@article {3497, title = {Long-Distance Nuclear Matrix Elements for Neutrinoless Double-Beta Decay from Lattice QCD}, year = {2024}, month = {2/14/2024}, abstract = {

Neutrinoless double-beta (0νββ) decay is a heretofore unobserved process which, if observed, would imply that neutrinos are Majorana particles. Interpretations of the stringent experimental constraints on 0νββ-decay half-lives require calculations of nuclear matrix elements. This work presents the first lattice quantum-chromodynamics (LQCD) calculation of the matrix element for 0νββ decay in a multi-nucleon system, specifically the nn\→ppee transition, mediated by a light left-handed Majorana neutrino propagating over nuclear-scale distances. This calculation is performed with quark masses corresponding to a pion mass of mπ=806 MeV at a single lattice spacing and volume. The statistically cleaner Σ\−\→Σ+ee transition is also computed in order to investigate various systematic uncertainties. The prospects for matching the results of LQCD calculations onto a nuclear effective field theory to determine a leading-order low-energy constant relevant for 0νββ decay with a light Majorana neutrino are investigated. This work, therefore, sets the stage for future calculations at physical values of the quark masses that, combined with effective field theory and nuclear many-body studies, will provide controlled theoretical inputs to experimental searches of 0νββ decay.

}, url = {https://arxiv.org/abs/2402.09362}, author = {Zohreh Davoudi and William Detmold and Zhenghao Fu and Anthony V. Grebe and William Jay and David Murphy and Patrick Oare and Phiala E. Shanahan and Michael L. Wagman} } @article {3422, title = {Lattice quantum chromodynamics at large isospin density: 6144 pions in a box}, year = {2023}, month = {7/27/2023}, abstract = {

We present an algorithm to compute correlation functions for systems with the quantum numbers of many identical mesons from lattice quantum chromodynamics (QCD). The algorithm is numerically stable and allows for the computation of n-pion correlation functions for n\∈{1,\…,N} using a single N\×N matrix decomposition, improving on previous algorithms. We apply the algorithm to calculations of correlation functions with up to 6144 π+s using two ensembles of gauge field configurations generated with quark masses corresponding to a pion mass mπ=170 MeV and spacetime volumes of (4.43\×8.8) fm4 and (5.83\×11.6) fm4. We also discuss statistical techniques for the analysis of such systems, in which the correlation functions vary over many orders of magnitude. In particular, we observe that the many-pion correlation functions are well approximated by log-normal distributions, allowing the extraction of the energies of these systems. Using these energies, the large-isospin-density, zero-baryon-density region of the QCD phase diagram is explored. A peak is observed in the energy density at an isospin chemical potential μI\∼1.5mπ, signalling the transition into a Bose-Einstein condensed phase. The isentropic speed of sound in the medium is seen to exceed the ideal-gas (conformal) limit (c2s\≤1/3) over a wide range of chemical potential before falling towards the asymptotic expectation at μI\∼15mπ. These, and other thermodynamic observables, indicate that the isospin chemical potential must be large for the system to be well described by an ideal gas or perturbative QCD.

}, url = {https://arxiv.org/abs/2307.15014}, author = {Ryan Abbott and William Detmold and Fernando Romero-L{\'o}pez and Zohreh Davoudi and Marc Illa and Assumpta Parre{\~n}o and Robert J. Perry and Phiala E. Shanahan and Michael L. Wagman} } @article {3267, title = {Linear combination of Hamiltonian simulation for non-unitary dynamics with optimal state preparation cost}, journal = {Phys. Rev. Lett.}, volume = {131}, year = {2023}, month = {10/13/2023}, abstract = {

We propose a simple method for simulating a general class of non-unitary dynamics as a linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on converting the problem into a dilated linear system problem, or on the spectral mapping theorem. The latter is the mathematical foundation of many quantum algorithms for solving a wide variety of tasks involving non-unitary processes, such as the quantum singular value transformation (QSVT). The LCHS method can achieve optimal cost in terms of state preparation. We also demonstrate an application for open quantum dynamics simulation using the complex absorbing potential method with near-optimal dependence on all parameters.

}, doi = {https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.131.150603}, url = {https://arxiv.org/abs/2303.01029}, author = {Dong An and Jin-Peng Liu and Lin Lin} } @article {3252, title = {Local Hamiltonians with no low-energy stabilizer states}, year = {2023}, month = {2/28/2023}, abstract = {

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

}, url = {https://arxiv.org/abs/2302.14755}, author = {Nolan J. Coble and Matthew Coudron and Jon Nelson and Seyed Sajjad Nezhadi} } @article {3401, title = {Logical quantum processor based on reconfigurable atom arrays}, journal = {Nature}, year = {2023}, month = {12/7/2023}, issn = {1476-4687}, doi = {10.1038/s41586-023-06927-3}, url = {https://arxiv.org/abs/2312.03982}, author = {Bluvstein, Dolev and Evered, Simon J. and Geim, Alexandra A. and Li, Sophie H. and Zhou, Hengyun and Manovitz, Tom and Ebadi, Sepehr and Cain, Madelyn and Kalinowski, Marcin and Dominik Hangleiter and Ataides, J. Pablo Bonilla and Maskara, Nishad and Cong, Iris and Gao, Xun and Rodriguez, Pedro Sales and Karolyshyn, Thomas and Semeghini, Giulia and Michael Gullans and Greiner, Markus and Vuletic, Vladan and Lukin, Mikhail D.} } @article {3185, title = {Lower Bounds on Quantum Annealing Times}, journal = {Phys. Rev. Lett.}, volume = {130}, year = {2023}, month = {4/5/2023}, abstract = {

