A Zhengfeng Ji %A Qiang Wang %A Bei Zeng %X 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. %B 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013) %V 22 %P 192-206 %8 2013/03/28 %G eng %U http://arxiv.org/abs/1303.7020v2 %R 10.4230/LIPIcs.TQC.2013.192 %0 Journal Article %J Physical Review A %D 2013 %T Testing quantum expanders is co-QMA-complete %A Adam D. Bookatz %A Stephen P. Jordan %A Yi-Kai Liu %A Pawel Wocjan %X A quantum expander is a unital quantum channel that is rapidly mixing, has only a few Kraus operators, and can be implemented efficiently on a quantum computer. We consider the problem of estimating the mixing time (i.e., the spectral gap) of a quantum expander. We show that this problem is co-QMA-complete. This has applications to testing randomized constructions of quantum expanders, and studying thermalization of open quantum systems. %B Physical Review A %V 87 %8 2013/4/15 %G eng %U http://arxiv.org/abs/1210.0787v2 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.87.042317 %0 Journal Article %D 2013 %T A Time-Efficient Quantum Walk for 3-Distinctness Using Nested Updates %A Andrew M. Childs %A Stacey Jeffery %A Robin Kothari %A Frederic Magniez %X 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}). %8 2013/02/28 %G eng %U http://arxiv.org/abs/1302.7316v1 %0 Journal Article %J Nature Communications %D 2013 %T Topologically Protected Quantum State Transfer in a Chiral Spin Liquid %A Norman Y. Yao %A Chris R. Laumann %A Alexey V. Gorshkov %A Hendrik Weimer %A Liang Jiang %A J. Ignacio Cirac %A Peter Zoller %A Mikhail D. Lukin %X 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. %B Nature Communications %V 4 %P 1585 %8 2013/3/12 %G eng %U http://arxiv.org/abs/1110.3788v1 %! Nat Comms %R 10.1038/ncomms2531 %0 Journal Article %J Physical Review A %D 2013 %T Uniqueness of Quantum States Compatible with Given Measurement Results %A Jianxin Chen %A Hillary Dawkins %A Zhengfeng Ji %A Nathaniel Johnston %A David Kribs %A Frederic Shultz %A Bei Zeng %X 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. %B Physical Review A %V 88 %8 2013/7/11 %G eng %U http://arxiv.org/abs/1212.3503v2 %N 1 %! Phys. Rev. A %R 10.1103/PhysRevA.88.012109 %0 Journal Article %J Quantum Information and Computation %D 2012 %T Achieving perfect completeness in classical-witness quantum Merlin-Arthur proof systems %A Stephen P. Jordan %A Hirotada Kobayashi %A Daniel Nagaj %A Harumichi Nishimura %X This paper proves that classical-witness quantum Merlin-Arthur proof systems can achieve perfect completeness. That is, QCMA = QCMA1. This holds under any gate set with which the Hadamard and arbitrary classical reversible transformations can be exactly implemented, e.g., {Hadamard, Toffoli, NOT}. The proof is quantumly nonrelativizing, and uses a simple but novel quantum technique that additively adjusts the success probability, which may be of independent interest. %B Quantum Information and Computation %V 12 %P 461-471 %8 2012/05/01 %G eng %U http://arxiv.org/abs/1111.5306v2 %N 5-6 %! Quantum Information and Computation Vol. 12 No. 5/6 pg. 461-471 (2012) %0 Journal Article %J New J. Phys. %D 2012 %T Cavity QED with atomic mirrors %A D E Chang %A Jiang, L %A Alexey V. Gorshkov %A H J Kimble %B New J. Phys. %V 14 %P 063003 %G eng %U http://iopscience.iop.org/1367-2630/14/6/063003/ %0 Journal Article %J Journal of Mathematical Physics %D 2012 %T Comment on some results of Erdahl and the convex structure of reduced density matrices %A Jianxin Chen %A Zhengfeng Ji %A Mary Beth Ruskai %A Bei Zeng %A Duan-Lu Zhou %X 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'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. %B Journal of Mathematical Physics %V 53 %P 072203 %8 2012/05/16 %G eng %U http://arxiv.org/abs/1205.3682v1 %N 7 %! J. Math. Phys. %R 10.1063/1.4736842 %0 Journal Article %J Physical Review A %D 2012 %T Correlations in excited states of local Hamiltonians %A Jianxin Chen %A Zhengfeng Ji %A Zhaohui Wei %A Bei Zeng %X 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). %B Physical Review A %V 85 %8 2012/4/9 %G eng %U http://arxiv.org/abs/1106.1373v2 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.85.040303 %0 Journal Article %J Physical Review A %D 2012 %T From Ground States to Local Hamiltonians %A Jianxin Chen %A Zhengfeng Ji %A Bei Zeng %A D. L. Zhou %X 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. %B Physical Review A %V 86 %8 2012/8/30 %G eng %U http://arxiv.org/abs/1110.6583v4 %N 2 %! Phys. Rev. A %R 10.1103/PhysRevA.86.022339 %0 Journal Article %J Journal of Mathematical Physics %D 2012 %T Ground-State Spaces of Frustration-Free Hamiltonians %A Jianxin Chen %A Zhengfeng Ji %A David Kribs %A Zhaohui Wei %A Bei Zeng %X We study the ground-state space properties for frustration-free Hamiltonians. We introduce a concept of `reduced spaces' 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. %B Journal of Mathematical Physics %V 53 %P 102201 %8 2012/01/01 %G eng %U http://arxiv.org/abs/1112.0762v1 %N 10 %! J. Math. Phys. %R 10.1063/1.4748527 %0 Journal Article %J Physical Review Letters %D 2012 %T Long-lived dipolar molecules and Feshbach molecules in a 3D optical lattice %A Amodsen Chotia %A Brian Neyenhuis %A Steven A. Moses %A Bo Yan %A Jacob P. Covey %A Michael Foss-Feig %A Ana Maria Rey %A Deborah S. Jin %A Jun Ye %X 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. %B Physical Review Letters %V 108 %8 2012/2/23 %G eng %U http://arxiv.org/abs/1110.4420v1 %N 8 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.108.080405 %0 Journal Article %D 2012 %T Minimum Entangling Power is Close to Its Maximum %A Jianxin Chen %A Zhengfeng Ji %A David W Kribs %A Bei Zeng %X 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 'weakest' 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 'weakest' 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. %8 2012/10/04 %G eng %U http://arxiv.org/abs/1210.1296v1 %0 Journal Article %J Science %D 2012 %T Quantum Algorithms for Quantum Field Theories %A Stephen P. Jordan %A Keith S. M. Lee %A John Preskill %X Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We develop a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (phi-fourth theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm. %B Science %V 336 %P 1130 - 1133 %8 2012/05/31 %G eng %U http://arxiv.org/abs/1111.3633v2 %N 6085 %! Science %R 10.1126/science.1217069 %0 Journal Article %J Journal of Mathematical Physics %D 2012 %T Rank Reduction for the Local Consistency Problem %A Jianxin Chen %A Zhengfeng Ji %A Alexander Klyachko %A David W. Kribs %A Bei Zeng %X 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. %B Journal of Mathematical Physics %V 53 %P 022202 %8 2012/02/09 %G eng %U http://arxiv.org/abs/1106.3235v2 %N 2 %! J. Math. Phys. %R 10.1063/1.3685644 %0 Journal Article %J Physical Review A %D 2012 %T Resonant control of polar molecules in an optical lattice %A Thomas M. Hanna %A Eite Tiesinga %A William F. Mitchell %A Paul S. Julienne %X We study the resonant control of two nonreactive polar molecules in an optical lattice site, focussing on the example of RbCs. Collisional control can be achieved by tuning bound states of the intermolecular dipolar potential, by varying the applied electric