01965nas a2200205 4500008004100000245009400041210006900135260001400204520132100218100002001539700002101559700001701580700002301597700001701620700001801637700001801655700002501673700002401698856003701722 2024 eng d00aLong-Distance Nuclear Matrix Elements for Neutrinoless Double-Beta Decay from Lattice QCD0 aLongDistance Nuclear Matrix Elements for Neutrinoless DoubleBeta c2/14/20243 a

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.

1 aDavoudi, Zohreh1 aDetmold, William1 aFu, Zhenghao1 aGrebe, Anthony, V.1 aJay, William1 aMurphy, David1 aOare, Patrick1 aShanahan, Phiala, E.1 aWagman, Michael, L. uhttps://arxiv.org/abs/2402.0936202278nas a2200205 4500008004100000245008100041210006900122260001400191520163500205100001701840700002101857700002801878700002001906700001501926700002301941700002201964700002501986700002402011856003702035 2023 eng d00aLattice quantum chromodynamics at large isospin density: 6144 pions in a box0 aLattice quantum chromodynamics at large isospin density 6144 pio c7/27/20233 a

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.

1 aAbbott, Ryan1 aDetmold, William1 aRomero-López, Fernando1 aDavoudi, Zohreh1 aIlla, Marc1 aParreño, Assumpta1 aPerry, Robert, J.1 aShanahan, Phiala, E.1 aWagman, Michael, L. uhttps://arxiv.org/abs/2307.1501401182nas a2200145 4500008004100000245011000041210006900151260001500220490000800235520071200243100001300955700001800968700001300986856003700999 2023 eng d00aLinear combination of Hamiltonian simulation for non-unitary dynamics with optimal state preparation cost0 aLinear combination of Hamiltonian simulation for nonunitary dyna c10/13/20230 v1313 a

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.

1 aAn, Dong1 aLiu, Jin-Peng1 aLin, Lin uhttps://arxiv.org/abs/2303.0102901454nas a2200145 4500008004100000245006000041210005900101260001400160520101200174100002101186700002101207700001601228700002701244856003701271 2023 eng d00aLocal Hamiltonians with no low-energy stabilizer states0 aLocal Hamiltonians with no lowenergy stabilizer states c2/28/20233 a

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.

1 aCoble, Nolan, J.1 aCoudron, Matthew1 aNelson, Jon1 aNezhadi, Seyed, Sajjad uhttps://arxiv.org/abs/2302.1475501026nas a2200349 4500008004100000022001400041245006600055210006600121260001400187100002100201700002200222700002400244700001900268700001800287700001800305700001800323700001800341700002300359700002400382700002800406700002000434700001500454700001300469700002800482700002300510700002200533700002100555700002000576700002000596700002300616856003700639 2023 eng d a1476-468700aLogical quantum processor based on reconfigurable atom arrays0 aLogical quantum processor based on reconfigurable atom arrays c12/7/20231 aBluvstein, Dolev1 aEvered, Simon, J.1 aGeim, Alexandra, A.1 aLi, Sophie, H.1 aZhou, Hengyun1 aManovitz, Tom1 aEbadi, Sepehr1 aCain, Madelyn1 aKalinowski, Marcin1 aHangleiter, Dominik1 aAtaides, Pablo, Bonilla1 aMaskara, Nishad1 aCong, Iris1 aGao, Xun1 aRodriguez, Pedro, Sales1 aKarolyshyn, Thomas1 aSemeghini, Giulia1 aGullans, Michael1 aGreiner, Markus1 aVuletic, Vladan1 aLukin, Mikhail, D. uhttps://arxiv.org/abs/2312.0398201350nas a2200181 4500008004100000245004400041210004400085260001300129490000800142520083200150653002700982653003101009100003201040700002101072700002201093700001601115856003701131 2023 eng d00aLower Bounds on Quantum Annealing Times0 aLower Bounds on Quantum Annealing Times c4/5/20230 v1303 a

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.

10aFOS: Physical sciences10aQuantum Physics (quant-ph)1 aGarcía-Pintos, Luis, Pedro1 aBrady, Lucas, T.1 aBringewatt, Jacob1 aLiu, Yi-Kai uhttps://arxiv.org/abs/2210.1568701505nas a2200205 4500008004100000245006200041210006100103260001500164520083500179653003801014653003401052653004301086653002701129653003101156100002301187700001701210700001701227700001801244856003701262 2022 eng d00aLattice-Based Quantum Advantage from Rotated Measurements0 aLatticeBased Quantum Advantage from Rotated Measurements c10/18/20223 a

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.

