02055nas a2200241 4500008004100000245005300041210005200094260001300146490000800159520125800167653002701425653004201452653003901494653003101533653004701564653005201611100002201663700002101685700002201706700002001728700002801748856003701776 2023 eng d00aNon-Abelian eigenstate thermalization hypothesis0 aNonAbelian eigenstate thermalization hypothesis c4/6/20230 v1303 a
The eigenstate thermalization hypothesis (ETH) explains why chaotic quantum many-body systems thermalize internally if the Hamiltonian lacks symmetries. If the Hamiltonian conserves one quantity ("charge"), the ETH implies thermalization within a charge sector -- in a microcanonical subspace. But quantum systems can have charges that fail to commute with each other and so share no eigenbasis; microcanonical subspaces may not exist. Furthermore, the Hamiltonian will have degeneracies, so the ETH need not imply thermalization. We adapt the ETH to noncommuting charges by positing a non-Abelian ETH and invoking the approximate microcanonical subspace introduced in quantum thermodynamics. Illustrating with SU(2) symmetry, we apply the non-Abelian ETH in calculating local observables' time-averaged and thermal expectation values. In many cases, we prove, the time average thermalizes. However, we also find cases in which, under a physically reasonable assumption, the time average converges to the thermal average unusually slowly as a function of the global-system size. This work extends the ETH, a cornerstone of many-body physics, to noncommuting charges, recently a subject of intense activity in quantum thermodynamics.
10aFOS: Physical sciences10aHigh Energy Physics - Theory (hep-th)10aQuantum Gases (cond-mat.quant-gas)10aQuantum Physics (quant-ph)10aStatistical Mechanics (cond-mat.stat-mech)10aStrongly Correlated Electrons (cond-mat.str-el)1 aMurthy, Chaitanya1 aBabakhani, Arman1 aIniguez, Fernando1 aSrednicki, Mark1 aHalpern, Nicole, Yunger uhttps://arxiv.org/abs/2206.0531001491nas a2200157 4500008004100000245005900041210005800100260001300158490000800171520102800179100001901207700002201226700002001248700002801268856003701296 2023 eng d00aNon-Abelian symmetry can increase entanglement entropy0 aNonAbelian symmetry can increase entanglement entropy c1/3/20230 v1073 aThe pillars of quantum theory include entanglement and operators' failure to commute. The Page curve quantifies the bipartite entanglement of a many-body system in a random pure state. This entanglement is known to decrease if one constrains extensive observables that commute with each other (Abelian ``charges''). Non-Abelian charges, which fail to commute with each other, are of current interest in quantum thermodynamics. For example, noncommuting charges were shown to reduce entropy-production rates and may enhance finite-size deviations from eigenstate thermalization. Bridging quantum thermodynamics to many-body physics, we quantify the effects of charges' noncommutation -- of a symmetry's non-Abelian nature -- on Page curves. First, we construct two models that are closely analogous but differ in whether their charges commute. We show analytically and numerically that the noncommuting-charge case has more entanglement. Hence charges' noncommutation can promote entanglement.
1 aMajidy, Shayan1 aLasek, Aleksander1 aHuse, David, A.1 aHalpern, Nicole, Yunger uhttps://arxiv.org/abs/2209.1430301843nas a2200157 4500008004100000245011500041210006900156260001500225300001100240490000800251520127800259100003501537700002501572700002801597856006001625 2023 eng d00aNonclassical Advantage in Metrology Established via Quantum Simulations of Hypothetical Closed Timelike Curves0 aNonclassical Advantage in Metrology Established via Quantum Simu c10/12/2023 a1502020 v1313 aWe construct a metrology experiment in which the metrologist can sometimes amend the input state by simulating a closed timelike curve, a worldline that travels backward in time. The existence of closed timelike curves is hypothetical. Nevertheless, they can be simulated probabilistically by quantum-teleportation circuits. We leverage such simulations to pinpoint a counterintuitive nonclassical advantage achievable with entanglement. Our experiment echoes a common information-processing task: A metrologist must prepare probes to input into an unknown quantum interaction. The goal is to infer as much information per probe as possible. If the input is optimal, the information gained per probe can exceed any value achievable classically. The problem is that, only after the interaction does the metrologist learn which input would have been optimal. The metrologist can attempt to change the input by effectively teleporting the optimal input back in time, via entanglement manipulation. The effective time travel sometimes fails but ensures that, summed over trials, the metrologist’s winnings are positive. Our Gedankenexperiment demonstrates that entanglement can generate operational advantages forbidden in classical chronology-respecting theories.
1 aArvidsson-Shukur, David, R. M.1 aMcConnell, Aidan, G.1 aHalpern, Nicole, Yunger uhttps://link.aps.org/doi/10.1103/PhysRevLett.131.15020201518nas a2200169 4500008004100000245007200041210006900113260001300182520098500195100001901180700002501199700002201224700002101246700001601267700002801283856003701311 2023 eng d00aNoncommuting conserved charges in quantum thermodynamics and beyond0 aNoncommuting conserved charges in quantum thermodynamics and bey c9/7/20233 aThermodynamic systems typically conserve quantities ("charges") such as energy and particle number. The charges are often assumed implicitly to commute with each other. Yet quantum phenomena such as uncertainty relations rely on observables' failure to commute. How do noncommuting charges affect thermodynamic phenomena? This question, upon arising at the intersection of quantum information theory and thermodynamics, spread recently across many-body physics. Charges' noncommutation has been found to invalidate derivations of the thermal state's form, decrease entropy production, conflict with the eigenstate thermalization hypothesis, and more. This Perspective surveys key results in, opportunities for, and work adjacent to the quantum thermodynamics of noncommuting charges. Open problems include a conceptual puzzle: Evidence suggests that noncommuting charges may hinder thermalization in some ways while enhancing thermalization in others.
1 aMajidy, Shayan1 aBraasch, William, F.1 aLasek, Aleksander1 aUpadhyaya, Twesh1 aKalev, Amir1 aHalpern, Nicole, Yunger uhttps://arxiv.org/abs/2306.0005401830nas a2200217 4500008004100000245007700041210006900118260001400187520122500201100001101426700001301437700001601450700001501466700001201481700001401493700001501507700002101522700001701543700001501560856003701575 2023 eng d00aNon-equilibrium critical scaling and universality in a quantum simulator0 aNonequilibrium critical scaling and universality in a quantum si c9/19/20233 aUniversality and scaling laws are hallmarks of equilibrium phase transitions and critical phenomena. However, extending these concepts to non-equilibrium systems is an outstanding challenge. Despite recent progress in the study of dynamical phases, the universality classes and scaling laws for non-equilibrium phenomena are far less understood than those in equilibrium. In this work, using a trapped-ion quantum simulator with single-ion resolution, we investigate the non-equilibrium nature of critical fluctuations following a quantum quench to the critical point. We probe the scaling of spin fluctuations after a series of quenches to the critical Hamiltonian of a long-range Ising model. With systems of up to 50 spins, we show that the amplitude and timescale of the post-quench fluctuations scale with system size with distinct universal critical exponents. While a generic quench can lead to thermal critical behaviour, we find that a second quench from one critical state to another (i.e. a double quench) results in critical behaviour that does not have an equilibrium counterpart. Our results demonstrate the ability of quantum simulators to explore universal scaling beyond the equilibrium paradigm.