field or trap frequency. We consider a wide range of electric fields and trapping geometries, showing that a three-dimensional optical lattice allows for significantly wider avoided crossings than free space or quasi-two dimensional geometries. Furthermore, we find that dipolar confinement induced resonances can be created with reasonable trapping frequencies and electric fields, and have widths that will enable useful control in forthcoming experiments. %B Physical Review A %V 85 %8 2012/2/8 %G eng %U http://arxiv.org/abs/1111.0227v1 %N 2 %! Phys. Rev. A %R 10.1103/PhysRevA.85.022703 %0 Journal Article %J Nature Communications %D 2012 %T Scalable Architecture for a Room Temperature Solid-State Quantum Information Processor %A Norman Y. Yao %A Liang Jiang %A Alexey V. Gorshkov %A Peter C. Maurer %A Geza Giedke %A J. Ignacio Cirac %A Mikhail D. Lukin %X 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. %B Nature Communications %V 3 %P 800 %8 2012/4/24 %G eng %U http://arxiv.org/abs/1012.2864v1 %! Nat Comms %R 10.1038/ncomms1788 %0 Journal Article %J Physical Review Letters %D 2012 %T Spontaneous emission by rotating objects: A scattering approach %A Mohammad F. Maghrebi %A Robert L. Jaffe %A Mehran Kardar %X We study the quantum electrodynamics (QED) vacuum in the presence of a body rotating along its axis of symmetry and show that the object spontaneously emits energy if it is lossy. The radiated power is expressed as a general trace formula solely in terms of the scattering matrix, making an explicit connection to the conjecture of Zel'dovich [JETP Lett. 14, 180 (1971)] on rotating objects. We further show that a rotating body drags along nearby objects while making them spin parallel to its own rotation axis. %B Physical Review Letters %V 108 %8 2012/6/7 %G eng %U http://arxiv.org/abs/1202.1485v2 %N 23 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.108.230403 %0 Conference Proceedings %B In Proceedings of the Sixth Conference on Theory of Quantum Computation, Communication and Cryptography (TQC11) %D 2011 %T Approximating the Turaev-Viro Invariant of Mapping Tori is Complete for One Clean Qubit %A Stephen P. Jordan %A Gorjan Alagic %XThe Turaev-Viro invariants are scalar topological invariants of three-dimensional manifolds. Here we show that the problem of estimating the Fibonacci version of the Turaev-Viro invariant of a mapping torus is a complete problem for the one clean qubit complexity class (DQC1). This complements a previous result showing that estimating the Turaev-Viro invariant for arbitrary manifolds presented as Heegaard splittings is a complete problem for the standard quantum computation model (BQP). We also discuss a beautiful analogy between these results and previously known results on the computational complexity of approximating the Jones polynomial.

%B In Proceedings of the Sixth Conference on Theory of Quantum Computation, Communication and Cryptography (TQC11) %8 2011/05/31 %G eng %U http://arxiv.org/abs/1105.5100 %0 Journal Article %J Proceedings of the National Academy of Sciences %D 2011 %T Casimir force between sharp-shaped conductors %A Mohammad F. Maghrebi %A Sahand Jamal Rahi %A Thorsten Emig %A Noah Graham %A Robert L. Jaffe %A Mehran Kardar %X Casimir forces between conductors at the sub-micron scale cannot be ignored in the design and operation of micro-electromechanical (MEM) devices. However, these forces depend non-trivially on geometry, and existing formulae and approximations cannot deal with realistic micro-machinery components with sharp edges and tips. Here, we employ a novel approach to electromagnetic scattering, appropriate to perfect conductors with sharp edges and tips, specifically to wedges and cones. The interaction of these objects with a metal plate (and among themselves) is then computed systematically by a multiple-scattering series. For the wedge, we obtain analytical expressions for the interaction with a plate, as functions of opening angle and tilt, which should provide a particularly useful tool for the design of MEMs. Our result for the Casimir interactions between conducting cones and plates applies directly to the force on the tip of a scanning tunneling probe; the unexpectedly large temperature dependence of the force in these configurations should attract immediate experimental interest. %B Proceedings of the National Academy of Sciences %V 108 %P 6867 - 6871 %8 2011/04/11 %G eng %U http://arxiv.org/abs/1010.3223v1 %N 17 %! Proceedings of the National Academy of Sciences %R 10.1073/pnas.1018079108 %0 Journal Article %J Physical Review D %D 2011 %T Implications of the Babinet Principle for Casimir Interactions %A Mohammad F. Maghrebi %A Ronen Abravanel %A Robert L. Jaffe %X We formulate the Babinet Principle (BP) as a relation between the scattering amplitudes for electromagnetic waves, and combine it with multiple scattering techniques to derive new properties of Casimir forces. We show that the Casimir force exerted by a planar conductor or dielectric on a self- complementary perforated planar mirror is approximately half that on a uniform mirror independent of the distance between them. The BP suggests that Casimir edge effects are anomalously small, supporting results obtained earlier in special cases. Finally, we illustrate how the BP can be used to estimate Casimir forces between perforated planar mirrors. %B Physical Review D %V 84 %8 2011/9/1 %G eng %U http://arxiv.org/abs/1103.5395v1 %N 6 %! Phys. Rev. D %R 10.1103/PhysRevD.84.061701 %0 Journal Article %J Physical Review A %D 2011 %T No-go Theorem for One-way Quantum Computing on Naturally Occurring Two-level Systems %A Jianxin Chen %A Xie Chen %A Runyao Duan %A Zhengfeng Ji %A Bei Zeng %X 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. %B Physical Review A %V 83 %8 2011/5/9 %G eng %U http://arxiv.org/abs/1004.3787v1 %N 5 %! Phys. Rev. A %R 10.1103/PhysRevA.83.050301 %0 Journal Article %J Physical Review Letters %D 2011 %T Robust Quantum State Transfer in Random Unpolarized Spin Chains %A Norman Y. Yao %A Liang Jiang %A Alexey V. Gorshkov %A Zhe-Xuan Gong %A Alex Zhai %A L. -M. Duan %A Mikhail D. Lukin %X We propose and analyze a new approach for quantum state transfer between remote spin qubits. Specifically, we demonstrate that coherent quantum coupling between remote qubits can be achieved via certain classes of random, unpolarized (infinite temperature) spin chains. Our method is robust to coupling strength disorder and does not require manipulation or control over individual spins. In principle, it can be used to attain perfect state transfer over arbitrarily long range via purely Hamiltonian evolution and may be particularly applicable in a solid-state quantum information processor. As an example, we demonstrate that it can be used to attain strong coherent coupling between Nitrogen-Vacancy centers separated by micrometer distances at room temperature. Realistic imperfections and decoherence effects are analyzed. %B Physical Review Letters %V 106 %8 2011/1/27 %G eng %U http://arxiv.org/abs/1011.2762v2 %N 4 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.106.040505 %0 Journal Article %J Physical Review A %D 2011 %T Spatial separation in a thermal mixture of ultracold $^174$Yb and $^87$Rb atoms %A