The adiabatic theorem provides sufficient conditions for the time needed to prepare a target ground state. While it is possible to prepare a target state much faster with more general quantum annealing protocols, rigorous results beyond the adiabatic regime are rare. Here, we provide such a result, deriving lower bounds on the time needed to successfully perform quantum annealing. The bounds are asymptotically saturated by three toy models where fast annealing schedules are known: the Roland and Cerf unstructured search model, the Hamming spike problem, and the ferromagnetic p-spin model. Our bounds demonstrate that these schedules have optimal scaling. Our results also show that rapid annealing requires coherent superpositions of energy eigenstates, singling out quantum coherence as a computational resource.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {https://doi.org/10.1103/PhysRevLett.130.140601}, url = {https://arxiv.org/abs/2210.15687}, author = {Garc{\'\i}a-Pintos, Luis Pedro and Brady, Lucas T. and Bringewatt, Jacob and Liu, Yi-Kai} } @article {3154, title = {Lattice-Based Quantum Advantage from Rotated Measurements}, year = {2022}, month = {10/18/2022}, abstract = {

Trapdoor claw-free functions (TCFs) are immensely valuable in cryptographic interactions between a classical client and a quantum server. Typically, a protocol has the quantum server prepare a superposition of two-bit strings of a claw and then measure it using Pauli-X or Z measurements. In this paper, we demonstrate a new technique that uses the entire range of qubit measurements from the XY-plane. We show the advantage of this approach in two applications. First, building on (Brakerski et al. 2018, Kalai et al. 2022), we show an optimized two-round proof of quantumness whose security can be expressed directly in terms of the hardness of the LWE (learning with errors) problem. Second, we construct a one-round protocol for blind remote preparation of an arbitrary state on the XY-plane up to a Pauli-Z correction.

}, keywords = {Cryptography and Security (cs.CR), Emerging Technologies (cs.ET), FOS: Computer and information sciences, FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2210.10143}, url = {https://arxiv.org/abs/2210.10143}, author = {Yusuf Alnawakhtha and Mantri, Atul and Carl Miller and Wang, Daochen} } @article {3027, title = {Linear growth of quantum circuit complexity}, journal = {Nat. Phys.}, year = {2022}, month = {3/28/2022}, abstract = {

The complexity of quantum states has become a key quantity of interest across various subfields of physics, from quantum computing to the theory of black holes. The evolution of generic quantum systems can be modelled by considering a collection of qubits subjected to sequences of random unitary gates. Here we investigate how the complexity of these random quantum circuits increases by considering how to construct a unitary operation from Haar-random two-qubit quantum gates. Implementing the unitary operation exactly requires a minimal number of gates\—this is the operation\’s exact circuit complexity. We prove a conjecture that this complexity grows linearly, before saturating when the number of applied gates reaches a threshold that grows exponentially with the number of qubits. Our proof overcomes difficulties in establishing lower bounds for the exact circuit complexity by combining differential topology and elementary algebraic geometry with an inductive construction of Clifford circuits.

}, doi = {https://doi.org/10.1038/s41567-022-01539-6}, author = {Jonas Haferkamp and Philippe Faist and Naga B. T. Kothakonda and Jens Eisert and Nicole Yunger Halpern} } @article {2869, title = {Learnability of the output distributions of local quantum circuits}, year = {2021}, month = {10/11/2021}, abstract = {

There is currently a large interest in understanding the potential advantages quantum devices can offer for probabilistic modelling. In this work we investigate, within two different oracle models, the probably approximately correct (PAC) learnability of quantum circuit Born machines, i.e., the output distributions of local quantum circuits. We first show a negative result, namely, that the output distributions of super-logarithmic depth Clifford circuits are not sample-efficiently learnable in the statistical query model, i.e., when given query access to empirical expectation values of bounded functions over the sample space. This immediately implies the hardness, for both quantum and classical algorithms, of learning from statistical queries the output distributions of local quantum circuits using any gate set which includes the Clifford group. As many practical generative modelling algorithms use statistical queries -- including those for training quantum circuit Born machines -- our result is broadly applicable and strongly limits the possibility of a meaningful quantum advantage for learning the output distributions of local quantum circuits. As a positive result, we show that in a more powerful oracle model, namely when directly given access to samples, the output distributions of local Clifford circuits are computationally efficiently PAC learnable by a classical learner. Our results are equally applicable to the problems of learning an algorithm for generating samples from the target distribution (generative modelling) and learning an algorithm for evaluating its probabilities (density modelling). They provide the first rigorous insights into the learnability of output distributions of local quantum circuits from the probabilistic modelling perspective.\ 

}, url = {https://arxiv.org/abs/2110.05517}, author = {Marcel Hinsche and Marios Ioannou and Alexander Nietner and Jonas Haferkamp and Yihui Quek and Dominik Hangleiter and Jean-Pierre Seifert and Jens Eisert and Ryan Sweke} } @article {2929, title = {Lefschetz Thimble Quantum Monte Carlo for Spin Systems}, year = {2021}, month = {10/20/2021}, abstract = {