1 aDe, A.1 aCook, P.1 aCollins, K.1 aMorong, W.1 aPaz, D.1 aTitum, P.1 aPagano, G.1 aGorshkov, A., V.1 aMaghrebi, M.1 aMonroe, C. uhttps://arxiv.org/abs/2309.1085601472nas a2200133 4500008004100000245008700041210006900128260001500197520101000212100002601222700003001248700002301278856003701301 2023 eng d00aNon-invertible symmetry-protected topological order in a group-based cluster state0 aNoninvertible symmetryprotected topological order in a groupbase c12/14/20233 aDespite growing interest in beyond-group symmetries in quantum condensed matter systems, there are relatively few microscopic lattice models explicitly realizing these symmetries, and many phenomena have yet to be studied at the microscopic level. We introduce a one-dimensional stabilizer Hamiltonian composed of group-based Pauli operators whose ground state is a G×Rep(G)-symmetric state: the G cluster state introduced in Brell, New Journal of Physics 17, 023029 (2015) [at this http URL]. We show that this state lies in a symmetry-protected topological (SPT) phase protected by G×Rep(G) symmetry, distinct from the symmetric product state by a duality argument. We identify several signatures of SPT order, namely protected edge modes, string order parameters, and topological response. We discuss how G cluster states may be used as a universal resource for measurement-based quantum computation, explicitly working out the case where G is a semidirect product of abelian groups.
1 aFechisin, Christopher1 aTantivasadakarn, Nathanan1 aAlbert, Victor, V. uhttps://arxiv.org/abs/2312.0927201181nas a2200145 4500008004100000245008000041210006900121260001300190490000800203520073200211100001300943700001800956700002400974856003700998 2022 eng d00aN-body interactions between trapped ion qubits via spin-dependent squeezing0 aNbody interactions between trapped ion qubits via spindependent c8/5/20220 v1293 aWe describe a simple protocol for the single-step generation of N-body entangling interactions between trapped atomic ion qubits. We show that qubit state-dependent squeezing operations and displacement forces on the collective atomic motion can generate full N-body interactions. Similar to the Mølmer-Sørensen two-body Ising interaction at the core of most trapped ion quantum computers and simulators, the proposed operation is relatively insensitive to the state of motion. We show how this N-body gate operation allows the single-step implementation of a family of N-bit gate operations such as the powerful N-Toffoli gate, which flips a single qubit if and only if all other N-1 qubits are in a particular state.
1 aKatz, Or1 aCetina, Marko1 aMonroe, Christopher uhttps://arxiv.org/abs/2202.0423002003nas a2200205 4500008004100000245008600041210006900127260001300196300001100209490000800220520132800228100002501556700002001581700003501601700002101636700002401657700002801681700002801709856006001737 2022 eng d00aNegative Quasiprobabilities Enhance Phase Estimation in Quantum-Optics Experiment0 aNegative Quasiprobabilities Enhance Phase Estimation in QuantumO c6/2/2022 a2205040 v1283 aOperator noncommutation, a hallmark of quantum theory, limits measurement precision, according to uncertainty principles. Wielded correctly, though, noncommutation can boost precision. A recent foundational result relates a metrological advantage with negative quasiprobabilities—quantum extensions of probabilities—engendered by noncommuting operators. We crystallize the relationship in an equation that we prove theoretically and observe experimentally. Our proof-of-principle optical experiment features a filtering technique that we term partially postselected amplification (PPA). Using PPA, we measure a wave plate’s birefringent phase. PPA amplifies, by over two orders of magnitude, the information obtained about the phase per detected photon. In principle, PPA can boost the information obtained from the average filtered photon by an arbitrarily large factor. The filter’s amplification of systematic errors, we find, bounds the theoretically unlimited advantage in practice. PPA can facilitate any phase measurement and mitigates challenges that scale with trial number, such as proportional noise and detector saturation. By quantifying PPA’s metrological advantage with quasiprobabilities, we reveal deep connections between quantum foundations and precision measurement.
1 aLupu-Gladstein, Noah1 aYilmaz, Batuhan1 aArvidsson-Shukur, David, R. M.1 aBrodutch, Aharon1 aPang, Arthur, O. T.1 aSteinberg, Aephraim, M.1 aHalpern, Nicole, Yunger uhttps://link.aps.org/doi/10.1103/PhysRevLett.128.22050401066nas a2200145 4500008004100000245006700041210006700108260001400175520061300189100002100802700001900823700002200842700001900864856003700883 2022 eng d00aNISQ algorithm for the matrix elements of a generic observable0 aNISQ algorithm for the matrix elements of a generic observable c5/20/20223 aThe calculation of off-diagonal matrix elements has various applications in fields such as nuclear physics and quantum chemistry. In this paper, we present a noisy intermediate scale quantum algorithm for estimating the diagonal and off-diagonal matrix elements of a generic observable in the energy eigenbasis of a given Hamiltonian. Several numerical simulations indicate that this approach can find many of the matrix elements even when the trial functions are randomly initialized across a wide range of parameter values without, at the same time, the need to prepare the energy eigenstates.
1 aErbanni, Rebecca1 aBharti, Kishor1 aKwek, Leong-Chuan1 aPoletti, Dario uhttps://arxiv.org/abs/2205.1005801657nas a2200205 4500008004100000245006800041210006700109260001500176300000900191490000700200520101600207100001701223700002001240700001501260700001801275700001601293700001901309700002301328856010001351 2021 eng d00aNoise-induced barren plateaus in variational quantum algorithms0 aNoiseinduced barren plateaus in variational quantum algorithms c11/29/2021 a69610 v123 aVariational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits n if the depth of the ansatz grows linearly with n. These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model.
1 aWang, Samson1 aFontana, Enrico1 aCerezo, M.1 aSharma, Kunal1 aSone, Akira1 aCincio, Lukasz1 aColes, Patrick, J. uhttps://quics.umd.edu/publications/noise-induced-barren-plateaus-variational-quantum-algorithms01105nas a2200157 4500008004100000024001900041245005600060210005300116260001500169520064400184100001700828700001700845700002700862700002100889856003700910 2021 eng d aLA-UR-21-3232200aOn nonlinear transformations in quantum computation0 anonlinear transformations in quantum computation c12/23/20213 aWhile quantum computers are naturally well-suited to implementing linear operations, it is less clear how to implement nonlinear operations on quantum computers. However, nonlinear subroutines may prove key to a range of applications of quantum computing from solving nonlinear equations to data processing and quantum machine learning. Here we develop algorithms for implementing nonlinear transformations of input quantum states. Our algorithms are framed around the concept of a weighted state, a mathematical entity describing the output of an operational procedure involving both quantum circuits and classical post-processing.
