02008nas a2200181 4500008004100000245005800041210005800099260001400157300000900171490000600180520148900186100002201675700002001697700002401717700002301741700002501764856003701789 2023 eng d00aPage curves and typical entanglement in linear optics0 aPage curves and typical entanglement in linear optics c5/18/2023 a10170 v73 a
Bosonic Gaussian states are a special class of quantum states in an infinite dimensional Hilbert space that are relevant to universal continuous-variable quantum computation as well as to near-term quantum sampling tasks such as Gaussian Boson Sampling. In this work, we study entanglement within a set of squeezed modes that have been evolved by a random linear optical unitary. We first derive formulas that are asymptotically exact in the number of modes for the Rényi-2 Page curve (the average Rényi-2 entropy of a subsystem of a pure bosonic Gaussian state) and the corresponding Page correction (the average information of the subsystem) in certain squeezing regimes. We then prove various results on the typicality of entanglement as measured by the Rényi-2 entropy by studying its variance. Using the aforementioned results for the Rényi-2 entropy, we upper and lower bound the von Neumann entropy Page curve and prove certain regimes of entanglement typicality as measured by the von Neumann entropy. Our main proofs make use of a symmetry property obeyed by the average and the variance of the entropy that dramatically simplifies the averaging over unitaries. In this light, we propose future research directions where this symmetry might also be exploited. We conclude by discussing potential applications of our results and their generalizations to Gaussian Boson Sampling and to illuminating the relationship between entanglement and computational complexity.
1 aIosue, Joseph, T.1 aEhrenberg, Adam1 aHangleiter, Dominik1 aDeshpande, Abhinav1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2209.0683801762nas a2200133 4500008004100000245007100041210006900112260001400181520134900195100001601544700001801560700001301578856003701591 2023 eng d00aParallel self-testing of EPR pairs under computational assumptions0 aParallel selftesting of EPR pairs under computational assumption c3/29/20233 aSelf-testing is a fundamental feature of quantum mechanics that allows a classical verifier to force untrusted quantum devices to prepare certain states and perform certain measurements on them. The standard approach assumes at least two spatially separated devices. Recently, Metger and Vidick [Quantum, 2021] showed that a single EPR pair of a single quantum device can be self-tested under computational assumptions. In this work, we generalize their results to give the first parallel self-test of N EPR pairs and measurements on them in the single-device setting under the same computational assumptions. We show that our protocol can be passed with probability negligibly close to 1 by an honest quantum device using poly(N) resources. Moreover, we show that any quantum device that fails our protocol with probability at most ϵ must be poly(N,ϵ)-close to being honest in the appropriate sense. In particular, our protocol can test any distribution over tensor products of computational or Hadamard basis measurements, making it suitable for applications such as device-independent quantum key distribution under computational assumptions. Moreover, a simplified version of our protocol is the first that can efficiently certify an arbitrary number of qubits of a single cloud quantum computer using only classical communication.
1 aFu, Honghao1 aWang, Daochen1 aZhao, Qi uhttps://arxiv.org/abs/2201.1343001762nas a2200133 4500008004100000245007100041210006900112260001400181520134900195100001601544700001801560700001301578856003701591 2023 eng d00aParallel self-testing of EPR pairs under computational assumptions0 aParallel selftesting of EPR pairs under computational assumption c3/29/20233 aSelf-testing is a fundamental feature of quantum mechanics that allows a classical verifier to force untrusted quantum devices to prepare certain states and perform certain measurements on them. The standard approach assumes at least two spatially separated devices. Recently, Metger and Vidick [Quantum, 2021] showed that a single EPR pair of a single quantum device can be self-tested under computational assumptions. In this work, we generalize their results to give the first parallel self-test of N EPR pairs and measurements on them in the single-device setting under the same computational assumptions. We show that our protocol can be passed with probability negligibly close to 1 by an honest quantum device using poly(N) resources. Moreover, we show that any quantum device that fails our protocol with probability at most ϵ must be poly(N,ϵ)-close to being honest in the appropriate sense. In particular, our protocol can test any distribution over tensor products of computational or Hadamard basis measurements, making it suitable for applications such as device-independent quantum key distribution under computational assumptions. Moreover, a simplified version of our protocol is the first that can efficiently certify an arbitrary number of qubits of a single cloud quantum computer using only classical communication.
1 aFu, Honghao1 aWang, Daochen1 aZhao, Qi uhttps://arxiv.org/abs/2201.1343001544nas a2200133 4500008004100000024001800041245007500059210006900134260001400203520111400217100002201331700002001353856003701373 2023 eng d aUMD-PP-022-0600aParallelization techniques for quantum simulation of fermionic systems0 aParallelization techniques for quantum simulation of fermionic s c3/30/20233 aMapping fermionic operators to qubit operators is an essential step for simulating fermionic systems on a quantum computer. We investigate how the choice of such a mapping interacts with the underlying qubit connectivity of the quantum processor to enable (or impede) parallelization of the resulting Hamiltonian-simulation algorithm. It is shown that this problem can be mapped to a path coloring problem on a graph constructed from the particular choice of encoding fermions onto qubits and the fermionic interactions onto paths. The basic version of this problem is called the weak coloring problem. Taking into account the fine-grained details of the mapping yields what is called the strong coloring problem, which leads to improved parallelization performance. A variety of illustrative analytical and numerical examples are presented to demonstrate the amount of improvement for both weak and strong coloring-based parallelizations. Our results are particularly important for implementation on near-term quantum processors where minimizing circuit depth is necessary for algorithmic feasibility.
1 aBringewatt, Jacob1 aDavoudi, Zohreh uhttps://arxiv.org/abs/2207.1247001394nas a2200121 4500008004100000245006200041210006200103260001400165520101400179100002001193700002201213856003701235 2023 eng d00aPartial Syndrome Measurement for Hypergraph Product Codes0 aPartial Syndrome Measurement for Hypergraph Product Codes c9/26/20233 aHypergraph product codes are a promising avenue to achieving fault-tolerant quantum computation with constant overhead. When embedding these and other constant-rate qLDPC codes into 2D, a significant number of nonlocal connections are required, posing difficulties for some quantum computing architectures. In this work, we introduce a fault-tolerance scheme that aims to alleviate the effects of implementing this nonlocality by measuring generators acting on spatially distant qubits less frequently than those which do not. We investigate the performance of a simplified version of this scheme, where the measured generators are randomly selected. When applied to hypergraph product codes and a modified small-set-flip decoding algorithm, we prove that for a sufficiently high percentage of generators being measured, a threshold still exists. We also find numerical evidence that the logical error rate is exponentially suppressed even when a large constant fraction of generators are not measured.
1 aBerthusen, Noah1 aGottesman, Daniel uhttps://arxiv.org/abs/2306.1712201847nas a2200157 4500008004100000245008500041210006900126260001500195520132900210100002301539700002301562700002001585700002201605700002501627856003701652 2023 eng d00aPrecision Bounds on Continuous-Variable State Tomography using Classical Shadows0 aPrecision Bounds on ContinuousVariable State Tomography using Cl c12/15/20233 aShadow tomography is a framework for constructing succinct descriptions of quantum states using randomized measurement bases, called classical shadows, with powerful methods to bound the estimators used. We recast existing experimental protocols for continuous-variable quantum state tomography in the classical-shadow framework, obtaining rigorous bounds on the number of independent measurements needed for estimating density matrices from these protocols. We analyze the efficiency of homodyne, heterodyne, photon number resolving (PNR), and photon-parity protocols. To reach a desired precision on the classical shadow of an N-photon density matrix with a high probability, we show that homodyne detection requires an order O(N4+1/3) measurements in the worst case, whereas PNR and photon-parity detection require O(N4) measurements in the worst case (both up to logarithmic corrections). We benchmark these results against numerical simulation as well as experimental data from optical homodyne experiments. We find that numerical and experimental homodyne tomography significantly outperforms our bounds, exhibiting a more typical scaling of the number of measurements that is close to linear in N. We extend our single-mode results to an efficient construction of multimode shadows based on local measurements.
1 aGandhari, Srilekha1 aAlbert, Victor, V.1 aGerrits, Thomas1 aTaylor, Jacob, M.1 aGullans, Michael, J. uhttps://arxiv.org/abs/2211.0514901855nas a2200145 4500008004100000245007300041210006900114260001500183520138800198100002201586700001901608700002001627700002501647856003701672 2023 eng d00aProjective toric designs, difference sets, and quantum state designs0 aProjective toric designs difference sets and quantum state desig c11/22/20233 aTrigonometric cubature rules of degree t are sets of points on the torus over which sums reproduce integrals of degree t monomials over the full torus. They can be thought of as t-designs on the torus. Motivated by the projective structure of quantum mechanics, we develop the notion of t-designs on the projective torus, which, surprisingly, have a much more restricted structure than their counterparts on full tori. We provide various constructions of these projective toric designs and prove some bounds on their size and characterizations of their structure. We draw connections between projective toric designs and a diverse set of mathematical objects, including difference and Sidon sets from the field of additive combinatorics, symmetric, informationally complete positive operator valued measures (SIC-POVMs) and complete sets of mutually unbiased bases (MUBs) (which are conjectured to relate to finite projective geometry) from quantum information theory, and crystal ball sequences of certain root lattices. Using these connections, we prove bounds on the maximal size of dense Btmodm sets. We also use projective toric designs to construct families of quantum state designs. Finally, we discuss many open questions about the properties of these projective toric designs and how they relate to other questions in number theory, geometry, and quantum information.