Monte Carlo simulations are often useful tools for modeling quantum systems, but in some cases they suffer from a sign problem, which manifests as an oscillating phase attached to the probabilities being sampled. This sign problem generally leads to an exponential slow down in the time taken by a Monte Carlo algorithm to reach any given level of accuracy, and it has been shown that completely solving the sign problem for an arbitrary quantum system is NP-hard. However, a variety of techniques exist for mitigating the sign problem in specific cases; in particular, the technique of deforming the Monte Carlo simulation\&$\#$39;s plane of integration onto Lefschetz thimbles (that is, complex hypersurfaces of stationary phase) has seen success for many problems of interest in the context of quantum field theories. We extend this methodology to discrete spin systems by utilizing spin coherent state path integrals to re-express the spin system\&$\#$39;s partition function in terms of continuous variables. This translation to continuous variables introduces additional challenges into the Lefschetz thimble method, which we address. We show that these techniques do indeed work to lessen the sign problem on some simple spin systems.

}, url = {https://arxiv.org/abs/2110.10699}, author = {T. C. Mooney and Jacob Bringewatt and Lucas T. Brady} } @article {2759, title = {The Lieb-Robinson light cone for power-law interactions}, year = {2021}, month = {3/29/2021}, abstract = {

The Lieb-Robinson theorem states that information propagates with a finite velocity in quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits on information propagation in quantum systems with power-law interactions, which decay as 1/rα at distance r? Here, we present a definitive answer to this question for all exponents α\>2d and all spatial dimensions d. Schematically, information takes time at least rmin{1,α\−2d} to propagate a distance~r. As recent state transfer protocols saturate this bound, our work closes a decades-long hunt for optimal Lieb-Robinson bounds on quantum information dynamics with power-law interactions.

}, url = {https://arxiv.org/abs/2103.15828}, author = {Minh C. Tran and Andrew Y. Guo and Christopher L. Baldwin and Adam Ehrenberg and Alexey V. Gorshkov and Andrew Lucas} } @article {2934, title = {Limits to Perception by Quantum Monitoring with Finite Efficiency}, journal = {Entropy}, volume = {23}, year = {2021}, month = {11/17/2021}, pages = {1527}, abstract = {

We formulate limits to perception under continuous quantum measurements by comparing the quantum states assigned by agents that have partial access to measurement outcomes. To this end, we provide bounds on the trace distance and the relative entropy between the assigned state and the actual state of the system. These bounds are expressed solely in terms of the purity and von Neumann entropy of the state assigned by the agent, and are shown to characterize how an agent\’s perception of the system is altered by access to additional information. We apply our results to Gaussian states and to the dynamics of a system embedded in an environment illustrated on a quantum Ising chain.

}, issn = {1099-4300}, doi = {10.3390/e23111527}, url = {https://www.mdpi.com/1099-4300/23/11/1527}, author = {Garc{\'\i}a-Pintos, Luis Pedro and del Campo, Adolfo} } @article {2865, title = {Linear and continuous variable spin-wave processing using a cavity-coupled atomic ensemble}, year = {2021}, month = {9/30/2021}, abstract = {

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

}, url = {https://arxiv.org/abs/2109.15246}, author = {Kevin C. Cox and Przemyslaw Bienias and David H. Meyer and Donald P. Fahey and Paul D. Kunz and Alexey V. Gorshkov} } @article {2871, title = {Localization crossover and subdiffusive transport in a classical facilitated network model of a disordered, interacting quantum spin chain}, year = {2021}, month = {9/22/2021}, abstract = {

We consider the random-field Heisenberg model, a paradigmatic model for many-body localization (MBL), and add a Markovian dephasing bath coupled to the Anderson orbitals of the model\&$\#$39;s non-interacting limit. We map this system to a classical facilitated hopping model that is computationally tractable for large system sizes, and investigate its dynamics. The classical model exhibits a robust crossover between an ergodic (thermal) phase and a frozen (localized) phase. The frozen phase is destabilized by thermal subregions (bubbles), which thermalize surrounding sites by providing a fluctuating interaction energy and so enable off-resonance particle transport. Investigating steady state transport, we observe that the interplay between thermal and frozen bubbles leads to a clear transition between diffusive and subdiffusive regimes. This phenomenology both describes the MBL system coupled to a bath, and provides a classical analogue for the many-body localization transition in the corresponding quantum model, in that the classical model displays long local memory times. It also highlights the importance of the details of the bath coupling in studies of MBL systems coupled to thermal environments.

}, url = {https://arxiv.org/abs/2109.10926}, author = {Kai Klocke and Christopher David White and Michael Buchhold} } @article {2593, title = {Limits on Classical Simulation of Free Fermions with Dissipation}, year = {2020}, month = {5/21/2020}, abstract = {

Free-fermionic systems are a valuable, but limited, class of many-body problems efficiently simulable on a classical computer. We examine how classical simulability of noninteracting fermions is modified in the presence of Markovian dissipation described by quadratic Lindblad operators, including, for example, incoherent transitions or pair losses. On the one hand, we establish three broad classes of Markovian dynamics that are efficiently simulable classically, by devising efficient algorithms. On the other hand, we demonstrate that, in the worst case, simulating Markovian dynamics with quadratic Lindblad operators is at least as hard as simulating universal quantum circuits. This result is applicable to an experimentally relevant setting in cold atomic systems, where magnetic Feshbach resonances can be used to engineer the desired dissipation. For such systems, our hardness result provides a direct scheme for dissipation-assisted quantum computing with a potential significant advantage in the speed of two-qubit gates and, therefore, in error tolerance.