1 aHolmes, Zoë1 aCoble, Nolan1 aSornborger, Andrew, T.1 aSubaşı, Yiğit uhttps://arxiv.org/abs/2112.1230702079nas a2200133 4500008004100000245007300041210006900114260001400183520164800197100002001845700002701865700001601892856003701908 2021 eng d00aNonlocal Games, Compression Theorems, and the Arithmetical Hierarchy0 aNonlocal Games Compression Theorems and the Arithmetical Hierarc c10/9/20213 aWe investigate the connection between the complexity of nonlocal games and the arithmetical hierarchy, a classification of languages according to the complexity of arithmetical formulas defining them. It was recently shown by Ji, Natarajan, Vidick, Wright and Yuen that deciding whether the (finite-dimensional) quantum value of a nonlocal game is 1 or at most 12 is complete for the class Σ1 (i.e., RE). A result of Slofstra implies that deciding whether the commuting operator value of a nonlocal game is equal to 1 is complete for the class Π1 (i.e., coRE). We prove that deciding whether the quantum value of a two-player nonlocal game is exactly equal to 1 is complete for Π2; this class is in the second level of the arithmetical hierarchy and corresponds to formulas of the form "∀x∃yϕ(x,y)". This shows that exactly computing the quantum value is strictly harder than approximating it, and also strictly harder than computing the commuting operator value (either exactly or approximately). We explain how results about the complexity of nonlocal games all follow in a unified manner from a technique known as compression. At the core of our Π2-completeness result is a new "gapless" compression theorem that holds for both quantum and commuting operator strategies. Our compression theorem yields as a byproduct an alternative proof of Slofstra's result that the set of quantum correlations is not closed. We also show how a "gap-preserving" compression theorem for commuting operator strategies would imply that approximating the commuting operator value is complete for Π1.
1 aMousavi, Hamoon1 aNezhadi, Seyed, Sajjad1 aYuen, Henry uhttps://arxiv.org/abs/2110.0465101544nas a2200145 4500008004100000245006100041210006000102260001300162520109800175100002101273700001901294700002501313700002301338856003701361 2020 eng d00aNearly optimal time-independent reversal of a spin chain0 aNearly optimal timeindependent reversal of a spin chain c3/5/20203 aWe propose a time-independent Hamiltonian protocol for the reversal of qubit ordering in a chain of N spins. Our protocol has an easily implementable nearest-neighbor, transverse-field Ising model Hamiltonian with time-independent, non-uniform couplings. Under appropriate normalization, we implement this state reversal three times faster than a naive approach using SWAP gates, in time comparable to a protocol of Raussendorf [Phys. Rev. A 72, 052301 (2005)] that requires dynamical control. We also prove lower bounds on state reversal by using results on the entanglement capacity of Hamiltonians and show that we are within a factor 1.502(1+1/N) of the shortest time possible. Our lower bound holds for all nearest-neighbor qubit protocols with arbitrary finite ancilla spaces and local operations and classical communication. Finally, we extend our protocol to an infinite family of nearest-neighbor, time-independent Hamiltonian protocols for state reversal. This includes chains with nearly uniform coupling that may be especially feasible for experimental implementation.
1 aBapat, Aniruddha1 aSchoute, Eddie1 aGorshkov, Alexey, V.1 aChilds, Andrew, M. uhttps://arxiv.org/abs/2003.0284302031nas a2200145 4500008004100000245007100041210006900112260001400181490000800195520154100203100002801744700002701772700001601799856007001815 2020 eng d00aNoncommuting conserved charges in quantum many-body thermalization0 aNoncommuting conserved charges in quantum manybody thermalizatio c4/15/20200 v1013 aIn statistical mechanics, a small system exchanges conserved quantities—heat, particles, electric charge, etc.—with a bath. The small system thermalizes to the canonical ensemble or the grand canonical ensemble, etc., depending on the quantities. The conserved quantities are represented by operators usually assumed to commute with each other. This assumption was removed within quantum-information-theoretic (QI-theoretic) thermodynamics recently. The small system's long-time state was dubbed “the non-Abelian thermal state (NATS).” We propose an experimental protocol for observing a system thermalize to the NATS. We illustrate with a chain of spins, a subset of which forms the system of interest. The conserved quantities manifest as spin components. Heisenberg interactions push the conserved quantities between the system and the effective bath, the rest of the chain. We predict long-time expectation values, extending the NATS theory from abstract idealization to finite systems that thermalize with finite couplings for finite times. Numerical simulations support the analytics: The system thermalizes to near the NATS, rather than to the canonical prediction. Our proposal can be implemented with ultracold atoms, nitrogen-vacancy centers, trapped ions, quantum dots, and perhaps nuclear magnetic resonance. This work introduces noncommuting conserved quantities from QI-theoretic thermodynamics into quantum many-body physics: atomic, molecular, and optical physics and condensed matter.
1 aHalpern, Nicole, Yunger1 aBeverland, Michael, E.1 aKalev, Amir uhttps://journals.aps.org/pre/abstract/10.1103/PhysRevE.101.04211702329nas a2200157 4500008004100000245005700041210005600098260001400154490000700168520186200175100002202037700002502059700002302084700002702107856003702134 2020 eng d00aNon-equilibrium fixed points of coupled Ising models0 aNonequilibrium fixed points of coupled Ising models c2/26/20200 v103 aDriven-dissipative systems can exhibit non-equilibrium phenomena that are absent in their equilibrium counterparts. However, phase transitions present in these systems generically exhibit an effectively classical equilibrium behavior in spite of their quantum non-equilibrium origin. In this paper, we show that multicritical points in driven-dissipative systems can give rise to genuinely non-equilibrium behavior. We investigate a non-equilibrium driven-dissipative model of interacting bosons that exhibits two distinct phase transitions: one from a high- to a low-density phase---reminiscent of a liquid-gas transition---and another to an antiferromagnetic phase. Each phase transition is described by the Ising universality class characterized by an (emergent or microscopic) Z2 symmetry. They, however, coalesce at a multicritical point giving rise to a non-equilibrium model of coupled Ising-like order parameters described by a Z2×Z2 symmetry. Using a dynamical renormalization-group approach, we show that a pair of non-equilibrium fixed points (NEFPs) emerge that govern the long-distance critical behavior of the system. We elucidate various exotic features of these NEFPs. In particular, we show that a generic continuous scale invariance at criticality is reduced to a discrete scale invariance. This further results in complex-valued critical exponents, spiraling phase boundaries, and a complex Liouvillian gap even close to the phase transition. As direct evidence of the non-equilibrium nature of the NEFPs, we show that the fluctuation-dissipation relation is violated at all scales, leading to an effective temperature that becomes "hotter" and "hotter" at longer and longer wavelengths. Finally, we argue that this non-equilibrium behavior can be observed in cavity arrays with cross-Kerr nonlinearities.