Florian Baumer %A Frank Münchow %A Axel Görlitz %A Stephen E. Maxwell %A Paul S. Julienne %A Eite Tiesinga %X We report on the observation of unusually strong interactions in a thermal mixture of ultracold atoms which cause a significant modification of the spatial distribution. A mixture of $^{87}$Rb and $^{174}$Yb with a temperature of a few $\mu$K is prepared in a hybrid trap consisting of a bichromatic optical potential superimposed on a magnetic trap. For suitable trap parameters and temperatures, a spatial separation of the two species is observed. We infer that the separation is driven by a large interaction strength between $^{174}$Yb and $^{87}$Rb accompanied by a large three-body recombination rate. Based on this assumption we have developed a diffusion model which reproduces our observations. %B Physical Review A %V 83 %8 2011/4/21 %G eng %U http://arxiv.org/abs/1104.1722v1 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.83.040702 %0 Journal Article %J Physical Review A %D 2010 %T Approximating Turaev-Viro 3-manifold invariants is universal for quantum computation %A Gorjan Alagic %A Stephen P. Jordan %A Robert Koenig %A Ben W. Reichardt %X The Turaev-Viro invariants are scalar topological invariants of compact, orientable 3-manifolds. We give a quantum algorithm for additively approximating Turaev-Viro invariants of a manifold presented by a Heegaard splitting. The algorithm is motivated by the relationship between topological quantum computers and (2+1)-D topological quantum field theories. Its accuracy is shown to be nontrivial, as the same algorithm, after efficient classical preprocessing, can solve any problem efficiently decidable by a quantum computer. Thus approximating certain Turaev-Viro invariants of manifolds presented by Heegaard splittings is a universal problem for quantum computation. This establishes a novel relation between the task of distinguishing non-homeomorphic 3-manifolds and the power of a general quantum computer. %B Physical Review A %V 82 %8 2010/10/8 %G eng %U http://arxiv.org/abs/1003.0923v1 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.82.040302 %0 Journal Article %J New Journal of Physics %D 2010 %T Creation and manipulation of Feshbach resonances with radio-frequency radiation %A Thomas M. Hanna %A Eite Tiesinga %A Paul S. Julienne %X We present a simple technique for studying collisions of ultracold atoms in the presence of a magnetic field and radio-frequency radiation (rf). Resonant control of scattering properties can be achieved by using rf to couple a colliding pair of atoms to a bound state. We show, using the example of 6Li, that in some ranges of rf frequency and magnetic field this can be done without giving rise to losses. We also show that halo molecules of large spatial extent require much less rf power than deeply bound states. Another way to exert resonant control is with a set of rf-coupled bound states, linked to the colliding pair through the molecular interactions that give rise to magnetically tunable Feshbach resonances. This was recently demonstrated for 87Rb [Kaufman et al., Phys. Rev. A 80:050701(R), 2009]. We examine the underlying atomic and molecular physics which made this possible. Lastly, we consider the control that may be exerted over atomic collisions by placing atoms in superpositions of Zeeman states, and suggest that it could be useful where small changes in scattering length are required. We suggest other species for which rf and magnetic field control could together provide a useful tuning mechanism. %B New Journal of Physics %V 12 %P 083031 %8 2010/08/12 %G eng %U http://arxiv.org/abs/1004.0636v1 %N 8 %! New J. Phys. %R 10.1088/1367-2630/12/8/083031 %0 Journal Article %D 2010 %T On the degeneracy of SU(3)k topological phases %A Stephen P. Jordan %A Toufik Mansour %A Simone Severini %XThe ground state degeneracy of an $SU(N)_k$ topological phase with $n$ quasiparticle excitations is relevant quantity for quantum computation, condensed matter physics, and knot theory. It is an open question to find a closed formula for this degeneracy for any $N > 2$. Here we present the problem in an explicit combinatorial way and analyze the case N=3. While not finding a complete closed-form solution, we obtain generating functions and solve some special cases.

%8 2010/09/01 %G eng %U http://arxiv.org/abs/1009.0114v1 %0 Journal Article %J Nature Phys. %D 2010 %T Far-field optical imaging and manipulation of individual spins with nanoscale resolution %A Maurer, P C %A Maze, J R %A Stanwix, P L %A Jiang, L %A Alexey V. Gorshkov %A Zibrov, A A %A Harke, B %A Hodges, J S %A Zibrov, A S %A Yacoby, A %A Twitchen, D %A Hell, S W %A Walsworth, R L %A Lukin, M D %B Nature Phys. %V 6 %P 912 %G eng %U http://www.nature.com/nphys/journal/v6/n11/abs/nphys1774.html %0 Journal Article %J Physical Review A %D 2010 %T Fast Entanglement Distribution with Atomic Ensembles and Fluorescent Detection %A Jonatan B. Brask %A Liang Jiang %A Alexey V. Gorshkov %A Vladan Vuletic %A Anders S. Sorensen %A Mikhail D. Lukin %X Quantum repeaters based on atomic ensemble quantum memories are promising candidates for achieving scalable distribution of entanglement over long distances. Recently, important experimental progress has been made towards their implementation. However, the entanglement rates and scalability of current approaches are limited by relatively low retrieval and single-photon detector efficiencies. We propose a scheme, which makes use of fluorescent detection of stored excitations to significantly increase the efficiency of connection and hence the rate. Practical performance and possible experimental realizations of the new protocol are discussed. %B Physical Review A %V 81 %8 2010/2/12 %G eng %U http://arxiv.org/abs/0907.3839v2 %N 2 %! Phys. Rev. A %R 10.1103/PhysRevA.81.020303 %0 Journal Article %J Reviews of Modern Physics %D 2010 %T Feshbach Resonances in Ultracold Gases %A Cheng Chin %A Rudolf Grimm %A Paul Julienne %A Eite Tiesinga %X 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. %B Reviews of Modern Physics %V 82 %P 1225 - 1286 %8 2010/4/29 %G eng %U http://arxiv.org/abs/0812.1496v2 %N 2 %! Rev. Mod. Phys. %R 10.1103/RevModPhys.82.1225 %0 Journal Article %J Quantum Information & Computation %D 2010 %T Permutational Quantum Computing %A Stephen P. Jordan %XIn topological quantum computation the geometric details of a particle trajectory are irrelevant; only the topology matters. Taking this one step further, we consider a model of computation that disregards even the topology of the particle trajectory, and computes by permuting particles. Whereas topological quantum computation requires anyons, permutational quantum computation can be performed with ordinary spin-1/2 particles, using a variant of the spin-network scheme of Marzuoli and Rasetti. We do not know whether permutational computation is universal. It may represent a new complexity class within BQP. Nevertheless, permutational quantum computers can in polynomial time approximate matrix elements of certain irreducible representations of the symmetric group and simulate certain processes in the Ponzano-Regge spin foam model of quantum gravity. No polynomial time classical algorithms for these problems are known.