}, url = {https://arxiv.org/abs/2005.10840}, author = {Oles Shtanko and Abhinav Deshpande and Paul S. Julienne and Alexey V. Gorshkov} } @article {2720, title = {Localization and criticality in antiblockaded 2D Rydberg atom arrays}, year = {2020}, month = {12/7/2020}, abstract = {

Controllable Rydberg atom arrays have provided new insights into fundamental properties of quantum matter both in and out of equilibrium. In this work, we study the effect of experimentally relevant positional disorder on Rydberg atoms trapped in a 2D square lattice under anti-blockade (facilitation) conditions. We show that the facilitation conditions lead the connectivity graph of a particular subspace of the full Hilbert space to form a 2D Lieb lattice, which features a singular flat band. Remarkably, we find three distinct regimes as the disorder strength is varied: a critical regime, a delocalized but nonergodic regime, and a regime with a disorder-induced flat band. The critical regime\&$\#$39;s existence depends crucially upon the singular flat band in our model, and is absent in any 1D array or ladder system. We propose to use quench dynamics to probe the three different regimes experimentally.\ 

}, url = {https://arxiv.org/abs/2012.03946}, author = {Fangli Liu and Zhi-Cheng Yang and Przemyslaw Bienias and Thomas Iadecola and Alexey V. Gorshkov} } @article {2310, title = {Limitations of semidefinite programs for separable states and entangled games}, journal = {Commun. Math. Phys.}, volume = {366}, year = {2019}, month = {03/04/2019}, chapter = {423-468}, abstract = {

Semidefinite programs (SDPs) are a framework for exact or approximate optimization that have widespread application in quantum information theory. We introduce a new method for using reductions to construct integrality gaps for SDPs. These are based on new limitations on the sum-of-squares (SoS) hierarchy in approximating two particularly important sets in quantum information theory, where previously no ω(1)-round integrality gaps were known: the set of separable (i.e. unentangled) states, or equivalently, the 2\→4 norm of a matrix, and the set of quantum correlations; i.e. conditional probability distributions achievable with local measurements on a shared entangled state. In both cases no-go theorems were previously known based on computational assumptions such as the Exponential Time Hypothesis (ETH) which asserts that 3-SAT requires exponential time to solve. Our unconditional results achieve the same parameters as all of these previous results (for separable states) or as some of the previous results (for quantum correlations). In some cases we can make use of the framework of Lee-Raghavendra-Steurer (LRS) to establish integrality gaps for any SDP, not only the SoS hierarchy. Our hardness result on separable states also yields a dimension lower bound of approximate disentanglers, answering a question of Watrous and Aaronson et al. These results can be viewed as limitations on the monogamy principle, the PPT test, the ability of Tsirelson-type bounds to restrict quantum correlations, as well as the SDP hierarchies of Doherty-Parrilo-Spedalieri, Navascues-Pironio-Acin and Berta-Fawzi-Scholz.

}, doi = {https://doi.org/10.1007/s00220-019-03382-y}, url = {https://arxiv.org/abs/1612.09306}, author = {Aram W. Harrow and Anand Natarajan and Xiaodi Wu} } @article {2195, title = {Locality and digital quantum simulation of power-law interactions}, journal = {Phys. Rev. X 9, 031006}, volume = {9}, year = {2019}, month = {07/10/2019}, abstract = {

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

}, doi = {https://doi.org/10.1103/PhysRevX.9.031006}, url = {https://arxiv.org/abs/1808.05225}, author = {Minh C. Tran and Andrew Y. Guo and Yuan Su and James R. Garrison and Zachary Eldredge and Michael Foss-Feig and Andrew M. Childs and Alexey V. Gorshkov} } @article {2458, title = {Locality and Heating in Periodically Driven, Power-law Interacting Systems}, journal = {Phys. Rev. A }, volume = {100}, year = {2019}, month = {2019/11/12}, abstract = {

We study the heating time in periodically driven D-dimensional systems with interactions that decay with the distance r as a power-law 1/rα. Using linear response theory, we show that the heating time is exponentially long as a function of the drive frequency for α\>D. For systems that may not obey linear response theory, we use a more general Magnus-like expansion to show the existence of quasi-conserved observables, which imply exponentially long heating time, for α\>2D. We also generalize a number of recent state-of-the-art Lieb-Robinson bounds for power-law systems from two-body interactions to k-body interactions and thereby obtain a longer heating time than previously established in the literature. Additionally, we conjecture that the gap between the results from the linear response theory and the Magnus-like expansion does not have physical implications, but is, rather, due to the lack of tight Lieb-Robinson bounds for power-law interactions. We show that the gap vanishes in the presence of a hypothetical, tight bound.\ 

}, doi = {https://doi.org/10.1103/PhysRevA.100.052103}, url = {https://arxiv.org/abs/1908.02773}, author = {Minh C. Tran and Adam Ehrenberg and Andrew Y. Guo and Paraj Titum and Dmitry A. Abanin and Alexey V. Gorshkov} } @article {2253, title = {Locality, Quantum Fluctuations, and Scrambling}, journal = {Phys. Rev. X }, volume = {9}, year = {2019}, month = {9/18/2019}, abstract = {