1 aYoung, Jeremy, T.1 aGorshkov, Alexey, V.1 aFoss-Feig, Michael1 aMaghrebi, Mohammad, F. uhttps://arxiv.org/abs/1903.0256901744nas a2200133 4500008004100000245008400041210006900125260001400194520131100208100001801519700001701537700001901554856003701573 2020 eng d00aNon-equilibrium steady state phases of the interacting Aubry-Andre-Harper model0 aNonequilibrium steady state phases of the interacting AubryAndre c5/21/20203 aHere we study the phase diagram of the Aubry-Andre-Harper model in the presence of strong interactions as the strength of the quasiperiodic potential is varied. Previous work has established the existence of many-body localized phase at large potential strength; here, we find a rich phase diagram in the delocalized regime characterized by spin transport and unusual correlations. We calculate the non-equilibrium steady states of a boundary-driven strongly interacting Aubry-Andre-Harper model by employing the time-evolving block decimation algorithm on matrix product density operators. From these steady states, we extract spin transport as a function of system size and quasiperiodic potential strength. This data shows spin transport going from superdiffusive to subdiffusive well before the localization transition; comparing to previous results, we also find that the transport transition is distinct from a transition observed in the speed of operator growth in the model. We also investigate the correlation structure of the steady state and find an unusual oscillation pattern for intermediate values of the potential strength. The unusual spin transport and quantum correlation structure suggest multiple dynamical phases between the much-studied thermal and many-body-localized phases.
1 aYoo, Yongchan1 aLee, Junhyun1 aSwingle, Brian uhttps://arxiv.org/abs/2005.1083501889nas a2200169 4500008004100000245006600041210006500107260001300172300001200185490004400197520136000241100001901601700002301620700002001643700001901663856003701682 2020 eng d00aNon-interactive classical verification of quantum computation0 aNoninteractive classical verification of quantum computation c3/9/2020 a153-1800 vLecture Notes in Computer Science 125523 aIn a recent breakthrough, Mahadev constructed an interactive protocol that enables a purely classical party to delegate any quantum computation to an untrusted quantum prover. In this work, we show that this same task can in fact be performed non-interactively and in zero-knowledge.
Our protocols result from a sequence of significant improvements to the original four-message protocol of Mahadev. We begin by making the first message instance-independent and moving it to an offline setup phase. We then establish a parallel repetition theorem for the resulting three-message protocol, with an asymptotically optimal rate. This, in turn, enables an application of the Fiat-Shamir heuristic, eliminating the second message and giving a non-interactive protocol. Finally, we employ classical non-interactive zero-knowledge (NIZK) arguments and classical fully homomorphic encryption (FHE) to give a zero-knowledge variant of this construction. This yields the first purely classical NIZK argument system for QMA, a quantum analogue of NP.
We establish the security of our protocols under standard assumptions in quantum-secure cryptography. Specifically, our protocols are secure in the Quantum Random Oracle Model, under the assumption that Learning with Errors is quantumly hard. The NIZK construction also requires circuit-private FHE.
The current COVID-19 pandemic highlights the utility of contact tracing, when combined with case isolation and social distancing, as an important tool for mitigating the spread of a disease [1]. Contact tracing provides a mechanism of identifying individuals with a high likelihood of previous exposure to a contagious disease, allowing additional precautions to be put in place to prevent continued transmission. Here we consider a cryptographic approach to contact tracing based on secure two-party computation (2PC). We begin by considering the problem of comparing a set of location histories held by two parties to determine whether they have come within some threshold distance while at the same time maintaining the privacy of the location histories. We propose a solution to this problem using pre-shared keys, adapted from an equality testing protocol due to Ishai et al [2]. We discuss how this protocol can be used to maintain privacy within practical contact tracing scenarios, including both app-based approaches and approaches which leverage location history held by telecoms and internet service providers. We examine the efficiency of this approach and show that existing infrastructure is sufficient to support anonymised contact tracing at a national level.
1 aFitzsimons, Jack, K.1 aMantri, Atul1 aPisarczyk, Robert1 aRainforth, Tom1 aZhao, Zhikuan uhttps://arxiv.org/abs/2004.0511602137nas a2200133 4500008004100000245009800041210006900139260001400208520167400222100001801896700002501914700002701939856003701966 2019 eng d00aOn the nature of the non-equilibrium phase transition in the non-Markovian driven Dicke model0 anature of the nonequilibrium phase transition in the nonMarkovia c2019/10/93 aThe Dicke model famously exhibits a phase transition to a superradiant phase with a macroscopic population of photons and is realized in multiple settings in open quantum systems. In this work, we study a variant of the Dicke model where the cavity mode is lossy due to the coupling to a Markovian environment while the atomic mode is coupled to a colored bath. We analytically investigate this model by inspecting its low-frequency behavior via the Schwinger-Keldysh field theory and carefully examine the nature of the corresponding superradiant phase transition. Integrating out the fast modes, we can identify a simple effective theory allowing us to derive analytical expressions for various critical exponents, including those, such as the dynamical critical exponent, that have not been previously considered. We find excellent agreement with previous numerical results when the non-Markovian bath is at zero temperature; however, contrary to these studies, our low-frequency approach reveals that the same exponents govern the critical behavior when the colored bath is at finite temperature unless the chemical potential is zero. Furthermore, we show that the superradiant phase transition is classical in nature, while it is genuinely non-equilibrium. We derive a fractional Langevin equation and conjecture the associated fractional Fokker-Planck equation that capture the system's long-time memory as well as its non-equilibrium behavior. Finally, we consider finite-size effects at the phase transition and identify the finite-size scaling exponents, unlocking a rich behavior in both statics and dynamics of the photonic and atomic observables.
1 aLundgren, Rex1 aGorshkov, Alexey, V.1 aMaghrebi, Mohammad, F. uhttps://arxiv.org/abs/1910.0431901490nas a2200133 4500008004100000245005800041210005800099260001500157490000800172520110300180100002301283700001301306856003701319 2019 eng d00aNearly optimal lattice simulation by product formulas0 aNearly optimal lattice simulation by product formulas c12/17/20190 v1233 aProduct formulas provide a straightforward yet surprisingly efficient approach to quantum simulation. We show that this algorithm can simulate an n-qubit Hamiltonian with nearest-neighbor interactions evolving for time t using only (nt)1+o(1) gates. While it is reasonable to expect this complexity---in particular, this was claimed without rigorous justification by Jordan, Lee, and Preskill---we are not aware of a straightforward proof. Our approach is based on an analysis of the local error structure of product formulas, as introduced by Descombes and Thalhammer and significantly simplified here. We prove error bounds for canonical product formulas, which include well-known constructions such as the Lie-Trotter-Suzuki formulas. We also develop a local error representation for time-dependent Hamiltonian simulation, and we discuss generalizations to periodic boundary conditions, constant-range interactions, and higher dimensions. Combined with a previous lower bound, our result implies that product formulas can simulate lattice Hamiltonians with nearly optimal gate complexity.