10aCryptography and Security (cs.CR)10aEmerging Technologies (cs.ET)10aFOS: Computer and information sciences10aFOS: Physical sciences10aQuantum Physics (quant-ph)1 aAlnawakhtha, Yusuf1 aMantri, Atul1 aMiller, Carl1 aWang, Daochen uhttps://arxiv.org/abs/2210.1014301537nas a2200157 4500008004100000245004800041210004800089260001400137520103000151100002101181700002001202700002801222700001701250700002801267856008401295 2022 eng d00aLinear growth of quantum circuit complexity0 aLinear growth of quantum circuit complexity c3/28/20223 a

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.

1 aHaferkamp, Jonas1 aFaist, Philippe1 aKothakonda, Naga, B. T.1 aEisert, Jens1 aHalpern, Nicole, Yunger uhttps://www.quics.umd.edu/publications/linear-growth-quantum-circuit-complexity02430nas a2200205 4500008004100000245007100041210006900112260001500181520180900196100002002005700002002025700002302045700002102068700001602089700002402105700002502129700001702154700001602171856003702187 2021 eng d00aLearnability of the output distributions of local quantum circuits0 aLearnability of the output distributions of local quantum circui c10/11/20213 a

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. 

1 aHinsche, Marcel1 aIoannou, Marios1 aNietner, Alexander1 aHaferkamp, Jonas1 aQuek, Yihui1 aHangleiter, Dominik1 aSeifert, Jean-Pierre1 aEisert, Jens1 aSweke, Ryan uhttps://arxiv.org/abs/2110.0551701652nas a2200133 4500008004100000245005900041210005900100260001500159520124500174100001901419700002201438700002101460856003701481 2021 eng d00aLefschetz Thimble Quantum Monte Carlo for Spin Systems0 aLefschetz Thimble Quantum Monte Carlo for Spin Systems c10/20/20213 a

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'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'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.

1 aMooney, T., C.1 aBringewatt, Jacob1 aBrady, Lucas, T. uhttps://arxiv.org/abs/2110.1069901198nas a2200169 4500008004100000245006000041210005400101260001400155520069100169100001900860700002000879700002900899700002000928700002500948700001800973856003700991 2021 eng d00aThe Lieb-Robinson light cone for power-law interactions0 aLiebRobinson light cone for powerlaw interactions c3/29/20213 a

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.

1 aTran, Minh, C.1 aGuo, Andrew, Y.1 aBaldwin, Christopher, L.1 aEhrenberg, Adam1 aGorshkov, Alexey, V.1 aLucas, Andrew uhttps://arxiv.org/abs/2103.1582801186nas a2200157 4500008004100000022001400041245007000055210006900125260001500194300000900209490000700218520070300225100003200928700002200960856004600982 2021 eng d a1099-430000aLimits to Perception by Quantum Monitoring with Finite Efficiency0 aLimits to Perception by Quantum Monitoring with Finite Efficienc c11/17/2021 a15270 v233 a

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.

1 aGarcía-Pintos, Luis, Pedro1 adel Campo, Adolfo uhttps://www.mdpi.com/1099-4300/23/11/152701631nas a2200169 4500008004100000245009500041210006900136260001400205520107500219100001901294700002401313700002101337700002201358700001901380700002501399856003701424 2021 eng d00aLinear and continuous variable spin-wave processing using a cavity-coupled atomic ensemble0 aLinear and continuous variable spinwave processing using a cavit c9/30/20213 a

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. 

1 aCox, Kevin, C.1 aBienias, Przemyslaw1 aMeyer, David, H.1 aFahey, Donald, P.1 aKunz, Paul, D.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2109.1524601733nas a2200133 4500008004100000245014300041210006900184260001400253520122700267100001601494700003001510700002201540856003701562 2021 eng d00aLocalization crossover and subdiffusive transport in a classical facilitated network model of a disordered, interacting quantum spin chain0 aLocalization crossover and subdiffusive transport in a classical c9/22/20213 a

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'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.