Thermalization of chaotic quantum many-body systems under unitary time evolution is related to the growth in complexity of initially simple Heisenberg operators. Operator growth is a manifestation of information scrambling and can be diagnosed by out-of-time-order correlators (OTOCs). However, the behavior of OTOCs of local operators in generic chaotic local Hamiltonians remains poorly understood, with some semiclassical and large N models exhibiting exponential growth of OTOCs and a sharp chaos wavefront and other random circuit models showing a diffusively broadened wavefront. In this paper we propose a unified physical picture for scrambling in chaotic local Hamiltonians. We construct a random time-dependent Hamiltonian model featuring a large N limit where the OTOC obeys a Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) type equation and exhibits exponential growth and a sharp wavefront. We show that quantum fluctuations manifest as noise (distinct from the randomness of the couplings in the underlying Hamiltonian) in the FKPP equation and that the noise-averaged OTOC exhibits a cross-over to a diffusively broadened wavefront. At small N we demonstrate that operator growth dynamics, averaged over the random couplings, can be efficiently simulated for all time using matrix product state techniques. To show that time-dependent randomness is not essential to our conclusions, we push our previous matrix product operator methods to very large size and show that data for a time-independent Hamiltonian model are also consistent with a diffusively-broadened wavefront.

}, doi = {https://doi.org/10.1103/PhysRevX.9.031048}, url = {https://arxiv.org/abs/1805.05376}, author = {Shenglong Xu and Brian Swingle} } @article {2222, title = {Local randomness: Examples and application}, journal = {Phys. Rev. A}, year = {2018}, month = {03/2018}, pages = {032324}, abstract = {

When two players achieve a superclassical score at a nonlocal game, their outputs must contain intrinsic randomness. This fact has many useful implications for quantum cryptography. Recently it has been observed [C. Miller and Y. Shi, Quantum Inf. Computat. 17, 0595 (2017)] that such scores also imply the existence of local randomness\—that is, randomness known to one player but not to the other. This has potential implications for cryptographic tasks between two cooperating but mistrustful players. In the current paper we bring this notion toward practical realization, by offering near-optimal bounds on local randomness for the CHSH game, and also proving the security of a cryptographic application of local randomness (single-bit certified deletion).

}, doi = {https://doi.org/10.1103/PhysRevA.97.032324}, url = {https://arxiv.org/abs/1708.04338}, author = {Honghao Fu and Carl Miller} } @article {2277, title = {Lieb-Robinson bounds on n-partite connected correlation functions}, journal = {Phys. Rev. A 96, 052334}, year = {2017}, abstract = {

Lieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an n-partite connected correlator can reach unit value in constant time. Remarkably, the bounds also allow for an n-partite connected correlator to reach a value that is exponentially large with system size in constant time, a feature which stands in contrast to bipartite connected correlations. We provide explicit examples of such systems.

}, doi = {https://doi.org/10.1103/PhysRevA.96.052334}, url = {https://arxiv.org/abs/1705.04355}, author = {Minh C. Tran and James R. Garrison and Zhe-Xuan Gong and Alexey V. Gorshkov} } @article {1987, title = {Lieb-Robinson bounds on n-partite connected correlations}, journal = {Physical Review A}, volume = {96}, year = {2017}, month = {2017/11/27}, abstract = {

Lieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an\ n-partite connected correlator can reach unit value in constant time. Remarkably, the bounds also allow for an\ n-partite connected correlator to reach a value that is exponentially large with system size in constant time, a feature which stands in contrast to bipartite connected correlations. We provide explicit examples of such systems.

}, doi = {10.1103/PhysRevA.96.052334}, url = {https://arxiv.org/abs/1705.04355}, author = {Minh C. Tran and James R. Garrison and Zhe-Xuan Gong and Alexey V. Gorshkov} } @article {2061, title = {Light-induced fractional quantum Hall phases in graphene}, journal = {Physical Review Letters}, volume = {119}, year = {2017}, month = {2017/12/15}, pages = {247403}, abstract = {

We show how to realize two-component fractional quantum Hall phases in monolayer graphene by optically driving the system. A laser is tuned into resonance between two Landau levels, giving rise to an effective tunneling between these two synthetic layers. Remarkably, because of this coupling, the interlayer interaction at non-zero relative angular momentum can become dominant, resembling a hollow-core pseudo-potential. In the weak tunneling regime, this interaction favors the formation of singlet states, as we explicitly show by numerical diagonalization, at fillings ν = 1/2 and ν = 2/3. We discuss possible candidate phases, including the Haldane-Rezayi phase, the interlayer Pfaffian phase, and a Fibonacci phase. This demonstrates that our method may pave the way towards the realization of non-Abelian phases, as well as the control of topological phase transitions, in graphene quantum Hall systems using optical fields and integrated photonic structures.