1 aChilds, Andrew, M.1 aSu, Yuan uhttps://arxiv.org/abs/1901.0056401194nas a2200121 4500008004100000245004200041210004200083260001400125520083200139100001400971700001800985856006901003 2019 eng d00aNew stepsizes for the gradient method0 aNew stepsizes for the gradient method c1/28/20193 aGradient methods are famous for their simplicity and low complexity, which attract more and more attention for large scale optimization problems. A good stepsize plays an important role to construct an efficient gradient method. This paper proposes a new framework to generate stepsizes for gradient methods applied to convex quadratic function minimization problems. By adopting different criterions, we propose four new gradient methods. For 2-dimensional unconstrained problems with convex quadratic objective functions, we prove that the new methods either terminate in finite iterations or converge R-superlinearly; for n-dimensional problems, we prove that all the new methods converge R-linearly. Numerical experiments show that the new methods enjoy lower complexity and outperform the existing gradient methods.
1 aSun, Cong1 aLiu, Jin-Peng uhttps://quics.umd.edu/publications/new-stepsizes-gradient-method02399nas a2200145 4500008004100000245007900041210006900120300001400189520193400203100001902137700002002156700001702176700002302193856003702216 2019 eng d00aOn non-adaptive quantum chosen-ciphertext attacks and Learning with Errors0 anonadaptive quantum chosenciphertext attacks and Learning with E a1:1-1:23 3 aLarge-scale quantum computing is a significant threat to classical public-key cryptography. In strong "quantum access" security models, numerous symmetric-key cryptosystems are also vulnerable. We consider classical encryption in a model which grants the adversary quantum oracle access to encryption and decryption, but where the latter is restricted to non-adaptive (i.e., pre-challenge) queries only. We define this model formally using appropriate notions of ciphertext indistinguishability and semantic security (which are equivalent by standard arguments) and call it QCCA1 in analogy to the classical CCA1 security model. Using a bound on quantum random-access codes, we show that the standard PRF- and PRP-based encryption schemes are QCCA1-secure when instantiated with quantum-secure primitives. We then revisit standard IND-CPA-secure Learning with Errors (LWE) encryption and show that leaking just one quantum decryption query (and no other queries or leakage of any kind) allows the adversary to recover the full secret key with constant success probability. In the classical setting, by contrast, recovering the key uses a linear number of decryption queries, and this is optimal. The algorithm at the core of our attack is a (large-modulus version of) the well-known Bernstein-Vazirani algorithm. We emphasize that our results should *not* be interpreted as a weakness of these cryptosystems in their stated security setting (i.e., post-quantum chosen-plaintext secrecy). Rather, our results mean that, if these cryptosystems are exposed to chosen-ciphertext attacks (e.g., as a result of deployment in an inappropriate real-world setting) then quantum attacks are even more devastating than classical ones.
1 aAlagic, Gorjan1 aJeffery, Stacey1 aOzols, Maris1 aPoremba, Alexander uhttps://arxiv.org/abs/1808.0965501475nas a2200181 4500008004100000245010000041210006900141260001400210520088000224100001901104700002201123700002401145700002201169700002201191700001801213700002501231856003701256 2019 eng d00aNondestructive cooling of an atomic quantum register via state-insensitive Rydberg interactions0 aNondestructive cooling of an atomic quantum register via statein c7/28/20193 aWe propose a protocol for sympathetically cooling neutral atoms without destroying the quantum information stored in their internal states. This is achieved by designing state-insensitive Rydberg interactions between the data-carrying atoms and cold auxiliary atoms. The resulting interactions give rise to an effective phonon coupling, which leads to the transfer of heat from the data atoms to the auxiliary atoms, where the latter can be cooled by conventional methods. This can be used to extend the lifetime of quantum storage based on neutral atoms and can have applications for long quantum computations. The protocol can also be modified to realize state-insensitive interactions between the data and the auxiliary atoms but tunable and non-trivial interactions among the data atoms, allowing one to simultaneously cool and simulate a quantum spin-model.
1 aBelyansky, Ron1 aYoung, Jeremy, T.1 aBienias, Przemyslaw1 aEldredge, Zachary1 aKaufman, Adam, M.1 aZoller, Peter1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1907.1115601571nas a2200133 4500008004100000245007800041210006900119260001400188520113700202100001701339700002501356700001901381856003701400 2019 eng d00aNumber-Theoretic Characterizations of Some Restricted Clifford+T Circuits0 aNumberTheoretic Characterizations of Some Restricted CliffordT C c8/16/20193 aKliuchnikov, Maslov, and Mosca proved in 2012 that a 2×2 unitary matrix V can be exactly represented by a single-qubit Clifford+T circuit if and only if the entries of V belong to the ring Z[1/2–√,i]. Later that year, Giles and Selinger showed that the same restriction applies to matrices that can be exactly represented by a multi-qubit Clifford+T circuit. These number-theoretic characterizations shed new light upon the structure of Clifford+T circuits and led to remarkable developments in the field of quantum compiling. In the present paper, we provide number-theoretic characterizations for certain restricted Clifford+T circuits by considering unitary matrices over subrings of Z[1/2–√,i]. We focus on the subrings Z[1/2], Z[1/2–√], Z[1/-2−−√], and Z[1/2,i], and we prove that unitary matrices with entries in these rings correspond to circuits over well-known universal gate sets. In each case, the desired gate set is obtained by extending the set of classical reversible gates {X,CX,CCX} with an analogue of the Hadamard gate and an optional phase gate.
1 aAmy, Matthew1 aGlaudell, Andrew, N.1 aRoss, Neil, J. uhttps://arxiv.org/abs/1908.0607601248nas a2200157 4500008004100000245003400041210002700075260000900102490000800111520082700119100001900946700002300965700002300988700002101011856005801032 2018 eng d00aOn the need for soft dressing0 aneed for soft dressing c20180 v1213 aIn order to deal with IR divergences arising in QED or perturbative quantum gravity scattering processes, one can either calculate inclusive quantities or use dressed asymptotic states. We consider incoming superpositions of momentum eigenstates and show that in calculations of cross-sections these two approaches yield different answers: in the inclusive formalism no interference occurs for incoming finite superpositions and wavepackets do not scatter at all, while the dressed formalism yields the expected interference terms. This suggests that rather than Fock space states, one should use Faddeev-Kulish-type dressed states to correctly describe physical processes involving incoming superpositions. We interpret this in terms of selection rules due to large U(1) gauge symmetries and BMS supertranslations.