%B Quantum Information & Computation %V 10 %P 470-497 %8 2010/05/01 %G eng %U http://dl.acm.org/citation.cfm?id=2011369 %N 5 %! Quantum Information and Computation Vol. 10 pg. 470 (2010) %0 Journal Article %D 2010 %T Principle of Maximum Entropy and Ground Spaces of Local Hamiltonians %A Jianxin Chen %A Zhengfeng Ji %A Mary Beth Ruskai %A Bei Zeng %A Duanlu Zhou %X 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. %8 2010/10/13 %G eng %U http://arxiv.org/abs/1010.2739v4 %0 Journal Article %J Physical Review A %D 2010 %T QMA-complete problems for stoquastic Hamiltonians and Markov matrices %A Stephen P. Jordan %A David Gosset %A Peter J. Love %X We show that finding the lowest eigenvalue of a 3-local symmetric stochastic matrix is QMA-complete. We also show that finding the highest energy of a stoquastic Hamiltonian is QMA-complete and that adiabatic quantum computation using certain excited states of a stoquastic Hamiltonian is universal. We also show that adiabatic evolution in the ground state of a stochastic frustration free Hamiltonian is universal. Our results give a new QMA-complete problem arising in the classical setting of Markov chains, and new adiabatically universal Hamiltonians that arise in many physical systems. %B Physical Review A %V 81 %8 2010/3/29 %G eng %U http://arxiv.org/abs/0905.4755v2 %N 3 %! Phys. Rev. A %R 10.1103/PhysRevA.81.032331 %0 Journal Article %J Nature %D 2010 %T Quantum Computing %A Thaddeus D. Ladd %A Fedor Jelezko %A Raymond Laflamme %A Yasunobu Nakamura %A Christopher Monroe %A Jeremy L. O'Brien %X Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and instantaneously linked. These predictions have been the topic of intense metaphysical debate ever since the theory's inception early last century. However, supreme predictive power combined with direct experimental observation of some of these unusual phenomena leave little doubt as to its fundamental correctness. In fact, without quantum mechanics we could not explain the workings of a laser, nor indeed how a fridge magnet operates. Over the last several decades quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit these unique quantum properties? Today it is understood that the answer is yes. Many research groups around the world are working towards one of the most ambitious goals humankind has ever embarked upon: a quantum computer that promises to exponentially improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for this task---ranging from single particles of light to superconducting circuits---and it is not yet clear which, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain what the major challenges are for the future. %B Nature %V 464 %P 45 - 53 %8 2010/3/4 %G eng %U http://arxiv.org/abs/1009.2267v1 %N 7285 %! Nature %R 10.1038/nature08812 %0 Journal Article %J Nature Phys. %D 2010 %T Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms %A Alexey V. Gorshkov %A Hermele, M %A Gurarie, V %A Xu, C %A Julienne, P S %A Ye, J %A Zoller, P %A Demler, E %A Lukin, M D %A Rey, A M %B Nature Phys. %V 6 %P 289 %G eng %U http://www.nature.com/nphys/journal/v6/n4/abs/nphys1535.html %0 Journal Article %J Physical Review A %D 2009 %T Collisional cooling of ultra-cold atom ensembles using Feshbach resonances %A L. Mathey %A Eite Tiesinga %A Paul S. Julienne %A Charles W. Clark %X 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. %B Physical Review A %V 80 %8 2009/9/8 %G eng %U http://arxiv.org/abs/0903.2568v1 %N 3 %! Phys. Rev. A %R 10.1103/PhysRevA.80.030702 %0 Journal Article %J Theory of Computing %D 2009 %T Discrete-query quantum algorithm for NAND trees %A Andrew M. Childs %A Richard Cleve %A Stephen P. Jordan %A David Yeung %X 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. %B Theory of Computing %V 5 %P 119 - 123 %8 2009/07/01 %G eng %U http://arxiv.org/abs/quant-ph/0702160v1 %N 1 %! Theory of Comput. %R 10.4086/toc.2009.v005a005 %0 Journal Article %J Physical Review A %D 2009 %T Efficient quantum circuits for arbitrary sparse unitaries %A Stephen P. Jordan %A Pawel Wocjan %X Arbitrary exponentially large unitaries cannot be implemented efficiently by quantum circuits. However, we show that quantum circuits can efficiently implement any unitary provided it has at most polynomially many nonzero entries in any row or column, and these entries are efficiently computable. One can formulate a model of computation based on the composition of sparse unitaries which includes the quantum Turing machine model, the quantum circuit model, anyonic models, permutational quantum computation, and discrete time quantum walks as special cases. Thus we obtain a simple unified proof that these models are all contained in BQP. Furthermore our general method for implementing sparse unitaries simplifies several existing quantum algorithms. %B Physical Review A %V 80 %8 2009/12/1 %G eng %U http://arxiv.org/abs/0904.2211v2 %N 6 %! Phys. Rev. A %R 10.1103/PhysRevA.80.062301 %0 Journal Article %D 2009 %T Efficient quantum processing of ideals in finite rings %A Pawel M. Wocjan %A Stephen P. Jordan %A Hamed Ahmadi %A Joseph P. Brennan %X Suppose we are given black-box access to a finite ring R, and a list of generators for an ideal I in R. We show how to find an additive basis representation for I in poly(log |R|) time. This generalizes a recent quantum algorithm of Arvind et al. which finds a basis representation for R itself. We then show that our algorithm is a useful primitive allowing quantum computers to rapidly solve a wide variety of problems regarding finite rings. In particular we show how to test whether two ideals are identical, find their intersection, find their quotient, prove whether a given ring element belongs to a given ideal, prove whether a given element is a unit, and if so find its inverse, find the additive and multiplicative identities, compute the order of an ideal, solve linear equations over rings, decide whether an ideal is maximal, find annihilators, and test the injectivity and surjectivity of ring homomorphisms. These problems appear to be hard classically. %8 2009/07/31 %G eng %U http://arxiv.org/abs/0908.0022v1 %0 Journal Article %J Quantum Information and Computation %D 2009 %T Estimating Jones and HOMFLY polynomials with One Clean Qubit %A Stephen P. Jordan %A Pawel Wocjan %XThe Jones and HOMFLY polynomials are link invariants with close connections to quantum computing. It was recently shown that finding a certain approximation to the Jones polynomial of the trace closure of a braid at the fifth root of unity is a complete problem for the one clean qubit complexity class. This is the class of problems solvable in polynomial time on a quantum computer acting on an initial state in which one qubit is pure and the rest are maximally mixed. Here we generalize this result by showing that one clean qubit computers can efficiently approximate the Jones and single-variable HOMFLY polynomials of the trace closure of a braid at any root of unity.