1 aKlocke, Kai1 aWhite, Christopher, David1 aBuchhold, Michael uhttps://arxiv.org/abs/2109.1092601547nas a2200145 4500008004100000245006900041210006900110260001400179520108200193100001801275700002301293700002301316700002501339856003701364 2020 eng d00aLimits on Classical Simulation of Free Fermions with Dissipation0 aLimits on Classical Simulation of Free Fermions with Dissipation c5/21/20203 a

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.

1 aShtanko, Oles1 aDeshpande, Abhinav1 aJulienne, Paul, S.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2005.1084001427nas a2200157 4500008004100000245007300041210006900114260001400183520092900197100001601126700002001142700002401162700002101186700002501207856003701232 2020 eng d00aLocalization and criticality in antiblockaded 2D Rydberg atom arrays0 aLocalization and criticality in antiblockaded 2D Rydberg atom ar c12/7/20203 a

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'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. 

1 aLiu, Fangli1 aYang, Zhi-Cheng1 aBienias, Przemyslaw1 aIadecola, Thomas1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2012.0394602093nas a2200145 4500008004100000245008200041210006900123260001500192490000800207520163800215100002101853700002101874700001501895856003701910 2019 eng d00aLimitations of semidefinite programs for separable states and entangled games0 aLimitations of semidefinite programs for separable states and en c03/04/20190 v3663 a

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.

1 aHarrow, Aram, W.1 aNatarajan, Anand1 aWu, Xiaodi uhttps://arxiv.org/abs/1612.0930601741nas a2200205 4500008004100000245007000041210006900111260001500180490000600195520112800201100001901329700002001348700001301368700002401381700002201405700002301427700002301450700002501473856003701498 2019 eng d00aLocality and digital quantum simulation of power-law interactions0 aLocality and digital quantum simulation of powerlaw interactions c07/10/20190 v93 a

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).

1 aTran, Minh, C.1 aGuo, Andrew, Y.1 aSu, Yuan1 aGarrison, James, R.1 aEldredge, Zachary1 aFoss-Feig, Michael1 aChilds, Andrew, M.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1808.0522501621nas a2200181 4500008004100000245007900041210006900120260001500189490000800204520106600212100001901278700002001297700002001317700001701337700002301354700002501377856003701402 2019 eng d00aLocality and Heating in Periodically Driven, Power-law Interacting Systems0 aLocality and Heating in Periodically Driven Powerlaw Interacting c2019/11/120 v1003 a

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. 

1 aTran, Minh, C.1 aEhrenberg, Adam1 aGuo, Andrew, Y.1 aTitum, Paraj1 aAbanin, Dmitry, A.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1908.0277301967nas a2200133 4500008004100000245005100041210004900092260001400141490000600155520159800161100001801759700001901777856003701796 2019 eng d00aLocality, Quantum Fluctuations, and Scrambling0 aLocality Quantum Fluctuations and Scrambling c9/18/20190 v93 a

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.

1 aXu, Shenglong1 aSwingle, Brian uhttps://arxiv.org/abs/1805.0537601139nas a2200133 4500008004100000245004700041210004600088260001200134300001100146520077800157100001600935700001700951856003700968 2018 eng d00aLocal randomness: Examples and application0 aLocal randomness Examples and application c03/2018 a0323243 a

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).

1 aFu, Honghao1 aMiller, Carl uhttps://arxiv.org/abs/1708.0433801058nas a2200133 4500008004100000245007000041210006800111520062100179100001900800700002400819700001900843700002500862856003700887 2017 eng d00aLieb-Robinson bounds on n-partite connected correlation functions0 aLiebRobinson bounds on npartite connected correlation functions3 a

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.

1 aTran, Minh, C.1 aGarrison, James, R.1 aGong, Zhe-Xuan1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1705.0435504237nas a2200157 4500008004100000245006100041210005900102260001500161490000700176520377200183100001903955700002403974700001903998700002504017856003704042 2017 eng d00aLieb-Robinson bounds on n-partite connected correlations0 aLiebRobinson bounds on npartite connected correlations c2017/11/270 v963 a

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.

1 aTran, Minh, C.1 aGarrison, James, R.1 aGong, Zhe-Xuan1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1705.0435501495nas a2200181 4500008004100000245006100041210006000102260001500162300001100177490000800188520098100196100002001177700001801197700002101215700001901236700002101255856003701276 2017 eng d00aLight-induced fractional quantum Hall phases in graphene0 aLightinduced fractional quantum Hall phases in graphene c2017/12/15 a2474030 v1193 a

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.