1 aCarney, Daniel1 aChaurette, Laurent1 aNeuenfeld, Dominik1 aSemenoff, Gordon uhttps://quics.umd.edu/publications/need-soft-dressing02361nas a2200109 4500008004100000245014200041210006900183520192900252100001702181700001602198856003702214 2018 eng d00aThe Non-Disjoint Ontic States of the Grassmann Ontological Model, Transformation Contextuality, and the Single Qubit Stabilizer Subtheory0 aNonDisjoint Ontic States of the Grassmann Ontological Model Tran3 aWe show that it is possible to construct a preparation non-contextual ontological model that does not exhibit "transformation contextuality" for single qubits in the stabilizer subtheory. In particular, we consider the "blowtorch" map and show that it does not exhibit transformation contextuality under the Grassmann Wigner-Weyl-Moyal (WWM) qubit formalism. Furthermore, the transformation in this formalism can be fully expressed at order ℏ0 and so does not qualify as a candidate quantum phenomenon. In particular, we find that the Grassmann WWM formalism at order ℏ0 corresponds to an ontological model governed by an additional set of constraints arising from the relations defining the Grassmann algebra. Due to this additional set of constraints, the allowed probability distributions in this model do not form a single convex set when expressed in terms of disjoint ontic states and so cannot be mapped to models whose states form a single convex set over disjoint ontic states. However, expressing the Grassmann WWM ontological model in terms of non-disjoint ontic states corresponding to the monomials of the Grassmann algebra results in a single convex set. We further show that a recent result by Lillystone et al. that proves a broad class of preparation and measurement non-contextual ontological models must exhibit transformation contextuality lacks the generality to include the ontological model considered here; Lillystone et al.'s result is appropriately limited to ontological models whose states produce a single convex set when expressed in terms of disjoint ontic states. Therefore, we prove that for the qubit stabilizer subtheory to be captured by a preparation, transformation and measurement non-contextual ontological theory, it must be expressed in terms of non-disjoint ontic states, unlike the case for the odd-dimensional single-qudit stabilizer subtheory.
1 aKocia, Lucas1 aLove, Peter uhttps://arxiv.org/abs/1805.0951401239nas a2200121 4500008004100000245006800041210006600109260001500175520085000190100001701040700002301057856003701080 2017 eng d00aNonlocal games, synchronous correlations, and Bell inequalities0 aNonlocal games synchronous correlations and Bell inequalities c2017/09/213 aA nonlocal game with a synchronous correlation is a natural generalization of a function between two finite sets, and has recently appeared in the context of quantum graph homomorphisms. In this work we examine analogues of Bell's inequalities for synchronous correlations. We show that, unlike general correlations and the CHSH inequality, there can be no quantum Bell violation among synchronous correlations with two measurement settings. However we exhibit explicit analogues of Bell's inequalities for synchronous correlations with three measurement settings and two outputs, provide an analogue of Tsirl'son's bound in this setting, and give explicit quantum correlations that saturate this bound.
1 aLackey, Brad1 aRodrigues, Nishant uhttps://arxiv.org/abs/1707.0620001599nas a2200145 4500008004100000245006500041210006400106260001500170300001100185490000700196520116200203100002701365700002501392856003601417 2016 eng d00aNonequilibrium many-body steady states via Keldysh formalism0 aNonequilibrium manybody steady states via Keldysh formalism c2016/01/27 a0143070 v933 a Many-body systems with both coherent dynamics and dissipation constitute a rich class of models which are nevertheless much less explored than their dissipationless counterparts. The advent of numerous experimental platforms that simulate such dynamics poses an immediate challenge to systematically understand and classify these models. In particular, nontrivial many-body states emerge as steady states under non-equilibrium dynamics. While these states and their phase transitions have been studied extensively with mean field theory, the validity of the mean field approximation has not been systematically investigated. In this paper, we employ a field-theoretic approach based on the Keldysh formalism to study nonequilibrium phases and phase transitions in a variety of models. In all cases, a complete description via the Keldysh formalism indicates a partial or complete failure of the mean field analysis. Furthermore, we find that an effective temperature emerges as a result of dissipation, and the universal behavior including the dynamics near the steady state is generically described by a thermodynamic universality class. 1 aMaghrebi, Mohammad, F.1 aGorshkov, Alexey, V. uhttp://arxiv.org/abs/1507.0193901522nas a2200169 4500008004100000245007200041210006900113260001500182300001100197490000800208520100900216100002301225700001901248700002301267700002501290856003701315 2015 eng d00aNearly-linear light cones in long-range interacting quantum systems0 aNearlylinear light cones in longrange interacting quantum system c2015/04/13 a1572010 v1143 a In non-relativistic quantum theories with short-range Hamiltonians, a velocity $v$ can be chosen such that the influence of any local perturbation is approximately confined to within a distance $r$ until a time $t \sim r/v$, thereby defining a linear light cone and giving rise to an emergent notion of locality. In systems with power-law ($1/r^{\alpha}$) interactions, when $\alpha$ exceeds the dimension $D$, an analogous bound confines influences to within a distance $r$ only until a time $t\sim(\alpha/v)\log r$, suggesting that the velocity, as calculated from the slope of the light cone, may grow exponentially in time. We rule out this possibility; light cones of power-law interacting systems are algebraic for $\alpha>2D$, becoming linear as $\alpha\rightarrow\infty$. Our results impose strong new constraints on the growth of correlations and the production of entangled states in a variety of rapidly emerging, long-range interacting atomic, molecular, and optical systems. 1 aFoss-Feig, Michael1 aGong, Zhe-Xuan1 aClark, Charles, W.1 aGorshkov, Alexey, V. uhttp://arxiv.org/abs/1410.3466v101828nas a2200145 4500008004100000245015000041210006900191260001400260490000700274520129600281100002701577700002201604700001901626856003701645 2014 eng d00aNonequilibrium quantum fluctuations of a dispersive medium: Spontaneous emission, photon statistics, entropy generation, and stochastic motion 0 aNonequilibrium quantum fluctuations of a dispersive medium Spont c2014/7/160 v903 a We study the implications of quantum fluctuations of a dispersive medium, under steady rotation, either in or out of thermal equilibrium with its environment. A rotating object exhibits a quantum instability by dissipating its mechanical motion via spontaneous emission of photons, as well as internal heat generation. Universal relations are derived for the radiated energy and angular momentum as trace formulas involving the object's scattering matrix. We also compute the quantum noise by deriving the full statistics of the radiated photons out of thermal and/or dynamic equilibrium. The (entanglement) entropy generation is quantified, and the total entropy is shown to be always increasing. Furthermore, we derive a Fokker-Planck equation governing the stochastic angular motion resulting from the fluctuating back-reaction frictional torque. As a result, we find a quantum limit on the uncertainty of the object's