%B Quantum Information and Computation %V 9 %P 264-289 %8 2009/03/01 %G eng %U http://dl.acm.org/citation.cfm?id=2011787 %N 3 %0 Journal Article %J New Journal of Physics %D 2009 %T Multi-channel modelling of the formation of vibrationally cold polar KRb molecules %A Svetlana Kotochigova %A Eite Tiesinga %A Paul S. Julienne %X We describe the theoretical advances that influenced the experimental creation of vibrationally and translationally cold polar $^{40}$K$^{87}$Rb molecules \cite{nphys08,science08}. Cold molecules were created from very-weakly bound molecules formed by magnetic field sweeps near a Feshbach resonance in collisions of ultra-cold $^{40}$K and $^{87}$Rb atoms. Our analysis include the multi-channel bound-state calculations of the hyperfine and Zeeman mixed X$^1\Sigma^+$ and a$^3\Sigma^+$ vibrational levels. We find excellent agreement with the hyperfine structure observed in experimental data. In addition, we studied the spin-orbit mixing in the intermediate state of the Raman transition. This allowed us to investigate its effect on the vibrationally-averaged transition dipole moment to the lowest ro-vibrational level of the X$^1\Sigma^+$ state. Finally, we obtained an estimate of the polarizability of the initial and final ro-vibrational states of the Raman transition near frequencies relevant for optical trapping of the molecules. %B New Journal of Physics %V 11 %P 055043 %8 2009/05/14 %G eng %U http://arxiv.org/abs/0901.1486v1 %N 5 %! New J. Phys. %R 10.1088/1367-2630/11/5/055043 %0 Journal Article %J Physical Review A %D 2009 %T Prediction of Feshbach resonances from three input parameters %A Thomas M. Hanna %A Eite Tiesinga %A Paul S. Julienne %X We have developed a model of Feshbach resonances in gases of ultracold alkali metal atoms using the ideas of multichannel quantum defect theory. Our model requires just three parameters describing the interactions - the singlet and triplet scattering lengths, and the long range van der Waals coefficient - in addition to known atomic properties. Without using any further details of the interactions, our approach can accurately predict the locations of resonances. It can also be used to find the singlet and triplet scattering lengths from measured resonance data. We apply our technique to $^{6}$Li--$^{40}$K and $^{40}$K--$^{87}$Rb scattering, obtaining good agreement with experimental results, and with the more computationally intensive coupled channels technique. %B Physical Review A %V 79 %8 2009/4/30 %G eng %U http://arxiv.org/abs/0903.0884v2 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.79.040701 %0 Journal Article %J Physical Review Letters %D 2009 %T Quantum Phase Transitions and Continuous Observation of Spinor Dynamics in an Antiferromagnetic Condensate %A Yingmei Liu %A Sebastian Jung %A Stephen E. Maxwell %A Lincoln D. Turner %A Eite Tiesinga %A Paul. D. Lett %X Condensates of spin-1 sodium display rich spin dynamics due to the antiferromagnetic nature of the interactions in this system. We use Faraday rotation spectroscopy to make a continuous and minimally destructive measurement of the dynamics over multiple spin oscillations on a single evolving condensate. This method provides a sharp signature to locate a magnetically tuned separatrix in phase space which depends on the net magnetization. We also observe a phase transition from a two- to a three-component condensate at a low but finite temperature using a Stern-Gerlach imaging technique. This transition should be preserved as a zero-temperature quantum phase transition. %B Physical Review Letters %V 102 %8 2009/3/23 %G eng %U http://arxiv.org/abs/0902.3189v1 %N 12 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.102.125301 %0 Journal Article %J Nature Physics %D 2008 %T Anyonic interferometry and protected memories in atomic spin lattices %A Liang Jiang %A Gavin K. Brennen %A Alexey V. Gorshkov %A Klemens Hammerer %A Mohammad Hafezi %A Eugene Demler %A Mikhail D. Lukin %A Peter Zoller %X Strongly correlated quantum systems can exhibit exotic behavior called topological order which is characterized by non-local correlations that depend on the system topology. Such systems can exhibit remarkable phenomena such as quasi-particles with anyonic statistics and have been proposed as candidates for naturally fault-tolerant quantum computation. Despite these remarkable properties, anyons have never been observed in nature directly. Here we describe how to unambiguously detect and characterize such states in recently proposed spin lattice realizations using ultra-cold atoms or molecules trapped in an optical lattice. We propose an experimentally feasible technique to access non-local degrees of freedom by performing global operations on trapped spins mediated by an optical cavity mode. We show how to reliably read and write topologically protected quantum memory using an atomic or photonic qubit. Furthermore, our technique can be used to probe statistics and dynamics of anyonic excitations. %B Nature Physics %V 4 %P 482 - 488 %8 2008/4/20 %G eng %U http://arxiv.org/abs/0711.1365v1 %N 6 %! Nat Phys %R 10.1038/nphys943 %0 Journal Article %J Physical Review A %D 2008 %T Avoided crossings between bound states of ultracold Cesium dimers %A Jeremy M. Hutson %A Eite Tiesinga %A Paul S. Julienne %X We present an efficient new computational method for calculating the binding energies of the bound states of ultracold alkali-metal dimers in the presence of magnetic fields. The method is based on propagation of coupled differential equations and does not use a basis set for the interatomic distance coordinate. It is much more efficient than the previous method based on a radial basis set and allows many more spin channels to be included. This is particularly important in the vicinity of avoided crossings between bound states. We characterize a number of different avoided crossings in Cs_2 and compare our converged calculations with experimental results. Small but significant discrepancies are observed in both crossing strengths and level positions, especially for levels with l symmetry (rotational angular momentum L=8). The discrepancies should allow the development of improved potential models in the future. %B Physical Review A %V 78 %8 2008/11/5 %G eng %U http://arxiv.org/abs/0806.2583v1 %N 5 %! Phys. Rev. A %R 10.1103/PhysRevA.78.052703 %0 Journal Article %J Physical Review Letters %D 2008 %T Coherence of an optically illuminated single nuclear spin qubit %A Liang Jiang %A M. V. Gurudev Dutt %A Emre Togan %A Lily Childress %A Paola Cappellaro %A J. M. Taylor %A Mikhail D. Lukin %X 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. %B Physical Review Letters %V 100 %8 2008/2/19 %G eng %U http://arxiv.org/abs/0707.1341v2 %N 7 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.100.073001 %0 Journal Article %J Physical Review Letters %D 2008 %T Coherent