1 aGhazaryan, Areg1 aGraß, Tobias1 aGullans, Michael1 aGhaemi, Pouyan1 aHafezi, Mohammad uhttps://arxiv.org/abs/1612.0874801666nas a2200145 4500008004100000245006300041210006300104260001500167300001100182490000700193520123200200100002201432700001901454856004701473 2016 eng d00aLandauer formulation of photon transport in driven systems0 aLandauer formulation of photon transport in driven systems c2016/10/20 a1554370 v943 a

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 `gases', 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's functions, we can extend it to the case of an interacting region between two photonic `leads' 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.

1 aWang, Chiao-Hsuan1 aTaylor, J., M. uhttps://doi.org/10.1103/PhysRevB.94.15543701583nas a2200145 4500008004100000245006900041210006900110260001500179300001100194490000900205520112300214100002301337700002301360856005401383 2016 eng d00aLattice Laughlin states on the torus from conformal field theory0 aLattice Laughlin states on the torus from conformal field theory c2016/01/28 a0131020 v20163 aConformal 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.1 aDeshpande, Abhinav1 aNielsen, Anne, E B uhttp://stacks.iop.org/1742-5468/2016/i=1/a=01310200689nas a2200157 4500008004100000022001400041245006100055210006100116260001500177300001400192490000800206520020400214653002100418100002100439856007100460 2015 eng d a0024-379500aLaplacian matrices and Alexandrov topologies of digraphs0 aLaplacian matrices and Alexandrov topologies of digraphs c2015/09/15 a174 - 1850 v4813 aWe 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.10aLaplacian matrix1 aOstrander, Aaron uhttp://www.sciencedirect.com/science/article/pii/S002437951500284001804nas a2200145 4500008004100000245007600041210006900117260001500186300001100201490000700212520133400219100001801553700001901571856006801590 2015 eng d00aLarge effective three-body interaction in a double-well optical lattice0 aLarge effective threebody interaction in a doublewell optical la c2015/08/03 a0236020 v923 a 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. 1 aPaul, Saurabh1 aTiesinga, Eite uhttp://journals.aps.org/pra/abstract/10.1103/PhysRevA.92.02360200869nas a2200145 4500008004100000245003700041210003600078260001500114300001100129490000700140520049800147100002300645700001800668856003700686 2012 eng d00aLevinson's theorem for graphs II0 aLevinsons theorem for graphs II c2012/11/21 a1022070 v533 a We prove Levinson'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. 1 aChilds, Andrew, M.1 aGosset, David uhttp://arxiv.org/abs/1203.6557v201519nas a2200217 4500008004100000245008300041210006900124260001400193490000800207520087700215100002001092700002101112700002201133700001201155700002101167700002301188700002001211700002101231700001201252856003701264 2012 eng d00aLong-lived dipolar molecules and Feshbach molecules in a 3D optical lattice 0 aLonglived dipolar molecules and Feshbach molecules in a 3D optic c2012/2/230 v1083 a 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. 1 aChotia, Amodsen1 aNeyenhuis, Brian1 aMoses, Steven, A.1 aYan, Bo1 aCovey, Jacob, P.1 aFoss-Feig, Michael1 aRey, Ana, Maria1 aJin, Deborah, S.1 aYe, Jun uhttp://arxiv.org/abs/1110.4420v101053nas a2200157 4500008004100000245008200041210006900123260001500192490000800207520056400215100001900779700002200798700001900820700001900839856003700858 2011 eng d00aLaser cooling and optical detection of excitations in a LC electrical circuit0 aLaser cooling and optical detection of excitations in a LC elect c2011/12/270 v1073 aWe 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. 1 aTaylor, J., M.1 aSørensen, A., S.1 aMarcus, C., M.1 aPolzik, E., S. uhttp://arxiv.org/abs/1108.2035v100769nas a2200145 4500008004100000245003400041210003300075260001500108300001100123490000700134520040600141100002300547700001600570856003700586 2011 eng d00aLevinson's theorem for graphs0 aLevinsons theorem for graphs c2011/06/30 a0821020 v523 a We prove an analog of Levinson'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). 