1 aIosue, Joseph, T.1 aMooney, T., C.1 aEhrenberg, Adam1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2311.1347902360nas a2200145 4500008004100000245007900041210006900120260001500189520188900204100002002093700002002113700002802133700002202161856003102183 2023 eng d00aProvably Efficient Learning of Phases of Matter via Dissipative Evolutions0 aProvably Efficient Learning of Phases of Matter via Dissipative c11/13/20233 aThe combination of quantum many-body and machine learning techniques has recently proved to be a fertile ground for new developments in quantum computing. Several works have shown that it is possible to classically efficiently predict the expectation values of local observables on all states within a phase of matter using a machine learning algorithm after learning from data obtained from other states in the same phase. However, existing results are restricted to phases of matter such as ground states of gapped Hamiltonians and Gibbs states that exhibit exponential decay of correlations. In this work, we drop this requirement and show how it is possible to learn local expectation values for all states in a phase, where we adopt the Lindbladian phase definition by Coser \& Pérez-García [Coser \& Pérez-García, Quantum 3, 174 (2019)], which defines states to be in the same phase if we can drive one to other rapidly with a local Lindbladian. This definition encompasses the better-known Hamiltonian definition of phase of matter for gapped ground state phases, and further applies to any family of states connected by short unitary circuits, as well as non-equilibrium phases of matter, and those stable under external dissipative interactions. Under this definition, we show that N=O(log(n/δ)2polylog(1/ϵ)) samples suffice to learn local expectation values within a phase for a system with n qubits, to error ϵ with failure probability δ. This sample complexity is comparable to previous results on learning gapped and thermal phases, and it encompasses previous results of this nature in a unified way. Furthermore, we also show that we can learn families of states which go beyond the Lindbladian definition of phase, and we derive bounds on the sample complexity which are dependent on the mixing time between states under a Lindbladian evolution.
1 aOnorati, Emilio1 aRouzé, Cambyse1 aFrança, Daniel, Stilck1 aWatson, James, D. uarXiv:2311.07506 Search...01827nas a2200181 4500008004100000245005500041210005500096260001400151490000600165520130500171100002301476700001601499700001501515700002001530700003001550700002801580856003701608 2022 eng d00aPauli Stabilizer Models of Twisted Quantum Doubles0 aPauli Stabilizer Models of Twisted Quantum Doubles c3/30/20220 v33 aWe construct a Pauli stabilizer model for every two-dimensional Abelian topological order that admits a gapped boundary. Our primary example is a Pauli stabilizer model on four-dimensional qudits that belongs to the double semion (DS) phase of matter. The DS stabilizer Hamiltonian is constructed by condensing an emergent boson in a Z4 toric code, where the condensation is implemented by making certain two-body measurements. We rigorously verify the topological order of the DS stabilizer model by identifying an explicit finite-depth quantum circuit (with ancillary qubits) that maps its ground state subspace to that of a DS string-net model. We show that the construction of the DS stabilizer Hamiltonian generalizes to all twisted quantum doubles (TQDs) with Abelian anyons. This yields a Pauli stabilizer code on composite-dimensional qudits for each such TQD, implying that the classification of topological Pauli stabilizer codes extends well beyond stacks of toric codes - in fact, exhausting all Abelian anyon theories that admit a gapped boundary. We also demonstrate that symmetry-protected topological phases of matter characterized by type I and type II cocycles can be modeled by Pauli stabilizer Hamiltonians by gauging certain 1-form symmetries of the TQD stabilizer models.
1 aEllison, Tyler, D.1 aChen, Yu-An1 aDua, Arpit1 aShirley, Wilbur1 aTantivasadakarn, Nathanan1 aWilliamson, Dominic, J. uhttps://arxiv.org/abs/2112.1139402246nas a2200205 4500008004100000245006600041210006600107260001400173520157400187653002701761653003101788653005201819100002301871700001601894700001501910700002001925700003001945700002801975856003702003 2022 eng d00aPauli topological subsystem codes from Abelian anyon theories0 aPauli topological subsystem codes from Abelian anyon theories c11/7/20223 aWe construct Pauli topological subsystem codes characterized by arbitrary two-dimensional Abelian anyon theories--this includes anyon theories with degenerate braiding relations and those without a gapped boundary to the vacuum. Our work both extends the classification of two-dimensional Pauli topological subsystem codes to systems of composite-dimensional qudits and establishes that the classification is at least as rich as that of Abelian anyon theories. We exemplify the construction with topological subsystem codes defined on four-dimensional qudits based on the Z(1)4 anyon theory with degenerate braiding relations and the chiral semion theory--both of which cannot be captured by topological stabilizer codes. The construction proceeds by "gauging out" certain anyon types of a topological stabilizer code. This amounts to defining a gauge group generated by the stabilizer group of the topological stabilizer code and a set of anyonic string operators for the anyon types that are gauged out. The resulting topological subsystem code is characterized by an anyon theory containing a proper subset of the anyons of the topological stabilizer code. We thereby show that every Abelian anyon theory is a subtheory of a stack of toric codes and a certain family of twisted quantum doubles that generalize the double semion anyon theory. We further prove a number of general statements about the logical operators of translation invariant topological subsystem codes and define their associated anyon theories in terms of higher-form symmetries.
10aFOS: Physical sciences10aQuantum Physics (quant-ph)10aStrongly Correlated Electrons (cond-mat.str-el)1 aEllison, Tyler, D.1 aChen, Yu-An1 aDua, Arpit1 aShirley, Wilbur1 aTantivasadakarn, Nathanan1 aWilliamson, Dominic, J. uhttps://arxiv.org/abs/2211.0379801696nas a2200145 4500008004100000245005300041210005100094260001500145520127900160100001901439700001401458700001901472700002201491856003701513 2022 eng d00aPost-Quantum Security of the Even-Mansour Cipher0 aPostQuantum Security of the EvenMansour Cipher c12/14/20213 aThe Even-Mansour cipher is a simple method for constructing a (keyed) pseudorandom permutation E from a public random permutation~P:{0,1}n→{0,1}n. It is secure against classical attacks, with optimal attacks requiring qE queries to E and qP queries to P such that qE⋅qP≈2n. If the attacker is given \emph{quantum} access to both E and P, however, the cipher is completely insecure, with attacks using qE,qP=O(n) queries known. In any plausible real-world setting, however, a quantum attacker would have only \emph{classical} access to the keyed permutation~E implemented by honest parties, even while retaining quantum access to~P. Attacks in this setting with qE⋅q2P≈2n are known, showing that security degrades as compared to the purely classical case, but leaving open the question as to whether the Even-Mansour cipher can still be proven secure in this natural, "post-quantum" setting. We resolve this question, showing that any attack in that setting requires qE⋅q2P+qP⋅q2E≈2n. Our results apply to both the two-key and single-key variants of Even-Mansour. Along the way, we establish several generalizations of results from prior work on quantum-query lower bounds that may be of independent interest.
1 aAlagic, Gorjan1 aBai, Chen1 aKatz, Jonathan1 aMajenz, Christian uhttps://arxiv.org/abs/2112.0753001152nas a2200157 4500008004100000245007900041210006900120260001400189520065900203100001900862700001400881700001900895700002200914700002000936856003800956 2022 eng d00aPost-Quantum Security of the (Tweakable) FX Construction, and Applications0 aPostQuantum Security of the Tweakable FX Construction and Applic c8/29/20223 aThe FX construction provides a way to increase the effective key length of a block cipher E. We prove security of a tweakable version of the FX construction in the post-quantum setting, i.e., against a quantum attacker given only classical access to the secretly keyed construction while retaining quantum access to E, a setting that seems to be the most relevant one for real-world applications. We then use our results to prove post-quantum security—in the same model—of the (plain) FX construction, Elephant (a finalist of NIST's lightweight cryptography standardization effort), and Chaskey (an ISO-standardized lightweight MAC
1 aAlagic, Gorjan1 aBai, Chen1 aKatz, Jonathan1 aMajenz, Christian1 aStruck, Patrick uhttps://eprint.iacr.org/2022/109702380nas a2200181 4500008004100000245007100041210006900112260001400181300000800195490000600203520186000209100001302069700002302082700002402105700001902129700001302148856003702161 2022 eng d00aProvably accurate simulation of gauge theories and bosonic systems0 aProvably accurate simulation of gauge theories and bosonic syste c9/20/2022 a8160 v63 aQuantum many-body systems involving bosonic modes or gauge fields have infinite-dimensional local Hilbert spaces which must be truncated to perform simulations of real-time dynamics on classical or quantum computers. To analyze the truncation error, we develop methods for bounding the rate of growth of local quantum numbers such as the occupation number of a mode at a lattice site, or the electric field at a lattice link. Our approach applies to various models of bosons interacting with spins or fermions, and also to both abelian and non-abelian gauge theories. We show that if states in these models are truncated by imposing an upper limit Λ on each local quantum number, and if the initial state has low local quantum numbers, then an error at most ϵ can be achieved by choosing Λ to scale polylogarithmically with ϵ−1, an exponential improvement over previous bounds based on energy conservation. For the Hubbard-Holstein model, we numerically compute a bound on Λ that achieves accuracy ϵ, obtaining significantly improved estimates in various parameter regimes. We also establish a criterion for truncating the Hamiltonian with a provable guarantee on the accuracy of time evolution. Building on that result, we formulate quantum algorithms for dynamical simulation of lattice gauge theories and of models with bosonic modes; the gate complexity depends almost linearly on spacetime volume in the former case, and almost quadratically on time in the latter case. We establish a lower bound showing that there are systems involving bosons for which this quadratic scaling with time cannot be improved. By applying our result on the truncation error in time evolution, we also prove that spectrally isolated energy eigenstates can be approximated with accuracy ϵ by truncating local quantum numbers at Λ=polylog(ϵ−1).