}, doi = {10.1103/PhysRevLett.119.247403}, url = {https://arxiv.org/abs/1612.08748}, author = {Areg Ghazaryan and Tobias Gra{\ss} and Michael Gullans and Pouyan Ghaemi and Mohammad Hafezi} } @article {1821, title = {Landauer formulation of photon transport in driven systems}, journal = {Physical Review B}, volume = {94}, year = {2016}, month = {2016/10/20}, pages = {155437}, abstract = {

Understanding the behavior of light in non-equilibrium scenarios underpins much of quantum optics and optical physics. While lasers provide a severe example of a non-equilibrium problem, recent interests in the near-equilibrium physics of photon {\textquoteleft}gases\&$\#$39;, such as in Bose condensation of light or in attempts to make photonic quantum simulators, suggest one reexamine some near-equilibrium cases. Here we consider how a sinusoidal parametric coupling between two semi-infinite photonic transmission lines leads to the creation and flow of photons between the two lines. Our approach provides a photonic analogue to the Landauer transport formula, and using non-equilbrium Green\&$\#$39;s functions, we can extend it to the case of an interacting region between two photonic {\textquoteleft}leads\&$\#$39; where the sinusoid frequency plays the role of a voltage bias. Crucially, we identify both the mathematical framework and the physical regime in which photonic transport is directly analogous to electronic transport, and regimes in which other new behavior such as two-mode squeezing can emerge.