Quantum Optical Control with Subwavelength Resolution %A Alexey V. Gorshkov %A Liang Jiang %A Markus Greiner %A Peter Zoller %A Mikhail D. Lukin %X We suggest a new method for quantum optical control with nanoscale resolution. Our method allows for coherent far-field manipulation of individual quantum systems with spatial selectivity that is not limited by the wavelength of radiation and can, in principle, approach a few nanometers. The selectivity is enabled by the nonlinear atomic response, under the conditions of Electromagnetically Induced Transparency, to a control beam with intensity vanishing at a certain location. Practical performance of this technique and its potential applications to quantum information science with cold atoms, ions, and solid-state qubits are discussed. %B Physical Review Letters %V 100 %8 2008/3/7 %G eng %U http://arxiv.org/abs/0706.3879v2 %N 9 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.100.093005 %0 Journal Article %J Quantum Information & Computation %D 2008 %T Estimating Jones polynomials is a complete problem for one clean qubit %A Peter W. Shor %A Stephen P. Jordan %XIt is known that evaluating a certain approximation to the Jones polynomial for the plat closure of a braid is a BQP-complete problem. That is, this problem exactly captures the power of the quantum circuit model. The one clean qubit model is a model of quantum computation in which all but one qubit starts in the maximally mixed state. One clean qubit computers are believed to be strictly weaker than standard quantum computers, but still capable of solving some classically intractable problems. Here we show that evaluating a certain approximation to the Jones polynomial at a fifth root of unity for the trace closure of a braid is a complete problem for the one clean qubit complexity class. That is, a one clean qubit computer can approximate these Jones polynomials in time polynomial in both the number of strands and number of crossings, and the problem of simulating a one clean qubit computer is reducible to approximating the Jones polynomial of the trace closure of a braid.

%B Quantum Information & Computation %V 8 %P 681-714 %8 2008/09/01 %G eng %U http://dl.acm.org/citation.cfm?id=2017011.2017012 %N 8 %0 Journal Article %J Journal of Mathematical Physics %D 2008 %T Existence of Universal Entangler %A Jianxin Chen %A Runyao Duan %A Zhengfeng Ji %A Mingsheng Ying %A Jun Yu %X 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. %B Journal of Mathematical Physics %V 49 %P 012103 %8 2008/01/01 %G eng %U http://arxiv.org/abs/0704.1473v2 %N 1 %! J. Math. Phys. %R 10.1063/1.2829895 %0 Journal Article %D 2008 %T Fast quantum algorithms for approximating some irreducible representations of groups %A Stephen P. Jordan %X We consider the quantum complexity of estimating matrix elements of unitary irreducible representations of groups. For several finite groups including the symmetric group, quantum Fourier transforms yield efficient solutions to this problem. Furthermore, quantum Schur transforms yield efficient solutions for certain irreducible representations of the unitary group. Beyond this, we obtain poly(n)-time quantum algorithms for approximating matrix elements from all the irreducible representations of the alternating group A_n, and all the irreducible representations of polynomial highest weight of U(n), SU(n), and SO(n). These quantum algorithms offer exponential speedup in worst case complexity over the fastest known classical algorithms. On the other hand, we show that average case instances are classically easy, and that the techniques analyzed here do not offer a speedup over classical computation for the estimation of group characters. %8 2008/11/04 %G eng %U http://arxiv.org/abs/0811.0562v2 %0 Journal Article %J Nature Physics %D 2008 %T High-sensitivity diamond magnetometer with nanoscale resolution %A J. M. Taylor %A P. Cappellaro %A L. Childress %A L. Jiang %A D. Budker %A P. R. Hemmer %A A. Yacoby %A R. Walsworth %A M. D. Lukin %X 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$^{1/2}$. %B Nature Physics %V 4 %P 810 - 816 %8 2008/9/14 %G eng %U http://arxiv.org/abs/0805.1367v1 %N 10 %! Nat Phys %R 10.1038/nphys1075 %0 Journal Article %J Physical Review A %D 2008 %T Perturbative Gadgets at Arbitrary Orders %A Stephen P. Jordan %A Edward Farhi %X Adiabatic quantum algorithms are often most easily formulated using many-body interactions. However, experimentally available interactions are generally two-body. In 2004, Kempe, Kitaev, and Regev introduced perturbative gadgets, by which arbitrary three-body effective interactions can be obtained using Hamiltonians consisting only of two-body interactions. These three-body effective interactions arise from the third order in perturbation theory. Since their introduction, perturbative gadgets have become a standard tool in the theory of quantum computation. Here we construct generalized gadgets so that one can directly obtain arbitrary k-body effective interactions from two-body Hamiltonians. These effective interactions arise from the kth order in perturbation theory. %B Physical Review A %V 77 %8 2008/6/19 %G eng %U http://arxiv.org/abs/0802.1874v4 %N 6 %! Phys. Rev. A %R 10.1103/PhysRevA.77.062329 %0 Journal Article %J Proceedings of the National Academy of Sciences %D 2008 %T Polynomial-time quantum algorithm for the simulation of chemical dynamics %A Ivan Kassal %A Stephen P. Jordan %A Peter J. Love %A Masoud Mohseni %A Alán Aspuru-Guzik %X The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum computers could exactly simulate chemical reactions in polynomial time. Our algorithm uses the split-operator approach and explicitly simulates all electron-nuclear and inter-electronic interactions in quadratic time. Surprisingly, this treatment is not only more accurate than the Born-Oppenheimer approximation, but faster and more efficient as well, for all reactions with more than about four atoms. This is the case even though the entire electronic wavefunction is propagated on a grid with appropriately short timesteps. Although the preparation and measurement of arbitrary states on a quantum computer is inefficient, here we demonstrate how to prepare states of chemical interest efficiently. We also show how to efficiently obtain chemically relevant observables, such as state-to-state transition probabilities and thermal reaction rates. Quantum computers using these techniques could outperform current classical computers with one hundred qubits. %B Proceedings of the National Academy of Sciences %V 105 %P 18681 - 18686 %8 2008/11/24 %G eng %U http://arxiv.org/abs/0801.2986v3 %N 48 %! Proceedings of the National Academy of Sciences %R 10.1073/pnas.0808245105 %0 Journal Article %D 2008 %T Quantum Computation Beyond the Circuit Model %A Stephen P. Jordan %X The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other