1 aTong, Yu1 aAlbert, Victor, V.1 aMcClean, Jarrod, R.1 aPreskill, John1 aSu, Yuan uhttps://arxiv.org/abs/2110.0694201744nas a2200169 4500008004100000245007100041210006900112260001400181490000800195520123200203100002101435700001901456700002001475700002301495700001901518856003701537 2022 eng d00aProvably efficient machine learning for quantum many-body problems0 aProvably efficient machine learning for quantum manybody problem c9/26/20220 v3773 aClassical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over more traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently predict ground state properties of gapped Hamiltonians in finite spatial dimensions, after learning from data obtained by measuring other Hamiltonians in the same quantum phase of matter. In contrast, under widely accepted complexity theory assumptions, classical algorithms that do not learn from data cannot achieve the same guarantee. We also prove that classical ML algorithms can efficiently classify a wide range of quantum phases of matter. Our arguments are based on the concept of a classical shadow, a succinct classical description of a many-body quantum state that can be constructed in feasible quantum experiments and be used to predict many properties of the state. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, 2D random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases.
1 aHuang, Hsin-Yuan1 aKueng, Richard1 aTorlai, Giacomo1 aAlbert, Victor, V.1 aPreskill, John uhttps://arxiv.org/abs/2106.1262701481nas a2200193 4500008004100000245004300041210004200084260001400126300001100140490000800151520095100159100001501110700002001125700002301145700001801168700002001186700001701206856006401223 2021 eng d00aPhase-engineered bosonic quantum codes0 aPhaseengineered bosonic quantum codes c6/29/2021 a0624270 v1033 aContinuous-variable systems protected by bosonic quantum codes have emerged as a promising platform for quantum information. To date, the design of code words has centered on optimizing the state occupation in the relevant basis to generate the distance needed for error correction. Here, we show tuning the phase degree of freedom in the design of code words can affect, and potentially enhance, the protection against Markovian errors that involve excitation exchange with the environment. As illustrations, we first consider phase engineering bosonic codes with uniform spacing in the Fock basis that correct excitation loss with a Kerr unitary and show that these modified codes feature destructive interference between error code words and, with an adapted “two-level” recovery, the error protection is significantly enhanced. We then study protection against energy decay with the presence of mode nonlinearities …
1 aLi, Linshu1 aYoung, Dylan, J1 aAlbert, Victor, V.1 aNoh, Kyungjoo1 aZou, Chang-Ling1 aJiang, Liang uhttps://authors.library.caltech.edu/109764/2/1901.05358.pdf01886nas a2200145 4500008004100000245007800041210006900119260001400188520142500202100002401627700001501651700001701666700002001683856003701703 2021 eng d00aPrecise Hamiltonian identification of a superconducting quantum processor0 aPrecise Hamiltonian identification of a superconducting quantum c8/18/20213 aThe required precision to perform quantum simulations beyond the capabilities of classical computers imposes major experimental and theoretical challenges. Here, we develop a characterization technique to benchmark the implementation precision of a specific quantum simulation task. We infer all parameters of the bosonic Hamiltonian that governs the dynamics of excitations in a two-dimensional grid of nearest-neighbour coupled superconducting qubits. We devise a robust algorithm for identification of Hamiltonian parameters from measured times series of the expectation values of single-mode canonical coordinates. Using super-resolution and denoising methods, we first extract eigenfrequencies of the governing Hamiltonian from the complex time domain measurement; next, we recover the eigenvectors of the Hamiltonian via constrained manifold optimization over the orthogonal group. For five and six coupled qubits, we identify Hamiltonian parameters with sub-MHz precision and construct a spatial implementation error map for a grid of 27 qubits. Our approach enables us to distinguish and quantify the effects of state preparation and measurement errors and show that they are the dominant sources of errors in the implementation. Our results quantify the implementation accuracy of analog dynamics and introduce a diagnostic toolkit for understanding, calibrating, and improving analog quantum processors.
1 aHangleiter, Dominik1 aRoth, Ingo1 aEisert, Jens1 aRoushan, Pedram uhttps://arxiv.org/abs/2108.0831901810nas a2200121 4500008004100000245006600041210006600107260001400173520141900187100002101606700002401627856003701651 2021 eng d00aPreparing Renormalization Group Fixed Points on NISQ Hardware0 aPreparing Renormalization Group Fixed Points on NISQ Hardware c9/20/20213 aNoisy intermediate-scale quantum (NISQ) hardware is typically limited to low-depth quantum circuits to limit the number of opportunities for introduction of error by unreliable quantum gates. A less-explored alternative approach is to repeatedly apply a quantum channel with a desired quantum state as a stable fixed point. Increased circuit depth can in this case be beneficial rather than harmful due to dissipative self-correction. The quantum channels constructed from MERA circuits can be interpreted in terms of the renormalization group(RG), and their fixed points are RG fixed points, i.e. scale-invariant systems such as conformal field theories. Here, building upon the theoretical proposal of Kim and Swingle, we numerically and experimentally study the robust preparation of the ground state of the critical Ising model using circuits adapted from the work of Evenbly and White. The experimental implementation exhibits self-correction through renormalization seen in the convergence and stability of local observables, and makes essential use of the ability to measure and reset individual qubits afforded by the "quantum CCD" architecture of the Honeywell ion-trap. We also numerically test error mitigation by zero-noise extrapolation schemes specially adapted for renormalization circuits, which are able to outperform typical extrapolation schemes using lower gate overhead.
1 aSewell, Troy, J.1 aJordan, Stephen, P. uhttps://arxiv.org/abs/2109.0978701277nas a2200169 4500008004100000022001400041245006300055210006300118260001400181490000800195520078700203100001900990700001901009700002001028700002201048856003701070 2021 eng d a2470-002900aProposal for gravitational direct detection of dark matter0 aProposal for gravitational direct detection of dark matter c8/23/20210 v1023 aThe only coupling dark matter is guaranteed to have with the standard model is through gravity. Here we propose a concept for direct dark matter detection using only this gravitational coupling. We suggest that an array of quantum-limited mechanical impulse sensors may be capable of detecting the correlated gravitational force created by a passing dark matter particle. We consider the effects of irreducible noise from couplings of the sensors to the environment and noise due to the quantum measurement process. We show that the signal from Planck-scale dark matter is in principle detectable using a large number of gram-scale sensors in a meter-scale array with sufficiently low quantum noise, and discuss some experimental challenges en route to achieving this target.
1 aCarney, Daniel1 aGhosh, Sohitri1 aKrnjaic, Gordan1 aTaylor, Jacob, M. uhttps://arxiv.org/abs/1903.0049201637nas a2200181 4500008004100000022001400041245010300055210006900158260001300227490000600240520106000246100002201306700002001328700002101348700002401369700002501393856003701418 2021 eng d a2643-156400aProtocols for estimating multiple functions with quantum sensor networks: Geometry and performance0 aProtocols for estimating multiple functions with quantum sensor c5/3/20210 v33 aWe consider the problem of estimating multiple analytic functions of a set of local parameters via qubit sensors in a quantum sensor network. To address this problem, we highlight a generalization of the sensor symmetric performance bounds of Rubio et. al. [J. Phys. A: Math. Theor. 53 344001 (2020)] and develop a new optimized sequential protocol for measuring such functions. We compare the performance of both approaches to one another and to local protocols that do not utilize quantum entanglement, emphasizing the geometric significance of the coefficient vectors of the measured functions in determining the best choice of measurement protocol. We show that, in many cases, especially for a large number of sensors, the optimized sequential protocol results in more accurate measurements than the other strategies. In addition, in contrast to the the sensor symmetric approach, the sequential protocol is known to always be explicitly implementable. The sequential protocol is very general and has a wide range of metrological applications.
1 aBringewatt, Jacob1 aBoettcher, Igor1 aNiroula, Pradeep1 aBienias, Przemyslaw1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2104.0954001360nas a2200229 4500008004100000020002200041022001400063245003700077210003700114260001200151300001700163490000800180520076100188100001900949700001700968700001900985700001301004700001901017700001701036700002101053856005601074 2021 eng d a978-3-95977-188-7 a1868-896900aProving Quantum Programs Correct0 aProving Quantum Programs Correct c06/2021 a21:1–21:190 v1933 aAs quantum computing progresses steadily from theory into practice, programmers will face
a common problem: How can they be sure that their code does what they intend it to do? This
paper presents encouraging results in the application of mechanized proof to the domain of quantum
programming in the context of the sqir development. It verifies the correctness of a range of a
quantum algorithms including Grover’s algorithm and quantum phase estimation, a key component
of Shor’s algorithm. In doing so, it aims to highlight both the successes and challenges of formal
verification in the quantum context and motivate the theorem proving community to target quantum
computing as an application domain.
As quantum computing steadily progresses from theory to practice, programmers are faced with a common problem: How can they be sure that their code does what they intend it to do? This paper presents encouraging results in the application of mechanized proof to the domain of quantum programming in the context of the SQIR development. It verifies the correctness of a range of a quantum algorithms including Simon's algorithm, Grover's algorithm, and quantum phase estimation, a key component of Shor's algorithm. In doing so, it aims to highlight both the successes and challenges of formal verification in the quantum context and motivate the theorem proving community to target quantum computing as an application domain.
1 aHietala, Kesha1 aRand, Robert1 aHung, Shih-Han1 aLi, Liyi1 aHicks, Michael uhttps://arxiv.org/abs/2010.0124001468nas a2200157 4500008004100000245005700041210005600098260001200154300001400166490000700180520103700187100001601224700001701240700001601257856003701273 2020 eng d00aParallel Device-Independent Quantum Key Distribution0 aParallel DeviceIndependent Quantum Key Distribution c09/2020 a5567-55840 v663 aA prominent application of quantum cryptography is the distribution of cryptographic keys that are provably secure. Such security proofs were extended by Vazirani and Vidick ( Physical Review Letters , 113, 140501, 2014) to the device-independent (DI) scenario, where the users do not need to trust the integrity of the underlying quantum devices. The protocols analyzed by them and by subsequent authors all require a sequential execution of N multiplayer games, where N is the security parameter. In this work, we prove the security of a protocol where all games are executed in parallel. Besides decreasing the number of time-steps necessary for key generation, this result reduces the security requirements for DI-QKD by allowing arbitrary information leakage of each user’s inputs within his or her lab. To the best of our knowledge, this is the first parallel security proof for a fully device-independent QKD protocol. Our protocol tolerates a constant level of device imprecision and achieves a linear key rate.