}, doi = {10.1103/PhysRevB.94.155437}, url = {https://doi.org/10.1103/PhysRevB.94.155437}, author = {Chiao-Hsuan Wang and J. M. Taylor} } @article {1789, title = {Lattice Laughlin states on the torus from conformal field theory}, journal = {Journal of Statistical Mechanics: Theory and Experiment}, volume = {2016}, year = {2016}, month = {2016/01/28}, pages = {013102}, abstract = {Conformal field theory has turned out to be a powerful tool to derive two-dimensional lattice models displaying fractional quantum Hall physics. So far most of the work has been for lattices with open boundary conditions in at least one of the two directions, but it is desirable to also be able to handle the case of periodic boundary conditions. Here, we take steps in this direction by deriving analytical expressions for a family of conformal field theory states on the torus that is closely related to the family of bosonic and fermionic Laughlin states. We compute how the states transform when a particle is moved around the torus and when the states are translated or rotated, and we provide numerical evidence in particular cases that the states become orthonormal up to a common factor for large lattices. We use these results to find the S -matrix of the states, which turns out to be the same as for the continuum Laughlin states. Finally, we show that when the states are defined on a square lattice with suitable lattice spacing they practically coincide with the Laughlin states restricted to a lattice.}, url = {http://stacks.iop.org/1742-5468/2016/i=1/a=013102}, author = {Abhinav Deshpande and Anne E B Nielsen} } @article {1790, title = {Laplacian matrices and Alexandrov topologies of digraphs}, journal = {Linear Algebra and its Applications}, volume = {481}, year = {2015}, month = {2015/09/15}, pages = {174 - 185}, abstract = {We explore the spectral properties of digraph Laplacians and how they relate to topological properties of digraphs (such as openness, closure, and strong connectedness) under the Alexandrov topology.}, keywords = {Laplacian matrix}, issn = {0024-3795}, doi = {http://dx.doi.org/10.1016/j.laa.2015.04.031}, url = {http://www.sciencedirect.com/science/article/pii/S0024379515002840}, author = {Aaron Ostrander} } @article {1274, title = {Large effective three-body interaction in a double-well optical lattice}, journal = {Phys. Rev. A 92, 023602}, volume = {92}, year = {2015}, month = {2015/08/03}, pages = {023602}, abstract = { We study ultracold atoms in an optical lattice with two local minima per unit cell and show that the low energy states of a multi-band Bose-Hubbard (BH) Hamiltonian with only pair-wise interactions is equivalent to an effective single-band Hamiltonian with strong three-body interactions. We focus on a double-well optical lattice with a symmetric double well along the $x$ axis and single well structure along the perpendicular directions. Tunneling and two-body interaction energies are obtained from an exact band-structure calculation and numerically-constructed Wannier functions in order to construct a BH Hamiltonian spanning the lowest two bands. Our effective Hamiltonian is constructed from the ground state of the $N$-atom Hamiltonian for each unit cell obtained within the subspace spanned by the Wannier functions of two lowest bands. The model includes hopping between ground states of neighboring unit cells. We show that such an effective Hamiltonian has strong three-body interactions that can be easily tuned by changing the lattice parameters. Finally, relying on numerical mean-field simulations, we show that the effective Hamiltonian is an excellent approximation of the two-band BH Hamiltonian over a wide range of lattice parameters, both in the superfluid and Mott insulator regions. }, url = {http://journals.aps.org/pra/abstract/10.1103/PhysRevA.92.023602}, author = {Saurabh Paul and Eite Tiesinga} } @article {1228, title = {Levinson{\textquoteright}s theorem for graphs II}, journal = {Journal of Mathematical Physics}, volume = {53}, year = {2012}, month = {2012/11/21}, pages = {102207}, abstract = { We prove Levinson{\textquoteright}s theorem for scattering on an (m+n)-vertex graph with n semi-infinite paths each attached to a different vertex, generalizing a previous result for the case n=1. This theorem counts the number of bound states in terms of the winding of the determinant of the S-matrix. We also provide a proof that the bound states and incoming scattering states of the Hamiltonian together form a complete basis for the Hilbert space, generalizing another result for the case n=1. }, doi = {10.1063/1.4757665}, url = {http://arxiv.org/abs/1203.6557v2}, author = {Andrew M. Childs and David Gosset} } @article {1476, title = {Long-lived dipolar molecules and Feshbach molecules in a 3D optical lattice }, journal = {Physical Review Letters}, volume = {108}, year = {2012}, month = {2012/2/23}, abstract = { We have realized long-lived ground-state polar molecules in a 3D optical lattice, with a lifetime of up to 25 s, which is limited only by off-resonant scattering of the trapping light. Starting from a 2D optical lattice, we observe that the lifetime increases dramatically as a small lattice potential is added along the tube-shaped lattice traps. The 3D optical lattice also dramatically increases the lifetime for weakly bound Feshbach molecules. For a pure gas of Feshbach molecules, we observe a lifetime of >20 s in a 3D optical lattice; this represents a 100-fold improvement over previous results. This lifetime is also limited by off-resonant scattering, the rate of which is related to the size of the Feshbach molecule. Individually trapped Feshbach molecules in the 3D lattice can be converted to pairs of K and Rb atoms and back with nearly 100\% efficiency. }, doi = {10.1103/PhysRevLett.108.080405}, url = {http://arxiv.org/abs/1110.4420v1}, author = {Amodsen Chotia and Brian Neyenhuis and Steven A. Moses and Bo Yan and Jacob P. Covey and Michael Foss-Feig and Ana Maria Rey and Deborah S. Jin and Jun Ye} } @article {1349, title = {Laser cooling and optical detection of excitations in a LC electrical circuit}, journal = {Physical Review Letters}, volume = {107}, year = {2011}, month = {2011/12/27}, abstract = {We explore a method for laser cooling and optical detection of excitations in a LC electrical circuit. Our approach uses a nanomechanical oscillator as a transducer between optical and electronic excitations. An experimentally feasible system with the oscillator capacitively coupled to the LC and at the same time interacting with light via an optomechanical force is shown to provide strong electro-mechanical coupling. Conditions for improved sensitivity and quantum limited readout of electrical signals with such an "optical loud speaker" are outlined. }, doi = {10.1103/PhysRevLett.107.273601}, url = {http://arxiv.org/abs/1108.2035v1}, author = {J. M. Taylor and A. S. S{\o}rensen and C. M. Marcus and E. S. Polzik} } @article {1225, title = {Levinson{\textquoteright}s theorem for graphs}, journal = {Journal of Mathematical Physics}, volume = {52}, year = {2011}, month = {2011/06/30}, pages = {082102}, abstract = { We prove an analog of Levinson{\textquoteright}s theorem for scattering on a weighted (m+1)-vertex graph with a semi-infinite path attached to one of its vertices. In particular, we show that the number of bound states in such a scattering problem is equal to m minus half the winding number of the phase of the reflection coefficient (where each so-called half-bound state is counted as half a bound state). }, doi = {10.1063/1.3622608}, url = {http://arxiv.org/abs/1103.5077v2}, author = {Andrew M. Childs and DJ Strouse} } @article {1165, title = {Light storage in an optically thick atomic ensemble under conditions of electromagnetically induced transparency and four-wave mixing }, journal = {Physical Review A}, volume = {83}, year = {2011}, month = {2011/6/20}, abstract = { We study the modification of a traditional electromagnetically induced transparency (EIT) stored