models of quantum computation exist which provide useful alternative frameworks for both discovering new quantum algorithms and devising new physical implementations of quantum computers. In this thesis, I first present necessary background material for a general physics audience and discuss existing models of quantum computation. Then, I present three results relating to various models of quantum computation: a scheme for improving the intrinsic fault tolerance of adiabatic quantum computers using quantum error detecting codes, a proof that a certain problem of estimating Jones polynomials is complete for the one clean qubit complexity class, and a generalization of perturbative gadgets which allows k-body interactions to be directly simulated using 2-body interactions. Lastly, I discuss general principles regarding quantum computation that I learned in the course of my research, and using these principles I propose directions for future research. %8 2008/09/13 %G eng %U http://arxiv.org/abs/0809.2307v1 %0 Journal Article %J Physical Review Letters %D 2008 %T Two-body transients in coupled atomic-molecular BECs %A Pascal Naidon %A Eite Tiesinga %A Paul S. Julienne %X We discuss the dynamics of an atomic Bose-Einstein condensate when pairs of atoms are converted into molecules by single-color photoassociation. Three main regimes are found and it is shown that they can be understood on the basis of time-dependent two-body theory. In particular, the so-called rogue dissociation regime [Phys. Rev. Lett., 88, 090403 (2002)], which has a density-dependent limit on the photoassociation rate, is identified with a transient regime of the two-atom dynamics exhibiting universal properties. Finally, we illustrate how these regimes could be explored by photoassociating condensates of alkaline-earth atoms. %B Physical Review Letters %V 100 %8 2008/3/3 %G eng %U http://arxiv.org/abs/0707.2963v2 %N 9 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.100.093001 %0 Journal Article %D 2007 %T Coherent, adiabatic and dissociation regimes in coupled atomic-molecular Bose-Einstein condensates %A Pascal Naidon %A Eite Tiesinga %A Paul S. Julienne %X We discuss the dynamics of a Bose-Einstein condensate of atoms which is suddenly coupled to a condensate of molecules by an optical or magnetic Feshbach resonance. Three limiting regimes are found and can be understood from the transient dynamics occuring for each pair of atoms. This transient dynamics can be summarised into a time-dependent shift and broadening of the molecular state. A simple Gross-Pitaevskii picture including this shift and broadening is proposed to describe the system in the three regimes. Finally, we suggest how to explore these regimes experimentally. %8 2007/11/02 %G eng %U http://arxiv.org/abs/0711.0397v2 %0 Journal Article %J New Journal of Physics %D 2007 %T Effective-range description of a Bose gas under strong one- or two-dimensional confinement %A Pascal Naidon %A Eite Tiesinga %A William F. Mitchell %A Paul S. Julienne %X We point out that theories describing s-wave collisions of bosonic atoms confined in one- or two-dimensional geometries can be extended to much tighter confinements than previously thought. This is achieved by replacing the scattering length by an energy-dependent scattering length which was already introduced for the calculation of energy levels under 3D confinement. This replacement accurately predicts the position of confinement-induced resonances in strongly confined geometries. %B New Journal of Physics %V 9 %P 19 - 19 %8 2007/01/29 %G eng %U http://arxiv.org/abs/physics/0607140v2 %N 1 %! New J. Phys. %R 10.1088/1367-2630/9/1/019 %0 Journal Article %J Physical Review A %D 2007 %T A fast and robust approach to long-distance quantum communication with atomic ensembles %A L. Jiang %A J. M. Taylor %A M. D. Lukin %X Quantum repeaters create long-distance entanglement between quantum systems while overcoming difficulties such as the attenuation of single photons in a fiber. Recently, an implementation of a repeater protocol based on single qubits in atomic ensembles and linear optics has been proposed [Nature 414, 413 (2001)]. Motivated by rapid experimental progress towards implementing that protocol, here we develop a more efficient scheme compatible with active purification of arbitrary errors. Using similar resources as the earlier protocol, our approach intrinsically purifies leakage out of the logical subspace and all errors within the logical subspace, leading to greatly improved performance in the presence of experimental inefficiencies. Our analysis indicates that our scheme could generate approximately one pair per 3 minutes over 1280 km distance with fidelity (F>78%) sufficient to violate Bell's inequality. %B Physical Review A %V 76 %8 2007/7/2 %G eng %U http://arxiv.org/abs/quant-ph/0609236v3 %N 1 %! Phys. Rev. A %R 10.1103/PhysRevA.76.012301 %0 Journal Article %D 2007 %T The LU-LC conjecture is false %A Zhengfeng Ji %A Jianxin Chen %A Zhaohui Wei %A Mingsheng Ying %X 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. %8 2007/09/09 %G eng %U http://arxiv.org/abs/0709.1266v2 %! Quantum Inf. Comput. %0 Journal Article %J Physical Review B %D 2007 %T Relaxation, dephasing, and quantum control of electron spins in double quantum dots %A J. M. Taylor %A J. R. Petta %A A. C. Johnson %A A. Yacoby %A C. M. Marcus %A M. D. Lukin %X Recent experiments have demonstrated quantum manipulation of two-electron spin states in double quantum dots using electrically controlled exchange interactions. Here, we present a detailed theory for electron spin dynamics in two-electron double dot systems that was used to guide these experiments and analyze experimental results. The theory treats both charge and spin degrees of freedom on an equal basis. Specifically, we analyze the relaxation and dephasing mechanisms that are relevant to experiments and discuss practical approaches for quantum control of two-electron system. We show that both charge and spin dephasing play important roles in the dynamics of the two-spin system, but neither represents a fundamental limit for electrical control of spin degrees of freedom in semiconductor quantum bits. %B Physical Review B %V 76 %8 2007/7/13 %G eng %U http://arxiv.org/abs/cond-mat/0602470v2 %N 3 %! Phys. Rev. B %R 10.1103/PhysRevB.76.035315 %0 Journal Article %J Physical Review A %D 2006 %T Error correcting codes for adiabatic quantum computation %A Stephen P. Jordan %A Edward Farhi %A Peter W. Shor %X Recently, there has been growing interest in using adiabatic quantum computation as an architecture for experimentally realizable quantum computers. One of the reasons for this is the idea that the energy gap should provide some inherent resistance to noise. It is now known that universal quantum computation can be achieved adiabatically using 2-local Hamiltonians. The