1 aJain, Rahul1 aMiller, Carl1 aShi, Yaoyun uhttps://arxiv.org/abs/1703.0542602249nas a2200133 4500008004100000245007900041210006900120260001500189520179100204100002401995700001902019700001902038856005802057 2020 eng d00aPosition Space Decoherence From Long-Range Interaction With Background Gas0 aPosition Space Decoherence From LongRange Interaction With Backg c06/05/20203 aExperiments in matter wave interferometry and optomechanics are increasing the spatial extent of wavefunctions of massive quantum systems; this gives rise to new sources of decoherence that must be characterized. Here we calculate the position space decoherence of a quantum particle due to interaction with a fluctuating classical background gas for several different force laws. We begin with the calculation of this effect for the Newton potential. To our knowledge, this calculation has not been done before. We then solve the same problem in the case of a Yukawa interaction, which interpolates between our long-range force result and the well-studied formula for collisional decoherence from a contact interaction. Unlike the contact interaction case, where the decoherence rate becomes independent of distance for large quantum particle separations, we observe that a long-range interaction leads to quadratic scaling of the decoherence rate with distance even at large separations. This work is relevant to the generation of massive superposition in optomechanical and atom beam experiments, and to conclude we comment on the use of this decoherence signal for gravitational detection of dark matter.
1 aKunjummen, Jonathan1 aCarney, Daniel1 aTaylor, J., M. uhttp://meetings.aps.org/Meeting/DAMOP20/Session/S08.501867nas a2200145 4500008004100000245007000041210006300111260001300174520141800187100001801605700001901623700002701642700001501669856003701684 2020 eng d00aOn the Principles of Differentiable Quantum Programming Languages0 aPrinciples of Differentiable Quantum Programming Languages c4/2/20203 aVariational Quantum Circuits (VQCs), or the so-called quantum neural-networks, are predicted to be one of the most important near-term quantum applications, not only because of their similar promises as classical neural-networks, but also because of their feasibility on near-term noisy intermediate-size quantum (NISQ) machines. The need for gradient information in the training procedure of VQC applications has stimulated the development of auto-differentiation techniques for quantum circuits. We propose the first formalization of this technique, not only in the context of quantum circuits but also for imperative quantum programs (e.g., with controls), inspired by the success of differentiable programming languages in classical machine learning. In particular, we overcome a few unique difficulties caused by exotic quantum features (such as quantum no-cloning) and provide a rigorous formulation of differentiation applied to bounded-loop imperative quantum programs, its code-transformation rules, as well as a sound logic to reason about their correctness. Moreover, we have implemented our code transformation in OCaml and demonstrated the resource-efficiency of our scheme both analytically and empirically. We also conduct a case study of training a VQC instance with controls, which shows the advantage of our scheme over existing auto-differentiation for quantum circuits without controls.
1 aZhu, Shaopeng1 aHung, Shih-Han1 aChakrabarti, Shouvanik1 aWu, Xiaodi uhttps://arxiv.org/abs/2004.0112201620nas a2200193 4500008004100000245006300041210006200104260001400166520106800180100001201248700001401260700001901274700002101293700002101314700001801335700001501353700002101368856003701389 2020 eng d00aProbing many-body localization on a noisy quantum computer0 aProbing manybody localization on a noisy quantum computer c6/22/20203 aA disordered system of interacting particles exhibits localized behavior when the disorder is large compared to the interaction strength. Studying this phenomenon on a quantum computer without error correction is challenging because even weak coupling to a thermal environment destroys most signatures of localization. Fortunately, spectral functions of local operators are known to contain features that can survive the presence of noise. In these spectra, discrete peaks and a soft gap at low frequencies compared to the thermal phase indicate localization. Here, we present the computation of spectral functions on a trapped-ion quantum computer for a one-dimensional Heisenberg model with disorder. Further, we design an error-mitigation technique which is effective at removing the noise from the measurement allowing clear signatures of localization to emerge as the disorder increases. Thus, we show that spectral functions can serve as a robust and scalable diagnostic of many-body localization on the current generation of quantum computers.
1 aZhu, D.1 aJohri, S.1 aNguyen, N., H.1 aAlderete, Huerta1 aLandsman, K., A.1 aLinke, N., M.1 aMonroe, C.1 aMatsuura, A., Y. uhttps://arxiv.org/abs/2006.1235501854nas a2200193 4500008004100000245008800041210006900129260001400198520128100212100001501493700001701508700001501525700001601540700001701556700001401573700001901587700001701606856003701623 2020 eng d00aProbing XY phase transitions in a Josephson junction array with tunable frustration0 aProbing XY phase transitions in a Josephson junction array with c1/22/20203 aThe seminal theoretical works of Berezinskii, Kosterlitz, and Thouless presented a new paradigm for phase transitions in condensed matter that are driven by topological excitations. These transitions have been extensively studied in the context of two-dimensional XY models -- coupled compasses -- and have generated interest in the context of quantum simulation. Here, we use a circuit quantum-electrodynamics architecture to study the critical behavior of engineered XY models through their dynamical response. In particular, we examine not only the unfrustrated case but also the fully-frustrated case which leads to enhanced degeneracy associated with the spin rotational [U(1)] and discrete chiral (Z2) symmetries. The nature of the transition in the frustrated case has posed a challenge for theoretical studies while direct experimental probes remain elusive. Here we identify the transition temperatures for both the unfrustrated and fully-frustrated XY models by probing a Josephson junction array close to equilibrium using weak microwave excitations and measuring the temperature dependence of the effective damping obtained from the complex reflection coefficient. We argue that our probing technique is primarily sensitive to the dynamics of the U(1) part.
1 aCosmic, R.1 aKawabata, K.1 aAshida, Y.1 aIkegami, H.1 aFurukawa, S.1 aPatil, P.1 aTaylor, J., M.1 aNakamura, Y. uhttps://arxiv.org/abs/2001.0787702048nas a2200145 4500008004100000245005900041210005900100260001500159520160200174100001801776700002201794700002601816700002301842856003701865 2020 eng d00aProgrammable Quantum Annealers as Noisy Gibbs Samplers0 aProgrammable Quantum Annealers as Noisy Gibbs Samplers c12/16/20203 aDrawing independent samples from high-dimensional probability distributions represents the major computational bottleneck for modern algorithms, including powerful machine learning frameworks such as deep learning. The quest for discovering larger families of distributions for which sampling can be efficiently realized has inspired an exploration beyond established computing methods and turning to novel physical devices that leverage the principles of quantum computation. Quantum annealing embodies a promising computational paradigm that is intimately related to the complexity of energy landscapes in Gibbs distributions, which relate the probabilities of system states to the energies of these states. Here, we study the sampling properties of physical realizations of quantum annealers which are implemented through programmable lattices of superconducting flux qubits. Comprehensive statistical analysis of the data produced by these quantum machines shows that quantum annealers behave as samplers that generate independent configurations from low-temperature noisy Gibbs distributions. We show that the structure of the output distribution probes the intrinsic physical properties of the quantum device such as effective temperature of individual qubits and magnitude of local qubit noise, which result in a non-linear response function and spurious interactions that are absent in the hardware implementation. We anticipate that our methodology will find widespread use in characterization of future generations of quantum annealers and other emerging analog computing devices.
1 aVuffray, Marc1 aCoffrin, Carleton1 aKharkov, Yaroslav, A.1 aLokhov, Andrey, Y. uhttps://arxiv.org/abs/2012.0882701481nas a2200157 4500008004100000245006800041210006700109260001500176300001000191490000800201520102300209100002101232700001601253700001701269856003701286 2019 eng d00aParallel Self-Testing of the GHZ State with a Proof by Diagrams0 aParallel SelfTesting of the GHZ State with a Proof by Diagrams c01/29/2019 a43-660 v2873 aQuantum self-testing addresses the following question: is it possible to verify the existence of a multipartite state even when one's measurement devices are completely untrusted? This problem has seen abundant activity in the last few years, particularly with the advent of parallel self-testing (i.e., testing several copies of a state at once), which has applications not only to quantum cryptography but also quantum computing. In this work we give the first error-tolerant parallel self-test in a three-party (rather than two-party) scenario, by showing that an arbitrary number of copies of the GHZ state can be self-tested. In order to handle the additional complexity of a three-party setting, we use a diagrammatic proof based on categorical quantum mechanics, rather than a typical symbolic proof. The diagrammatic approach allows for manipulations of the complicated tensor networks that arise in the proof, and gives a demonstration of the importance of picture-languages in quantum information.
1 aBreiner, Spencer1 aKalev, Amir1 aMiller, Carl uhttps://arxiv.org/abs/1806.0474401434nas a2200193 4500008004100000245005500041210005500096260001500151490000800166520090200174100001701076700001601093700001701109700001801126700002101144700001701165700002101182856003701203 2019 eng d00aPhoton pair condensation by engineered dissipation0 aPhoton pair condensation by engineered dissipation c04/02/20190 v1233 aDissipation can usually induce detrimental decoherence in a quantum system. However, engineered dissipation can be used to prepare and stabilize coherent quantum many-body states. Here, we show that by engineering dissipators containing photon pair operators, one can stabilize an exotic dark state, which is a condensate of photon pairs with a phase-nematic order. In this system, the usual superfluid order parameter, i.e. single-photon correlation, is absent, while the photon pair correlation exhibits long-range order. Although the dark state is not unique due to multiple parity sectors, we devise an additional type of dissipators to stabilize the dark state in a particular parity sector via a diffusive annihilation process which obeys Glauber dynamics in an Ising model. Furthermore, we propose an implementation of these photon-pair dissipators in circuit-QED architecture.