1 aChilds, Andrew, M.1 aStrouse, DJ uhttp://arxiv.org/abs/1103.5077v201416nas a2200145 4500008004100000245014100041210006900182260001400251490000700265520088800272100002801160700002501188700002001213856003701233 2011 eng d00aLight storage in an optically thick atomic ensemble under conditions of electromagnetically induced transparency and four-wave mixing 0 aLight storage in an optically thick atomic ensemble under condit c2011/6/200 v833 a 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. 1 aPhillips, Nathaniel, B.1 aGorshkov, Alexey, V.1 aNovikova, Irina uhttp://arxiv.org/abs/1103.2131v101322nas a2200121 4500008004100000245006100041210006000102260001500162520094400177100002301121700001901144856003701163 2009 eng d00aLimitations on the simulation of non-sparse Hamiltonians0 aLimitations on the simulation of nonsparse Hamiltonians c2009/08/313 a 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. 1 aChilds, Andrew, M.1 aKothari, Robin uhttp://arxiv.org/abs/0908.4398v201174nas a2200133 4500008004100000245005700041210005700098260001500155490000600170520076400176100002500940700002400965856005100989 2009 eng d00aLocality Bounds on Hamiltonians for Stabilizer Codes0 aLocality Bounds on Hamiltonians for Stabilizer Codes c2009/09/220 v93 aIn 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. 1 aBullock, Stephen, S.1 aO'Leary, Dianne, P. uhttp://www.cs.umd.edu/~oleary/reprints/j91.pdf01144nas a2200157 4500008004100000245005200041210004800093260001400141300001400155490000700169520070100176100002400877700002300901700001800924856004400942 2007 eng d00aThe limitations of nice mutually unbiased bases0 alimitations of nice mutually unbiased bases c2006/7/11 a111 - 1230 v253 a 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. 1 aAschbacher, Michael1 aChilds, Andrew, M.1 aWocjan, Pawel uhttp://arxiv.org/abs/quant-ph/0412066v101015nas a2200109 4500008004100000245007300041210006800114260001500182520065500197100001600852856003700868 2007 eng d00aThe Local Consistency Problem for Stoquastic and 1-D Quantum Systems0 aLocal Consistency Problem for Stoquastic and 1D Quantum Systems c2007/12/103 a 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 ``stoquastic'' 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. 1 aLiu, Yi-Kai uhttp://arxiv.org/abs/0712.1388v200857nas a2200145 4500008004100000245003400041210002900075260001500104520048200119100001800601700001800619700001700637700002000654856003700674 2007 eng d00aThe LU-LC conjecture is false0 aLULC conjecture is false c2007/09/093 a 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. 1 aJi, Zhengfeng1 aChen, Jianxin1 aWei, Zhaohui1 aYing, Mingsheng uhttp://arxiv.org/abs/0709.1266v200456nas a2200121 4500008004100000245005600041210005500097100002300152700002300175700001500198700002600213856009500239 2003 eng d00aLanguage-reconfigurable universal phone recognition0 aLanguagereconfigurable universal phone recognition1 aWalker, Brenton, D1 aLackey, Bradley, C1 aMuller, JS1 aSchone, Patrick, John uhttps://www.quics.umd.edu/publications/language-reconfigurable-universal-phone-recognition01085nas a2200145 4500008004100000245005000041210004900091260001400140490000700154520067800161100001900839700001900858700001800877856004400895 2003 eng d00aLong-lived memory for mesoscopic quantum bits0 aLonglived memory for mesoscopic quantum bits c2003/5/200 v903 aWe 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 ``engineering'' 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. 1 aTaylor, J., M.1 aMarcus, C., M.1 aLukin, M., D. uhttp://arxiv.org/abs/cond-mat/0301323v100715nas a2200145 4500008004100000245006300041210006300104260001500167490000700182520026200189100002300451700002600474700002500500856004400525 2003 eng d00aLower bounds on the complexity of simulating quantum gates0 aLower bounds on the complexity of simulating quantum gates c2003/11/180 v683 a 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. 1 aChilds, Andrew, M.1 aHaselgrove, Henry, L.1 aNielsen, Michael, A. uhttp://arxiv.org/abs/quant-ph/0307190v100394nas a2200109 4500008004100000245005600041210005400097260001300151300001400164100001700178856008900195 1998 eng d00aA Lichnerowicz Vanishing Theorem for Finsler Spaces0 aLichnerowicz Vanishing Theorem for Finsler Spaces bSpringer a227–2431 aLackey, Brad uhttps://www.quics.umd.edu/publications/lichnerowicz-vanishing-theorem-finsler-spaces