angular velocity in steady rotation. Finally, we show in some detail that a rotating object drags nearby objects, making them spin parallel to its axis of rotation. A scalar toy model is introduced in the first part to simplify the technicalities and ease the conceptual complexities; a detailed discussion of quantum electrodynamics is presented in the second part. 1 aMaghrebi, Mohammad, F.1 aJaffe, Robert, L.1 aKardar, Mehran uhttp://arxiv.org/abs/1401.0701v102028nas a2200229 4500008004100000245008700041210006900128260001300197300001400210490000800224520134100232100002101573700001901594700001501613700001901628700001701647700002301664700002501687700002501712700002401737856003701761 2014 eng d00aNon-local propagation of correlations in long-range interacting quantum systems 0 aNonlocal propagation of correlations in longrange interacting qu c2014/7/9 a198 - 2010 v5113 a The maximum speed with which information can propagate in a quantum many-body system directly affects how quickly disparate parts of the system can become correlated and how difficult the system will be to describe numerically. For systems with only short-range interactions, Lieb and Robinson derived a constant-velocity bound that limits correlations to within a linear effective light cone. However, little is known about the propagation speed in systems with long-range interactions, since the best long-range bound is too loose to give the correct light-cone shape for any known spin model and since analytic solutions rarely exist. In this work, we experimentally determine the spatial and time-dependent correlations of a far-from-equilibrium quantum many-body system evolving under a long-range Ising- or XY-model Hamiltonian. For several different interaction ranges, we extract the shape of the light cone and measure the velocity with which correlations propagate through the system. In many cases we find increasing propagation velocities, which violate the Lieb-Robinson prediction, and in one instance cannot be explained by any existing theory. Our results demonstrate that even modestly-sized quantum simulators are well-poised for studying complicated many-body systems that are intractable to classical computation. 1 aRicherme, Philip1 aGong, Zhe-Xuan1 aLee, Aaron1 aSenko, Crystal1 aSmith, Jacob1 aFoss-Feig, Michael1 aMichalakis, Spyridon1 aGorshkov, Alexey, V.1 aMonroe, Christopher uhttp://arxiv.org/abs/1401.5088v102350nas a2200133 4500008004100000245009000041210006900131260001500200520189100215100002302106700002402129700002602153856003702179 2014 eng d00aNormalizer circuits and a Gottesman-Knill theorem for infinite-dimensional systems 0 aNormalizer circuits and a GottesmanKnill theorem for infinitedim c2014/09/103 a $\textit{Normalizer circuits}$ [1,2] are generalized Clifford circuits that act on arbitrary finite-dimensional systems $\mathcal{H}_{d_1}\otimes ... \otimes \mathcal{H}_{d_n}$ with a standard basis labeled by the elements of a finite Abelian group $G=\mathbb{Z}_{d_1}\times... \times \mathbb{Z}_{d_n}$. Normalizer gates implement operations associated with the group $G$ and can be of three types: quantum Fourier transforms, group automorphism gates and quadratic phase gates. In this work, we extend the normalizer formalism [1,2] to infinite dimensions, by allowing normalizer gates to act on systems of the form $\mathcal{H}_\mathbb{Z}^{\otimes a}$: each factor $\mathcal{H}_\mathbb{Z}$ has a standard basis labeled by $\textit{integers}$ $\mathbb{Z}$, and a Fourier basis labeled by $\textit{angles}$, elements of the circle group $\mathbb{T}$. Normalizer circuits become hybrid quantum circuits acting both on continuous- and discrete-variable systems. We show that infinite-dimensional normalizer circuits can be efficiently simulated classically with a generalized $\textit{stabilizer formalism}$ for Hilbert spaces associated with groups of the form $\mathbb{Z}^a\times \mathbb{T}^b \times \mathbb{Z}_{d_1}\times...\times \mathbb{Z}_{d_n}$. We develop new techniques to track stabilizer-groups based on normal forms for group automorphisms and quadratic functions. We use our normal forms to reduce the problem of simulating normalizer circuits to that of finding general solutions of systems of mixed real-integer linear equations [3] and exploit this fact to devise a robust simulation algorithm: the latter remains efficient even in pathological cases where stabilizer groups become infinite, uncountable and non-compact. The techniques developed in this paper might find applications in the study of fault-tolerant quantum computation with superconducting qubits [4,5]. 1 aBermejo-Vega, Juan1 aLin, Cedric, Yen-Yu1 aVan den Nest, Maarten uhttp://arxiv.org/abs/1409.3208v201256nas a2200121 4500008004100000245004400041210004200085260001500127520092000142100001601062700001901078856003701097 2013 eng d00aA noise inequality for classical forces0 anoise inequality for classical forces c2013/11/183 aLorentz invariance requires local interactions, with force laws such as the Coulomb interaction arising via virtual exchange of force carriers such as photons. Many have considered the possibility that, at long distances or large mass scales, this process changes in some way to lead to classical behavior. Here we hypothesize that classical behavior could be due to an inability of some force carriers to convey entanglement, a characteristic measure of nonlocal, quantum behavior. We then prove that there exists a local test that allows one to verify entanglement generation, falsifying our hypothesis. Crucially, we show that noise measurements can directly verify entanglement generation. This provides a step forward for a wide variety of experimental systems where traditional entanglement tests are challenging, including entanglement generation by gravity alone between macroscopic torsional oscillators. 1 aKafri, Dvir1 aTaylor, J., M. uhttp://arxiv.org/abs/1311.4558v101346nas a2200157 4500008004100000245008400041210006900125260001300194490000700207520084400214100002301058700002601081700002401107700002001131856003701151 2013 eng d00aNon-equilibrium dynamics of Ising models with decoherence: an exact solution 0 aNonequilibrium dynamics of Ising models with decoherence an exac c2013/4/30 v873 a The interplay between interactions and decoherence in many-body systems is of fundamental importance in quantum physics: Decoherence can degrade correlations, but can also give rise to a variety of rich dynamical and steady-state behaviors. We obtain an exact analytic solution for the non-equilibrium dynamics of Ising models with arbitrary interactions and subject to the most general form of local Markovian decoherence. Our solution shows that decoherence affects the relaxation of observables more than predicted by single-particle considerations. It also reveals a dynamical phase transition, specifically a Hopf bifurcation, which is absent at the single-particle level. These calculations are applicable to ongoing quantum information and emulation efforts using a variety of atomic, molecular, optical, and solid-state systems. 1 aFoss-Feig, Michael1 aHazzard, Kaden, R. A.1 aBollinger, John, J.1 aRey, Ana, Maria uhttp://arxiv.org/abs/1209.5795v201154nas a2200205 4500008004100000245004700041210004700088260001400135490000800149520061400157100002100771700001500792700001800807700001400825700002100839700001800860700001500878700001800893856003700911 2012 eng d00aNanoplasmonic Lattices for Ultracold atoms0 aNanoplasmonic Lattices for Ultracold atoms c2012/12/60 v1093 a We propose to use sub-wavelength confinement of light associated with the near field of plasmonic systems to create nanoscale optical lattices for ultracold atoms. Our approach combines the unique coherence properties of isolated atoms with the sub-wavelength manipulation and strong light-matter interaction associated with nano-plasmonic systems. It allows one to considerably increase the energy scales in the realization of Hubbard models and to engineer effective long-range interactions in coherent and dissipative many-body dynamics. Realistic imperfections and potential applications are discussed. 