1 aCian, Ze-Pei1 aZhu, Guanyu1 aChu, Su-Kuan1 aSeif, Alireza1 aDeGottardi, Wade1 aJiang, Liang1 aHafezi, Mohammad uhttps://arxiv.org/abs/1904.0001601973nas a2200145 4500008004100000245008000041210006900121260001400190490000800204520151100212100002201723700002101745700002401766856003701790 2019 eng d00aPolynomial Time Algorithms for Estimating Spectra of Adiabatic Hamiltonians0 aPolynomial Time Algorithms for Estimating Spectra of Adiabatic H c10/1/20200 v1003 aMuch research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians with Hamming symmetric potentials, such as the well studied "spike" example. Due to the large amount of symmetry in these potentials such problems are readily open to analysis both analytically and computationally. However, more realistic potentials do not have such a high degree of symmetry and may have many local minima. Here we present a somewhat more realistic class of problems consisting of many individually Hamming symmetric potential wells. For two or three such wells we demonstrate that such a problem can be solved exactly in time polynomial in the number of qubits and wells. For greater than three wells, we present a tight binding approach with which to efficiently analyze the performance of such Hamiltonians in an adiabatic computation. We provide several basic examples designed to highlight the usefulness of this toy model and to give insight into using the tight binding approach to examining it, including: (1) adiabatic unstructured search with a transverse field driver and a prior guess to the marked item and (2) a scheme for adiabatically simulating the ground states of small collections of strongly interacting spins, with an explicit demonstration for an Ising model Hamiltonian.
1 aBringewatt, Jacob1 aDorland, William1 aJordan, Stephen, P. uhttps://arxiv.org/abs/1905.0746101348nas a2200121 4500008004100000245010600041210006900147260001400216520091000230100002501140700002401165856003701189 2019 eng d00aA Probabilistic Framework and a Homotopy Method for Real-time Hierarchical Freight Dispatch Decisions0 aProbabilistic Framework and a Homotopy Method for Realtime Hiera c2019/12/83 aWe propose a real-time decision framework for multimodal freight dispatch through a system of hierarchical hubs, using a probabilistic model for transit times. Instead of assigning a fixed time to each transit, we advocate using historical records to identify characteristics of the probability density function for each transit time. We formulate a nonlinear optimization problem that defines dispatch decisions that minimize expected cost, using this probabilistic information. Finally, we propose an effective homotopy algorithm that (empirically) outperforms standard optimization algorithms on this problem by taking advantage of its structure, and we demonstrate its effectiveness on numerical examples.
1 aYousefzadeh, Roozbeh1 aO'Leary, Dianne, P. uhttps://arxiv.org/abs/1912.0373301814nas a2200169 4500008004100000245006700041210006600108260001400174490000800188520130400196100001701500700002201517700002401539700002501563700001901588856003701607 2019 eng d00aProbing ground-state phase transitions through quench dynamics0 aProbing groundstate phase transitions through quench dynamics c9/11/20190 v1233 aThe study of quantum phase transitions requires the preparation of a many-body system near its ground state, a challenging task for many experimental systems. The measurement of quench dynamics, on the other hand, is now a routine practice in most cold atom platforms. Here we show that quintessential ingredients of quantum phase transitions can be probed directly with quench dynamics in integrable and nearly integrable systems. As a paradigmatic example, we study global quench dynamics in a transverse-field Ising model with either short-range or long-range interactions. When the model is integrable, we discover a new dynamical critical point with a non-analytic signature in the short-range correlators. The location of the dynamical critical point matches that of the quantum critical point and can be identified using a finite-time scaling method. We extend this scaling picture to systems near integrability and demonstrate the continued existence of a dynamical critical point detectable at prethermal time scales. Therefore, our method can be used to approximately locate the quantum critical point. The scaling method is also relevant to experiments with finite time and system size, and our predictions are testable in near-term experiments with trapped ions and Rydberg atoms.
1 aTitum, Paraj1 aIosue, Joseph, T.1 aGarrison, James, R.1 aGorshkov, Alexey, V.1 aGong, Zhe-Xuan uhttps://arxiv.org/abs/1809.0637701707nas a2200133 4500008004100000245006500041210006500106260001500171490000800186520130600194100001701500700001901517856003701536 2019 eng d00aProduct Spectrum Ansatz and the Simplicity of Thermal States0 aProduct Spectrum Ansatz and the Simplicity of Thermal States c2019/11/180 v1003 aCalculating the physical properties of quantum thermal states is a difficult problem for classical computers, rendering it intractable for most quantum many-body systems. A quantum computer, by contrast, would make many of these calculations feasible in principle, but it is still non-trivial to prepare a given thermal state or sample from it. It is also not known how to prepare special simple purifications of thermal states known as thermofield doubles, which play an important role in quantum many-body physics and quantum gravity. To address this problem, we propose a variational scheme to prepare approximate thermal states on a quantum computer by applying a series of two-qubit gates to a product mixed state. We apply our method to a non-integrable region of the mixed field Ising chain and the Sachdev-Ye-Kitaev model. We also demonstrate how our method can be easily extended to large systems governed by local Hamiltonians and the preparation of thermofield double states. By comparing our results with exact solutions, we find that our construction enables the efficient preparation of approximate thermal states on quantum devices. Our results can be interpreted as implying that the details of the many-body energy spectrum are not needed to capture simple thermal observables.
1 aMartyn, John1 aSwingle, Brian uhttps://arxiv.org/abs/1812.0101501709nas a2200241 4500008004100000245007100041210006900112260001500181520103600196100001501232700002101247700001801268700001801286700002501304700001301329700001401342700001201356700001501368700001701383700001401400700001601414856003701430 2019 eng d00aProgrammable Quantum Simulations of Spin Systems with Trapped Ions0 aProgrammable Quantum Simulations of Spin Systems with Trapped Io c12/17/20193 aLaser-cooled and trapped atomic ions form an ideal standard for the simulation of interacting quantum spin models. Effective spins are represented by appropriate internal energy levels within each ion, and the spins can be measured with near-perfect efficiency using state-dependent fluorescence techniques. By applying optical fields that exert optical dipole forces on the ions, their Coulomb interaction can be modulated in ways that give rise to long-range and tunable spin-spin interactions that can be reconfigured by shaping the spectrum and pattern of the laser fields. Here we review the theoretical mapping of atomic ions to interacting spin systems, the experimental preparation of complex equilibrium states, and the study of dynamical processes of this many-body interacting quantum system. The use of such quantum simulators for studying spin models may inform our understanding of exotic quantum materials and shed light on interacting quantum systems that cannot be modeled with conventional computers.
1 aMonroe, C.1 aCampbell, W., C.1 aDuan, L., -M.1 aGong, Z., -X.1 aGorshkov, Alexey, V.1 aHess, P.1 aIslam, R.1 aKim, K.1 aPagano, G.1 aRicherme, P.1 aSenko, C.1 aYao, N., Y. uhttps://arxiv.org/abs/1912.0784501943nas a2200169 4500008004100000245007600041210006900117520143500186100001601621700001801637700001801655700002101673700001201694700001501706700001501721856003701736 2018 eng d00aParallel Entangling Operations on a Universal Ion Trap Quantum Computer0 aParallel Entangling Operations on a Universal Ion Trap Quantum C3 aThe circuit model of a quantum computer consists of sequences of gate operations between quantum bits (qubits), drawn from a universal family of discrete operations. The ability to execute parallel entangling quantum gates offers clear efficiency gains in numerous quantum circuits as well as for entire algorithms such as Shor's factoring algorithm and quantum simulations. In cases such as full adders and multiple-control Toffoli gates, parallelism can provide an exponential improvement in overall execution time. More importantly, quantum gate parallelism is essential for the practical fault-tolerant error correction of qubits that suffer from idle errors. The implementation of parallel quantum gates is complicated by potential crosstalk, especially between qubits fully connected by a common-mode bus, such as in Coulomb-coupled trapped atomic ions or cavity-coupled superconducting transmons. Here, we present the first experimental results for parallel 2-qubit entangling gates in an array of fully-connected trapped ion qubits. We demonstrate an application of this capability by performing a 1-bit full addition operation on a quantum computer using a depth-4 quantum circuit. These results exploit the power of highly connected qubit systems through classical control techniques, and provide an advance toward speeding up quantum circuits and achieving fault tolerance with trapped ion quantum computers.
1 aFiggatt, C.1 aOstrander, A.1 aLinke, N., M.1 aLandsman, K., A.1 aZhu, D.1 aMaslov, D.1 aMonroe, C. uhttps://arxiv.org/abs/1810.1194801770nas a2200145 4500008004100000245006300041210006200104260001500166300001200181490000700193520134000200100001901540700001601559856004901575 2018 eng d00aPhase Retrieval Without Small-Ball Probability Assumptions0 aPhase Retrieval Without SmallBall Probability Assumptions c2018/01/01 a485-5000 v643 aIn the context of the phase retrieval problem, it is known that certain natural classes of measurements, such as Fourier measurements and random Bernoulli measurements, do not lead to the unique reconstruction of all possible signals, even in combination with certain practically feasible random masks. To avoid this difficulty, the analysis is often restricted to measurement ensembles (or masks) that satisfy a small-ball probability condition, in order to ensure that the reconstruction is unique. This paper shows a complementary result: for random Bernoulli measurements, there is still a large class of signals that can be reconstructed uniquely, namely, those signals that are non-peaky. In fact, this result is much more general: it holds for random measurements sampled from any subgaussian distribution 2), without any small-ball conditions. This is demonstrated in two ways: 1) a proof of stability and uniqueness and 2) a uniform recovery guarantee for the PhaseLift algorithm. In all of these cases, the number of measurements m approaches the information-theoretic lower bound. Finally, for random Bernoulli measurements with erasures, it is shown that PhaseLift achieves uniform recovery of all signals (including peaky ones).