light technique that includes both EIT and four-wave mixing (FWM) in an ensemble of hot Rb atoms. The standard treatment of light storage involves the coherent and reversible mapping of one photonic mode onto a collective spin coherence. It has been shown that unwanted, competing processes such as four-wave mixing are enhanced by EIT and can significantly modify the signal optical pulse propagation. We present theoretical and experimental evidence to indicate that while a Stokes field is indeed detected upon retrieval of the signal field, any information originally encoded in a seeded Stokes field is not independently preserved during the storage process. We present a simple model that describes the propagation dynamics of the fields and the impact of FWM on the spin wave. }, doi = {10.1103/PhysRevA.83.063823}, url = {http://arxiv.org/abs/1103.2131v1}, author = {Nathaniel B. Phillips and Alexey V. Gorshkov and Irina Novikova} } @article {1219, title = {Limitations on the simulation of non-sparse Hamiltonians}, year = {2009}, month = {2009/08/31}, abstract = { The problem of simulating sparse Hamiltonians on quantum computers is well studied. The evolution of a sparse N x N Hamiltonian H for time t can be simulated using O(||Ht||poly(log N)) operations, which is essentially optimal due to a no--fast-forwarding theorem. Here, we consider non-sparse Hamiltonians and show significant limitations on their simulation. We generalize the no--fast-forwarding theorem to dense Hamiltonians, ruling out generic simulations taking time o(||Ht||), even though ||H|| is not a unique measure of the size of a dense Hamiltonian $H$. We also present a stronger limitation ruling out the possibility of generic simulations taking time poly(||Ht||,log N), showing that known simulations based on discrete-time quantum walk cannot be dramatically improved in general. On the positive side, we show that some non-sparse Hamiltonians can be simulated efficiently, such as those with graphs of small arboricity. }, url = {http://arxiv.org/abs/0908.4398v2}, author = {Andrew M. Childs and Robin Kothari} } @article {1568, title = {Locality Bounds on Hamiltonians for Stabilizer Codes}, journal = {Quantum Information and Computation}, volume = {9}, year = {2009}, month = {2009/09/22}, abstract = {In this paper, we study the complexity of Hamiltonians whose groundstate is a stabilizer code. We introduce various notions of k-locality of a stabilizer code, inherited from the associated stabilizer group. A choice of generators leads to a Hamiltonian with the code in its groundspace. We establish bounds on the locality of any other Hamiltonian whose groundspace contains such a code, whether or not its Pauli tensor summands commute. Our results provide insight into the cost of creating an energy gap for passive error correction and for adiabatic quantum computing. The results simplify in the cases of XZ-split codes such as Calderbank-Shor-Steane stabilizer codes and topologically-ordered stabilizer codes arising from surface cellulations. }, url = {http://www.cs.umd.edu/~oleary/reprints/j91.pdf}, author = {Stephen S. Bullock and Dianne P. O{\textquoteright}Leary} } @article {1214, title = {The limitations of nice mutually unbiased bases}, journal = {Journal of Algebraic Combinatorics}, volume = {25}, year = {2007}, month = {2006/7/11}, pages = {111 - 123}, abstract = { Mutually unbiased bases of a Hilbert space can be constructed by partitioning a unitary error basis. We consider this construction when the unitary error basis is a nice error basis. We show that the number of resulting mutually unbiased bases can be at most one plus the smallest prime power contained in the dimension, and therefore that this construction cannot improve upon previous approaches. We prove this by establishing a correspondence between nice mutually unbiased bases and abelian subgroups of the index group of a nice error basis and then bounding the number of such subgroups. This bound also has implications for the construction of certain combinatorial objects called nets. }, doi = {10.1007/s10801-006-0002-y}, url = {http://arxiv.org/abs/quant-ph/0412066v1}, author = {Michael Aschbacher and Andrew M. Childs and Pawel Wocjan} } @article {1423, title = {The Local Consistency Problem for Stoquastic and 1-D Quantum Systems}, year = {2007}, month = {2007/12/10}, abstract = { The Local Hamiltonian problem (finding the ground state energy of a quantum system) is known to be QMA-complete. The Local Consistency problem (deciding whether descriptions of small pieces of a quantum system are consistent) is also known to be QMA-complete. Here we consider special cases of Local Hamiltonian, for {\textquoteleft}{\textquoteleft}stoquastic{\textquoteright}{\textquoteright} and 1-dimensional systems, that seem to be strictly easier than QMA. We show that there exist analogous special cases of Local Consistency, that have equivalent complexity (up to poly-time oracle reductions). Our main technical tool is a new reduction from Local Consistency to Local Hamiltonian, using SDP duality. }, url = {http://arxiv.org/abs/0712.1388v2}, author = {Yi-Kai Liu} } @article {1441, title = {The LU-LC conjecture is false}, year = {2007}, month = {2007/09/09}, abstract = { The LU-LC conjecture is an important open problem concerning the structure of entanglement of states described in the stabilizer formalism. It states that two local unitary equivalent stabilizer states are also local Clifford equivalent. If this conjecture were true, the local equivalence of stabilizer states would be extremely easy to characterize. Unfortunately, however, based on the recent progress made by Gross and Van den Nest, we find that the conjecture is false. }, url = {http://arxiv.org/abs/0709.1266v2}, author = {Zhengfeng Ji and Jianxin Chen and Zhaohui Wei and Mingsheng Ying} } @conference {1773, title = {Language-reconfigurable universal phone recognition}, booktitle = {Eighth European Conference on Speech Communication and Technology}, year = {2003}, author = {Walker, Brenton D and Lackey, Bradley C and Muller, JS and Schone, Patrick John} } @article {1367, title = {Long-lived memory for mesoscopic quantum bits}, journal = {Physical Review Letters}, volume = {90}, year = {2003}, month = {2003/5/20}, abstract = {We describe a technique to create long-lived quantum memory for quantum bits in mesoscopic systems. Specifically we show that electronic spin coherence can be reversibly mapped onto the collective state of the surrounding nuclei. The coherent transfer can be efficient and fast and it can be used, when combined with standard resonance techniques, to reversibly store coherent superpositions on the time scale of seconds. This method can also allow for {\textquoteleft}{\textquoteleft}engineering{\textquoteright}{\textquoteright} entangled states of nuclear ensembles and efficiently manipulating the stored states. We investigate the feasibility of this method through a detailed analysis of the coherence properties of the system. }, doi = {10.1103/PhysRevLett.90.206803}, url = {http://arxiv.org/abs/cond-mat/0301323v1}, author = {J. M. Taylor and C. M. Marcus and M. D. Lukin} } @article {1250, title = {Lower bounds on the complexity of simulating quantum gates}, journal = {Physical Review A}, volume = {68}, year = {2003}, month = {2003/11/18}, abstract = { We give a simple proof of a formula for the minimal time required to simulate a two-qubit unitary operation using a fixed two-qubit Hamiltonian together with fast local unitaries. We also note that a related lower bound holds for arbitrary n-qubit gates. }, doi = {10.1103/PhysRevA.68.052311}, url = {http://arxiv.org/abs/quant-ph/0307190v1}, author = {Andrew M. Childs and Henry L. Haselgrove and Michael A. Nielsen} } @inbook {1777, title = {A Lichnerowicz Vanishing Theorem for Finsler Spaces}, booktitle = {The Theory of Finslerian Laplacians and Applications}, year = {1998}, pages = {227{\textendash}243}, publisher = {Springer}, organization = {Springer}, author = {Lackey, Brad} }