energy gap in these Hamiltonians scales as an inverse polynomial in the problem size. Here we present stabilizer codes which can be used to produce a constant energy gap against 1-local and 2-local noise. The corresponding fault-tolerant universal Hamiltonians are 4-local and 6-local respectively, which is the optimal result achievable within this framework. %B Physical Review A %V 74 %8 2006/11/14 %G eng %U http://arxiv.org/abs/quant-ph/0512170v3 %N 5 %! Phys. Rev. A %R 10.1103/PhysRevA.74.052322 %0 Journal Article %J Physical Review Letters %D 2005 %T Fast quantum algorithm for numerical gradient estimation %A Stephen P. Jordan %X Given a blackbox for f, a smooth real scalar function of d real variables, one wants to estimate the gradient of f at a given point with n bits of precision. On a classical computer this requires a minimum of d+1 blackbox queries, whereas on a quantum computer it requires only one query regardless of d. The number of bits of precision to which f must be evaluated matches the classical requirement in the limit of large n. %B Physical Review Letters %V 95 %8 2005/7/28 %G eng %U http://arxiv.org/abs/quant-ph/0405146v2 %N 5 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.95.050501 %0 Journal Article %J Physical Review A %D 2005 %T Multichannel quantum-defect theory for slow atomic collisions %A Bo Gao %A Eite Tiesinga %A Carl J. Williams %A Paul S. Julienne %X We present a multichannel quantum-defect theory for slow atomic collisions that takes advantages of the analytic solutions for the long-range potential, and both the energy and the angular-momentum insensitivities of the short-range parameters. The theory provides an accurate and complete account of scattering processes, including shape and Feshbach resonances, in terms of a few parameters such as the singlet and the triplet scattering lengths. As an example, results for $^{23}$Na-$^{23}$Na scattering are presented and compared close-coupling calculations. %B Physical Review A %V 72 %8 2005/10/28 %G eng %U http://arxiv.org/abs/physics/0508060v1 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.72.042719 %0 Journal Article %J Physical Review A %D 2005 %T Sodium Bose-Einstein Condensates in an Optical Lattice %A K. Xu %A Y. Liu %A J. R. Abo-Shaeer %A T. Mukaiyama %A J. K. Chin %A D. E. Miller %A W. Ketterle %A Kevin M. Jones %A Eite Tiesinga %X 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. %B Physical Review A %V 72 %8 2005/10/10 %G eng %U http://arxiv.org/abs/cond-mat/0507288v1 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.72.043604 %0 Journal Article %J Physical Review Letters %D 2005 %T Spontaneous dissociation of long-range Feshbach molecules %A Thorsten Koehler %A Eite Tiesinga %A Paul S. Julienne %X We study the spontaneous dissociation of diatomic molecules produced in cold atomic gases via magnetically tunable Feshbach resonances. We provide a universal formula for the lifetime of these molecules that relates their decay to the scattering length and the loss rate constant for inelastic spin relaxation. Our universal treatment as well as our exact coupled channels calculations for $^{85}$Rb dimers predict a suppression of the decay over several orders of magnitude when the scattering length is increased. Our predictions are in good agreement with recent measurements of the lifetime of $^{85}$Rb$_2$. %B Physical Review Letters %V 94 %8 2005/1/18 %G eng %U http://arxiv.org/abs/cond-mat/0408387v2 %N 2 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.94.020402 %0 Journal Article %J Journal of Physics B: Atomic, Molecular and Optical Physics %D 2004 %T Adiabatic association of ultracold molecules via magnetic field tunable interactions %A Krzysztof Goral %A Thorsten Koehler %A Simon A. Gardiner %A Eite Tiesinga %A Paul S. Julienne %X We consider in detail the situation of applying a time dependent external magnetic field to a 87Rb atomic Bose-Einstein condensate held in a harmonic trap, in order to adiabatically sweep the interatomic interactions across a Feshbach resonance to produce diatomic molecules. To this end, we introduce a minimal two-body Hamiltonian depending on just five measurable parameters of a Feshbach resonance, which accurately determines all low energy binary scattering observables, in particular, the molecular conversion efficiency of just two atoms. Based on this description of the microscopic collision phenomena, we use the many-body theory of T. Koehler and K. Burnett [Phys. Rev. A 65, 033601 (2002)] to study the efficiency of the association of molecules in a 87Rb Bose-Einstein condensate during a linear passage of the magnetic field strength across the 100 mT Feshbach resonance. We explore different, experimentally accessible, parameter regimes, and compare the predictions of Landau-Zener, configuration interaction, and two level mean field calculations with those of the microscopic many-body approach. Our comparative studies reveal a remarkable insensitivity of the molecular conversion efficiency with respect to both the details of the microscopic binary collision physics and the coherent nature of the Bose-Einstein condensed gas, provided that the magnetic field strength is varied linearly. We provide the reasons for this universality of the molecular production achieved by linear ramps of the magnetic field strength, and identify the Landau-Zener coefficient determined by F.H. Mies et al. [Phys. Rev. A 61, 022721 (2000)] as the main parameter that controls the efficiency. %B Journal of Physics B: Atomic, Molecular and Optical Physics %V 37 %P 3457 - 3500 %8 2004/09/14 %G eng %U http://arxiv.org/abs/cond-mat/0312178v5 %N 17 %! J. Phys. B: At. Mol. Opt. Phys. %R 10.1088/0953-4075/37/17/006 %0 Journal Article %J Physical Review Letters %D 2003 %T Ultracold collision properties of metastable alkaline-earth atoms %A Andrei Derevianko %A Sergey G. Porsev %A Svetlana Kotochigova %A Eite Tiesinga %A Paul S. Julienne %X Ultra-cold collisions of spin-polarized 24Mg,40Ca, and 88Sr in the metastable 3P2 excited state are investigated. We calculate the long-range interaction potentials and estimate the scattering length and the collisional loss rate as a function of magnetic field. The estimates are based on molecular potentials between 3P2 alkaline-earth atoms obtained from ab initio atomic and molecular structure calculations. The scattering lengths show resonance behavior due to the appearance of a molecular bound state in a purely long-range interaction potential and are positive for magnetic fields below 50 mT. A loss-rate model shows that losses should be smallest near zero magnetic field and for fields slightly larger than the resonance field, where the scattering length is also positive. %B Physical Review Letters %V 90 %8 2003/2/13 %G eng %U http://arxiv.org/abs/physics/0210076v1 %N 6 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.90.063002