1 aKrahmer, Felix1 aLiu, Yi-Kai uhttp://ieeexplore.ieee.org/document/8052535/02076nas a2200229 4500008004100000245007800041210006900119520136400188100002401552700001901576700002401595700001701619700002301636700002101659700001801680700002101698700001901719700002701738700001901765700002501784856003701809 2018 eng d00aPhoton propagation through dissipative Rydberg media at large input rates0 aPhoton propagation through dissipative Rydberg media at large in3 aWe study the dissipative propagation of quantized light in interacting Rydberg media under the conditions of electromagnetically induced transparency (EIT). Rydberg blockade physics in optically dense atomic media leads to strong dissipative interactions between single photons. The regime of high incoming photon flux constitutes a challenging many-body dissipative problem. We experimentally study in detail for the first time the pulse shapes and the second-order correlation function of the outgoing field and compare our data with simulations based on two novel theoretical approaches well-suited to treat this many-photon limit. At low incoming flux, we report good agreement between both theories and the experiment. For higher input flux, the intensity of the outgoing light is lower than that obtained from theoretical predictions. We explain this discrepancy using a simple phenomenological model taking into account pollutants, which are nearly-stationary Rydberg excitations coming from the reabsorption of scattered probe photons. At high incoming photon rates, the blockade physics results in unconventional shapes of measured correlation functions.
1 aBienias, Przemyslaw1 aDouglas, James1 aParis-Mandoki, Asaf1 aTitum, Paraj1 aMirgorodskiy, Ivan1 aTresp, Christoph1 aZeuthen, Emil1 aGullans, Michael1 aManzoni, Marco1 aHofferberth, Sebastian1 aChang, Darrick1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1807.0758601386nas a2200193 4500008004100000245004800041210004700089260001500136520082300151100002300974700002300997700002101020700002101041700002401062700002501086700002701111700001701138856003701155 2018 eng d00aPhoton Subtraction by Many-Body Decoherence0 aPhoton Subtraction by ManyBody Decoherence c2018/03/133 aWe present an experimental and theoretical investigation of the scattering-induced decoherence of multiple photons stored in a strongly interacting atomic ensemble. We derive an exact solution to this many-body problem, allowing for a rigorous understanding of the underlying dissipative quantum dynamics. Combined with our experiments, this analysis demonstrates a correlated coherence-protection process, in which the induced decoherence of one photon can preserve the spatial coherence of all others. We discuss how this effect can be used to manipulate light at the quantum level, providing a robust mechanism for single-photon subtraction, and experimentally demonstrate this capability.
1 aMurray, Callum, R.1 aMirgorodskiy, Ivan1 aTresp, Christoph1 aBraun, Christoph1 aParis-Mandoki, Asaf1 aGorshkov, Alexey, V.1 aHofferberth, Sebastian1 aPohl, Thomas uhttps://arxiv.org/abs/1710.1004701932nas a2200157 4500008004100000245005300041210005300094260000900147520147500156100002201631700002101653700001801674700002601692700001901718856003701737 2018 eng d00aPhoton thermalization via laser cooling of atoms0 aPhoton thermalization via laser cooling of atoms c20183 aLaser cooling of atomic motion enables a wide variety of technological and scientific explorations using cold atoms. Here we focus on the effect of laser cooling on the photons instead of on the atoms. Specifically, we show that non-interacting photons can thermalize with the atoms to a grand canonical ensemble with a non-zero chemical potential. This thermalization is accomplished via scattering of light between different optical modes, mediated by the laser cooling process. While optically thin modes lead to traditional laser cooling of the atoms, the dynamics of multiple scattering in optically thick modes has been more challenging to describe. We find that in an appropriate set of limits, multiple scattering leads to thermalization of the light with the atomic motion in a manner that approximately conserves total photon number between the laser beams and optically thick modes. In this regime, the subsystem corresponding to the thermalized modes is describable by a grand canonical ensemble with a chemical potential set by the energy of a single laser photon. We consider realization of this regime using two-level atoms in Doppler cooling, and find physically realistic conditions for rare earth atoms. With the addition of photon-photon interactions, this system could provide a new platform for exploring many-body physics.
1 aWang, Chiao-Hsuan1 aGullans, Michael1 aPorto, J., V.1 aPhillips, William, D.1 aTaylor, J., M. uhttps://arxiv.org/abs/1712.0864302126nas a2200109 4500008004100000245010900041210006900150520172200219100001401941700002401955856003701979 2018 eng d00aPractitioner's guide to social network analysis: Examining physics anxiety in an active-learning setting0 aPractitioners guide to social network analysis Examining physics3 aThe application of social network analysis (SNA) has recently grown prevalent in science, technology, engineering, and mathematics education research. Research on classroom networks has led to greater understandings of student persistence in physics majors, changes in their career-related beliefs (e.g., physics interest), and their academic success. In this paper, we aim to provide a practitioner's guide to carrying out research using SNA, including how to develop data collection instruments, set up protocols for gathering data, as well as identify network methodologies relevant to a wide range of research questions beyond what one might find in a typical primer. We illustrate these techniques using student anxiety data from active-learning physics classrooms. We explore the relationship between students' physics anxiety and the social networks they participate in throughout the course of a semester. We find that students' with greater numbers of outgoing interactions are more likely to experience negative anxiety shifts even while we control for {\it pre} anxiety, gender, and final course grade. We also explore the evolution of student networks and find that the second half of the semester is a critical period for participating in interactions associated with decreased physics anxiety. Our study further supports the benefits of dynamic group formation strategies that give students an opportunity to interact with as many peers as possible throughout a semester. To complement our guide to SNA in education research, we also provide a set of tools for letting other researchers use this approach in their work -- the {\it SNA toolbox} -- that can be accessed on GitHub.
1 aDou, Remy1 aZwolak, Justyna, P. uhttps://arxiv.org/abs/1809.0033701748nas a2200157 4500008004100000245010900041210006900150260001500219300001100234490000700245520121100252100002101463700001901484700001801503856006901521 2018 eng d00aProbing electron-phonon interactions in the charge-photon dynamics of cavity-coupled double quantum dots0 aProbing electronphonon interactions in the chargephoton dynamics c2018/01/16 a0353050 v973 aElectron-phonon coupling is known to play an important role in the charge dynamics of semiconductor quantum dots. Here we explore its role in the combined charge-photon dynamics of cavity-coupled double quantum dots. Previous work on these systems has shown that strong electron-phonon coupling leads to a large contribution to photoemission and gain from phonon-assisted emission and absorption processes. We compare the effects of this phonon sideband in three commonly investigated gate-defined quantum dot material systems: InAs nanowires and GaAs and Si two-dimensional electron gases (2DEGs). We compare our theory with existing experimental data from cavity-coupled InAs nanowire and GaAs 2DEG double quantum dots and find quantitative agreement only when the phonon sideband and photoemission processes during lead tunneling are taken into account. Finally, we show that the phonon sideband also leads to a sizable renormalization of the cavity frequency, which allows for direct spectroscopic probes of the electron-phonon coupling in these systems.
1 aGullans, Michael1 aTaylor, J., M.1 aPetta, J., R. uhttps://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.03530501127nas a2200145 4500008004100000245006400041210006200105260001500167490001000182520070300192100001800895700001600913700001500929856003700944 2018 eng d00aPseudorandom States, Non-Cloning Theorems and Quantum Money0 aPseudorandom States NonCloning Theorems and Quantum Money c2017/11/010 v109933 aWe propose the concept of pseudorandom states and study their constructions, properties, and applications. Under the assumption that quantum-secure one-way functions exist, we present concrete and efficient constructions of pseudorandom states. The non-cloning theorem plays a central role in our study—it motivates the proper definition and characterizes one of the important properties of pseudorandom quantum states. Namely, there is no efficient quantum algorithm that can create more copies of the state from a given number of pseudorandom states. As the main application, we prove that any family of pseudorandom states naturally gives rise to a private-key quantum money scheme.
1 aJi, Zhengfeng1 aLiu, Yi-Kai1 aSong, Fang uhttps://arxiv.org/abs/1711.0038501351nas a2200157 4500008004100000245007200041210006900113260001500182300001100197490000700208520084900215100002401064700002301088700002701111856005501138 2017 eng d00aPartial breakdown of quantum thermalization in a Hubbard-like model0 aPartial breakdown of quantum thermalization in a Hubbardlike mod c2017/02/17 a0542040 v953 aWe study the possible breakdown of quantum thermalization in a model of itinerant electrons on a one-dimensional chain without disorder, with both spin and charge degrees of freedom. The eigenstates of this model exhibit peculiar properties in the entanglement entropy, the apparent scaling of which is modified from a “volume law” to an “area law” after performing a partial, site-wise measurement on the system. These properties and others suggest that this model realizes a new, nonthermal phase of matter, known as a quantum disentangled liquid (QDL). The putative existence of this phase has striking implications for the foundations of quantum statistical mechanics.
1 aGarrison, James, R.1 aMishmash, Ryan, V.1 aFisher, Matthew, P. A. uhttp://link.aps.org/doi/10.1103/PhysRevB.95.05420401001nas a2200109 4500008004100000245006100041210006100102260001500163520065900178100001700837856003700854 2017 eng d00aPenalty models for bitstrings of constant Hamming weight0 aPenalty models for bitstrings of constant Hamming weight c2017/04/243 aTo program a quantum annealer, one must construct objective functions whose minima encode hard constraints imposed by the underlying problem. For such "penalty models," one desires the additional property that the gap in the objective value between such minima and states that fail the constraints is maximized amongst the allowable objective functions. In this short note, we prove the standard penalty model for the constraint that a bitstring has given Hamming weight is optimal with respect to objective value gap.