1 aGullans, Michael1 aTiecke, T.1 aChang, D., E.1 aFeist, J.1 aThompson, J., D.1 aCirac, J., I.1 aZoller, P.1 aLukin, M., D. uhttp://arxiv.org/abs/1208.6293v301030nas a2200121 4500008004100000245008400041210006900125260001500194520062400209100001800833700002000851856003700871 2012 eng d00aNon-Additivity of the Entanglement of Purification (Beyond Reasonable Doubt) 0 aNonAdditivity of the Entanglement of Purification Beyond Reasona c2012/06/063 a We demonstrate the convexity of the difference between the regularized entanglement of purification and the entropy, as a function of the state. This is proved by means of a new asymptotic protocol to prepare a state from pre-shared entanglement and by local operations only. We go on to employ this convexity property in an investigation of the additivity of the (single-copy) entanglement of purification: using numerical results for two-qubit Werner states we find strong evidence that the entanglement of purification is different from its regularization, hence that entanglement of purification is not additive. 1 aChen, Jianxin1 aWinter, Andreas uhttp://arxiv.org/abs/1206.1307v100871nas a2200157 4500008004100000245006300041210006200104260001500166490000700181520037400188100001900562700002200581700002100603700001900624856007000643 2012 eng d00aNon-Recursively Constructible Recursive Families of Graphs0 aNonRecursively Constructible Recursive Families of Graphs c2012/04/160 v193 aIn a publication by Noy and Ribó, it was shown that recursively constructible families of graphs are recursive. The authors also conjecture that the converse holds; that is, recursive families are also recursively constructible. In this paper, we provide two specific counterexamples to this conjecture, which we then extend to an infinite family of counterexamples.1 aBouey, Colleen1 aGraves, Christina1 aOstrander, Aaron1 aPalma, Gregory uhttp://www.combinatorics.org/ojs/index.php/eljc/article/view/221102114nas a2200169 4500008004100000245009200041210006900133260001300202490000700215520160400222100001801826700001401844700001701858700001801875700001401893856003701907 2011 eng d00aNo-go Theorem for One-way Quantum Computing on Naturally Occurring Two-level Systems 0 aNogo Theorem for Oneway Quantum Computing on Naturally Occurring c2011/5/90 v833 a One-way quantum computing achieves the full power of quantum computation by performing single particle measurements on some many-body entangled state, known as the resource state. As single particle measurements are relatively easy to implement, the preparation of the resource state becomes a crucial task. An appealing approach is simply to cool a strongly correlated quantum many-body system to its ground state. In addition to requiring the ground state of the system to be universal for one-way quantum computing, we also want the Hamiltonian to have non-degenerate ground state protected by a fixed energy gap, to involve only two-body interactions, and to be frustration-free so that measurements in the course of the computation leave the remaining particles in the ground space. Recently, significant efforts have been made to the search of resource states that appear naturally as ground states in spin lattice systems. The approach is proved to be successful in spin-5/2 and spin-3/2 systems. Yet, it remains an open question whether there could be such a natural resource state in a spin-1/2, i.e., qubit system. Here, we give a negative answer to this question by proving that it is impossible for a genuinely entangled qubit states to be a non-degenerate ground state of any two-body frustration-free Hamiltonian. What is more, we prove that every spin-1/2 frustration-free Hamiltonian with two-body interaction always has a ground state that is a product of single- or two-qubit states, a stronger result that is interesting independent of the context of one-way quantum computing. 1 aChen, Jianxin1 aChen, Xie1 aDuan, Runyao1 aJi, Zhengfeng1 aZeng, Bei uhttp://arxiv.org/abs/1004.3787v101378nas a2200157 4500008004100000245007600041210006900117260001300186490000700199520090300206100001301109700001501122700002301137700002301160856003701183 2010 eng d00aNoise correlations of one-dimensional Bose mixtures in optical lattices0 aNoise correlations of onedimensional Bose mixtures in optical la c2010/6/20 v813 a We study the noise correlations of one-dimensional binary Bose mixtures, as a probe of their quantum phases. In previous work, we found a rich structure of many-body phases in such mixtures, such as paired and counterflow superfluidity. Here we investigate the signature of these phases in the noise correlations of the atomic cloud after time-of-flight expansion, using both Luttinger liquid theory and the time-evolving block decimation (TEBD) method. We find that paired and counterflow superfluidity exhibit distinctive features in the noise spectra. We treat both extended and inhomogeneous systems, and our numerical work shows that the essential physics of the extended systems is present in the trapped-atom systems of current experimental interest. For paired and counterflow superfluid phases, we suggest methods for extracting Luttinger parameters from noise correlation spectroscopy. 1 aHu, Anzi1 aMathey, L.1 aWilliams, Carl, J.1 aClark, Charles, W. uhttp://arxiv.org/abs/1002.4918v201306nas a2200181 4500008004100000245007600041210006900117260001300186490000800199520075700207100001700964700001900981700002501000700002401025700001901049700001901068856003701087 2009 eng d00aNumber Fluctuations and Energy Dissipation in Sodium Spinor Condensates0 aNumber Fluctuations and Energy Dissipation in Sodium Spinor Cond c2009/6/50 v1023 a We characterize fluctuations in atom number and spin populations in F=1 sodium spinor condensates. We find that the fluctuations enable a quantitative measure of energy dissipation in the condensate. The time evolution of the population fluctuations shows a maximum. We interpret this as evidence of a dissipation-driven separatrix crossing in phase space. For a given initial state, the critical time to the separatrix crossing is found to depend exponentially on the magnetic field and linearly on condensate density. This crossing is confirmed by tracking the energy of the spinor condensate as well as by Faraday rotation spectroscopy. We also introduce a phenomenological model that describes the observed dissipation with a single coefficient. 1 aLiu, Yingmei1 aGomez, Eduardo1 aMaxwell, Stephen, E.1 aTurner, Lincoln, D.1 aTiesinga, Eite1 aLett, Paul, D. uhttp://arxiv.org/abs/0906.2110v100845nas a2200145 4500008004100000245003900041210003700080260001500117490000700132520042900139100001600568700002500584700001900609856007100628 2007 eng d00aN-representability is QMA-complete0 aNrepresentability is QMAcomplete c2007/03/160 v983 aWe study the computational complexity of the N-representability problem in quantum chemistry. We show that this problem is quantum Merlin-Arthur complete, which is the quantum generalization of nondeterministic polynomial time complete. Our proof uses a simple mapping from spin systems to fermionic systems, as well as a convex optimization technique that reduces the problem of finding ground states to N representability.1 aLiu, Yi-Kai1 aChristandl, Matthias1 aVerstraete, F. uhttp://journals.aps.org/prl/abstract/10.1103/PhysRevLett.98.110503