1 aLackey, Brad uhttps://arxiv.org/abs/1704.0729017147nas a2200181 45000080041000002450100000412100069001412600015002103000011002254900007002365201657700243100001316820700002216833700002716855700001916882700002716901856003716928 2017 eng d00aPendular trapping conditions for ultracold polar molecules enforced by external electric fields0 aPendular trapping conditions for ultracold polar molecules enfor c2017/06/26 a0634220 v953 aWe theoretically investigate trapping conditions for ultracold polar molecules in optical lattices, when external magnetic and electric fields are simultaneously applied. Our results are based on an accurate electronic-structure calculation of the polar
We consider a variant of the phase retrieval problem, where vectors are replaced by unitary matrices, i.e., the unknown signal is a unitary matrix U, and the measurements consist of squared inner products |tr(C†U)|2 with unitary matrices C that are chosen by the observer. This problem has applications to quantum process tomography, when the unknown process is a unitary operation. We show that PhaseLift, a convex programming algorithm for phase retrieval, can be adapted to this matrix setting, using measurements that are sampled from unitary 4- and 2-designs. In the case of unitary 4-design measurements, we show that PhaseLift can reconstruct all unitary matrices, using a nearoptimal number of measurements. This extends previous work on PhaseLift using spherical 4-designs. In the case of unitary 2-design measurements, we show that PhaseLift still works pretty well on average: it recovers almost all signals, up to a constant additive error, using a near-optimal number of measurements. These 2-design measurements are convenient for quantum process tomography, as they can be implemented via randomized benchmarking techniques. This is the first positive result on PhaseLift using 2-designs.
1 aKimmel, Shelby1 aLiu, Yi-Kai uhttp://ieeexplore.ieee.org/document/8024414/01572nas a2200145 4500008004100000245008400041210006900125260001500194300001100209490000700220520112400227100001901351700001901370856003701389 2017 eng d00aPhase-space mixing in dynamically unstable, integrable few-mode quantum systems0 aPhasespace mixing in dynamically unstable integrable fewmode qua c2017/07/05 a0136040 v963 aQuenches in isolated quantum systems are currently a subject of intense study. Here, we consider quantum few-mode systems that are integrable in their classical mean-field limit and become dynamically unstable after a quench of a system parameter. Specifically, we study a Bose-Einstein condensate (BEC) in a double-well potential and an antiferromagnetic spinor BEC constrained to a single spatial mode. We study the time dynamics after the quench within the truncated Wigner approximation (TWA) and find that system relaxes to a steady state due to phase-space mixing. Using the action-angle formalism and a pendulum as an illustration, we derive general analytical expressions for the time evolution of expectation values of observables and their long-time limits. We find that the deviation of the long-time expectation value from its classical value scales as 1/O(ln N), where N is the number of atoms in the condensate. Furthermore, the relaxation of an observable to its steady state value is a damped oscillation and the damping is Gaussian in time. We confirm our results with numerical TWA simulations.
1 aMathew, Ranchu1 aTiesinga, Eite uhttps://arxiv.org/abs/1705.0170201398nas a2200169 4500008004100000245006100041210006000102260001500162520088000177100002701057700001601084700001801100700002601118700002701144700002001171856003701191 2017 eng d00aProvable quantum state tomography via non-convex methods0 aProvable quantum state tomography via nonconvex methods c2017/11/193 aWith nowadays steadily growing quantum processors, it is required to develop new quantum tomography tools that are tailored for high-dimensional systems. In this work, we describe such a computational tool, based on recent ideas from non-convex optimization. The algorithm excels in the compressed-sensing-like setting, where only a few data points are measured from a lowrank or highly-pure quantum state of a high-dimensional system. We show that the algorithm can practically be used in quantum tomography problems that are beyond the reach of convex solvers, and, moreover, is faster than other state-of-the-art non-convex approaches. Crucially, we prove that, despite being a non-convex program, under mild conditions, the algorithm is guaranteed to converge to the global minimum of the problem; thus, it constitutes a provable quantum state tomography protocol.
1 aKyrillidis, Anastasios1 aKalev, Amir1 aPark, Dohuyng1 aBhojanapalli, Srinadh1 aCaramanis, Constantine1 aSanghavi, Sujay uhttps://arxiv.org/abs/1711.0252401440nas a2200121 4500008004100000245010100041210006900142260001500211520101600226100002401242700001601266856003601282 2016 eng d00aPerformance of QAOA on Typical Instances of Constraint Satisfaction Problems with Bounded Degree0 aPerformance of QAOA on Typical Instances of Constraint Satisfact c2016/01/083 aWe consider constraint satisfaction problems of bounded degree, with a good notion of "typicality", e.g. the negation of the variables in each constraint is taken independently at random. Using the quantum approximate optimization algorithm (QAOA), we show that μ+Ω(1/D−−√) fraction of the constraints can be satisfied for typical instances, with the assignment efficiently produced by QAOA. We do so by showing that the averaged fraction of constraints being satisfied is μ+Ω(1/D−−√), with small variance. Here μ is the fraction that would be satisfied by a uniformly random assignment, and D is the number of constraints that each variable can appear. CSPs with typicality include Max-kXOR and Max-kSAT. We point out how it can be applied to determine the typical ground-state energy of some local Hamiltonians. We also give a similar result for instances with "no overlapping constraints", using the quantum algorithm. We sketch how the classical algorithm might achieve some partial result.1 aLin, Cedric, Yen-Yu1 aZhu, Yechao uhttp://arxiv.org/abs/1601.0174401486nas a2200181 4500008004100000245004800041210004800089260001500137300001100152490000700163520100000170100001801170700002101188700002301209700001901232700001701251856003601268 2016 eng d00aPhotoassociation of spin polarized Chromium0 aPhotoassociation of spin polarized Chromium c2016/02/29 a0214060 v933 aWe report the homonuclear photoassociation (PA) of ultracold 52Cr atoms in an optical dipole trap. This constitutes the first measurement of PA in an element with total electron spin S~>1. Although Cr, with its 7S3 ground and 7P4,3,2 excited states, is expected to have a complicated PA spectrum we show that a spin polarized cloud exhibits a remarkably simple PA spectrum when circularly polarized light is applied. Over a scan range of 20 GHz below the 7P3 asymptote we observe two distinct vibrational series each following a LeRoy-Bernstein law for a C3/R3 potential with excellent agreement. We determine the C3 coefficients of the Hund's case c) relativistic adiabatic potentials to be -1.83±0.02 a.u. and -1.46±0.01a.u.. Theoretical non-rotating Movre-Pichler calculations enable a first assignment of the series to Ω=6u and 5g potential energy curves. In a different set of experiments we disturb the selection rules by a transverse magnetic field which leads to additional PA series.1 aRührig, Jahn1 aBäuerle, Tobias1 aJulienne, Paul, S.1 aTiesinga, Eite1 aPfau, Tilman uhttp://arxiv.org/abs/1512.0437801464nas a2200169 4500008004100000022001400041245010200055210006900157260001500226300001400241490000700255520082200262100002301084700001901107700001901126856014901145 2016 eng d a0018-934000aPractical Approximation of Single-Qubit Unitaries by Single-Qubit Quantum Clifford and T Circuits0 aPractical Approximation of SingleQubit Unitaries by SingleQubit c2016/01/01 a161 - 1720 v653 aWe present an algorithm, along with its implementation that finds T-optimal approximations of single-qubit Z-rotations using quantum circuits consisting of Clifford and T gates. Our algorithm is capable of handling errors in approximation down to size 10-15, resulting in the optimal single-qubit circuit designs required for implementation of scalable quantum algorithms. Our implementation along with the experimental results are available in the public domain.
1 aKliuchnikov, Vadym1 aMaslov, Dmitri1 aMosca, Michele uhttp://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7056491http://xplorestaging.ieee.org/ielx7/12/7350319/7056491.pdf?arnumber=705649101933nas a2200277 4500008004100000245007200041210006900113260001500182300001100197490000700208520116900215100001301384700001901397700001401416700001801430700001401448700002501462700002301487700001701510700001701527700002101544700001801565700001401583700002201597856003601619 2016 eng d00aPure-state tomography with the expectation value of Pauli operators0 aPurestate tomography with the expectation value of Pauli operato c2016/03/31 a0321400 v933 aWe examine the problem of finding the minimum number of Pauli measurements needed to uniquely determine an arbitrary n-qubit pure state among all quantum states. We show that only 11 Pauli measurements are needed to determine an arbitrary two-qubit pure state compared to the full quantum state tomography with 16 measurements, and only 31 Pauli measurements are needed to determine an arbitrary three-qubit pure state compared to the full quantum state tomography with 64 measurements. We demonstrate that our protocol is robust under depolarizing error with simulated random pure states. We experimentally test the protocol on two- and three-qubit systems with nuclear magnetic resonance techniques. We show that the pure state tomography protocol saves us a number of measurements without considerable loss of fidelity. We compare our protocol with same-size sets of randomly selected Pauli operators and find that our selected set of Pauli measurements significantly outperforms those random sampling sets. As a direct application, our scheme can also be used to reduce the number of settings needed for pure-state tomography in quantum optical systems.
1 aMa, Xian1 aJackson, Tyler1 aZhou, Hui1 aChen, Jianxin1 aLu, Dawei1 aMazurek, Michael, D.1 aFisher, Kent, A.G.1 aPeng, Xinhua1 aKribs, David1 aResch, Kevin, J.1 aJi, Zhengfeng1 aZeng, Bei1 aLaflamme, Raymond uhttp://arxiv.org/abs/1601.0537901362nas a2200181 4500008004100000245005800041210005800099260001500157300001100172490000800183520083900191100002701030700002101057700002201078700002501100700001701125856003801142 2015 eng d00aParafermionic zero modes in ultracold bosonic systems0 aParafermionic zero modes in ultracold bosonic systems c2015/08/06 a0653010 v1153 a Exotic topologically protected zero modes with parafermionic statistics (also called fractionalized Majorana modes) have been proposed to emerge in devices fabricated from a fractional quantum Hall system and a superconductor. The fractionalized statistics of these modes takes them an important step beyond the simplest non-Abelian anyons, Majorana fermions. Building on recent advances towards the realization of fractional quantum Hall states of bosonic ultracold atoms, we propose a realization of parafermions in a system consisting of Bose-Einstein-condensate trenches within a bosonic fractional quantum Hall state. We show that parafermionic zero modes emerge at the endpoints of the trenches and give rise to a topologically protected degeneracy. We also discuss methods for preparing and detecting these modes. 1 aMaghrebi, Mohammad, F.1 aGaneshan, Sriram1 aClarke, David, J.1 aGorshkov, Alexey, V.1 aSau, Jay, D. uhttp://arxiv.org/abs/1504.04012v201564nas a2200133 4500008004100000245008900041210006900130260001500199300001200214520109500226100001901321700001601340856007401356 2015 eng d00aPhase Retrieval Without Small-Ball Probability Assumptions: Stability and Uniqueness0 aPhase Retrieval Without SmallBall Probability Assumptions Stabil c2015/05/25 a411-4143 aWe study stability and uniqueness for the phase retrieval problem. That is, we ask when is a signal x ∈ R n stably and uniquely determined (up to small perturbations), when one performs phaseless measurements of the form yi = |a T i x| 2 (for i = 1, . . . , N), where the vectors ai ∈ R n are chosen independently at random, with each coordinate aij ∈ R being chosen independently from a fixed sub-Gaussian distribution D. It is well known that for many common choices of D, certain ambiguities can arise that prevent x from being uniquely determined. In this note we show that for any sub-Gaussian distribution D, with no additional assumptions, most vectors x cannot lead to such ambiguities. More precisely, we show stability and uniqueness for all sets of vectors T ⊂ R n which are not too peaky, in the sense that at most a constant fraction of their mass is concentrated on any one coordinate. The number of measurements needed to recover x ∈ T depends on the complexity of T in a natural way, extending previous results of Eldar and Mendelson [12].1 aKrahmer, Felix1 aLiu, Yi-Kai uhttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7148923&tag=101003nas a2200181 4500008004100000245006900041210006800110260001500178300001100193490000800204520048000212100002100692700001700713700001600730700001800746700001900764856003800783 2015 eng d00aPhonon-Assisted Gain in a Semiconductor Double Quantum Dot Maser0 aPhononAssisted Gain in a Semiconductor Double Quantum Dot Maser c2015/05/13 a1968020 v1143 aWe develop a microscopic model for the recently demonstrated double quantum dot (DQD) maser. In characterizing the gain of this device we find that, in addition to the direct stimulated emission of photons, there is a large contribution from the simultaneous emission of a photon and a phonon, i.e., the phonon sideband. We show that this phonon-assisted gain typically dominates the overall gain which leads to masing. Recent experimental data are well fit with our model. 1 aGullans, Michael1 aLiu, Y., -Y.1 aStehlik, J.1 aPetta, J., R.1 aTaylor, J., M. uhttp://arxiv.org/abs/1501.03499v301818nas a2200121 4500008004100000245004200041210003800083260001500121520148500136100002001621700001701641856003801658 2015 eng d00aThe Power of Quantum Fourier Sampling0 aPower of Quantum Fourier Sampling c2015/07/203 a A line of work initiated by Terhal and DiVincenzo and Bremner, Jozsa, and Shepherd, shows that quantum computers can efficiently sample from probability distributions that cannot be exactly sampled efficiently on a classical computer, unless the PH collapses. Aaronson and Arkhipov take this further by considering a distribution that can be sampled efficiently by linear optical quantum computation, that under two feasible conjectures, cannot even be approximately sampled classically within bounded total variation distance, unless the PH collapses. In this work we use Quantum Fourier Sampling to construct a class of distributions that can be sampled by a quantum computer. We then argue that these distributions cannot be approximately sampled classically, unless the PH collapses, under variants of the Aaronson and Arkhipov conjectures. In particular, we show a general class of quantumly sampleable distributions each of which is based on an "Efficiently Specifiable" polynomial, for which a classical approximate sampler implies an average-case approximation. This class of polynomials contains the Permanent but also includes, for example, the Hamiltonian Cycle polynomial, and many other familiar #P-hard polynomials. Although our construction, unlike that proposed by Aaronson and Arkhipov, likely requires a universal quantum computer, we are able to use this additional power to weaken the conjectures needed to prove approximate sampling hardness results. 1 aFefferman, Bill1 aUmans, Chris uhttp://arxiv.org/abs/1507.05592v101473nas a2200181 4500008004100000245003500041210003500076260001500111300001000126490000700136520094600143100002101089700001901110700002001129700002401149700002101173856009701194 2015 eng d00aProgramming the Quantum Future0 aProgramming the Quantum Future c2015/08/01 a52-610 v583 aThe earliest computers, like the ENIAC, were rare and heroically difficult to program. That difficulty stemmed from the requirement that algorithms be expressed in a "vocabulary" suited to the particular hardware available, ranging from function tables for the ENIAC to more conventional arithmetic and movement operations on later machines. Introduction of symbolic programming languages, exemplified by FORTRAN, solved a major difficulty for the next generation of computing devices by enabling specification of an algorithm in a form more suitable for human understanding, then translating this specification to a form executable by the machine. The "programming language" used for such specification bridged a semantic gap between the human and the computing device. It provided two important features: high-level abstractions, taking care of automated bookkeeping, and modularity, making it easier to reason about sub-parts of programs.1 aAlexander, Scott1 aRoss, Neil, J.1 aSelinger, Peter1 aSmith, Jonathan, M.1 aValiron, Benoît uhttp://cacm.acm.org/magazines/2015/8/189851-programming-the-quantum-future/fulltext#comments01518nas a2200133 4500008004100000245005800041210005700099260001500156520111500171100001901286700002001305700002401325856003501349 2014 eng d00aPartial-indistinguishability obfuscation using braids0 aPartialindistinguishability obfuscation using braids c2014/08/213 aAn obfuscator is an algorithm that translates circuits into functionally-equivalent similarly-sized circuits that are hard to understand. Efficient obfuscators would have many applications in cryptography. Until recently, theoretical progress has mainly been limited to no-go results. Recent works have proposed the first efficient obfuscation algorithms for classical logic circuits, based on a notion of indistinguishability against polynomial-time adversaries. In this work, we propose a new notion of obfuscation, which we call partial-indistinguishability. This notion is based on computationally universal groups with efficiently computable normal forms, and appears to be incomparable with existing definitions. We describe universal gate sets for both classical and quantum computation, in which our definition of obfuscation can be met by polynomial-time algorithms. We also discuss some potential applications to testing quantum computers. We stress that the cryptographic security of these obfuscators, especially when composed with translation from other gate sets, remains an open question.
1 aAlagic, Gorjan1 aJeffery, Stacey1 aJordan, Stephen, P. uhttp://arxiv.org/abs/1212.635801399nas a2200157 4500008004100000245006700041210006600108260001400174490000800188520091600196100001901112700002301131700002501154700002501179856003701204 2014 eng d00aPersistence of locality in systems with power-law interactions0 aPersistence of locality in systems with powerlaw interactions c2014/7/160 v1133 a Motivated by recent experiments with ultra-cold matter, we derive a new bound on the propagation of information in $D$-dimensional lattice models exhibiting $1/r^{\alpha}$ interactions with $\alpha>D$. The bound contains two terms: One accounts for the short-ranged part of the interactions, giving rise to a bounded velocity and reflecting the persistence of locality out to intermediate distances, while the other contributes a power-law decay at longer distances. We demonstrate that these two contributions not only bound but, except at long times, \emph{qualitatively reproduce} the short- and long-distance dynamical behavior following a local quench in an $XY$ chain and a transverse-field Ising chain. In addition to describing dynamics in numerous intractable long-range interacting lattice models, our results can be experimentally verified in a variety of ultracold-atomic and solid-state systems. 1 aGong, Zhe-Xuan1 aFoss-Feig, Michael1 aMichalakis, Spyridon1 aGorshkov, Alexey, V. uhttp://arxiv.org/abs/1401.6174v201400nas a2200121 4500008004100000245005500041210005500096260001500151300001200166520104700178100001601225856003701241 2014 eng d00aPrivacy Amplification in the Isolated Qubits Model0 aPrivacy Amplification in the Isolated Qubits Model c2014/10/15 a785-8143 a Isolated qubits are a special class of quantum devices, which can be used to implement tamper-resistant cryptographic hardware such as one-time memories (OTM's). Unfortunately, these OTM constructions leak some information, and standard methods for privacy amplification cannot be applied here, because the adversary has advance knowledge of the hash function that the honest parties will use. In this paper we show a stronger form of privacy amplification that solves this problem, using a fixed hash function that is secure against all possible adversaries in the isolated qubits model. This allows us to construct single-bit OTM's which only leak an exponentially small amount of information. We then study a natural generalization of the isolated qubits model, where the adversary is allowed to perform a polynomially-bounded number of entangling gates, in addition to unbounded local operations and classical communication (LOCC). We show that our technique for privacy amplification is also secure in this setting. 1 aLiu, Yi-Kai uhttp://arxiv.org/abs/1410.3918v200657nas a2200229 4500008004100000245006300041210006200104300000800166490000800174100001400182700002500196700001600221700001700237700001400254700001900268700001300287700001300300700001000313700001600323700001700339856007100356 2014 eng d00aProbing many-body interactions in an optical lattice clock0 aProbing manybody interactions in an optical lattice clock a3110 v3401 aRey, A, M1 aGorshkov, Alexey, V.1 aKraus, C, V1 aMartin, M, J1 aBishof, M1 aSwallows, M, D1 aZhang, X1 aBenko, C1 aYe, J1 aLemke, N, D1 aLudlow, A, D uhttp://www.sciencedirect.com/science/article/pii/S000349161300254601759nas a2200169 4500008004100000245008100041210006900122260001400191490000700205520124300212100002101455700001801476700001901494700002101513700001801534856003701552 2013 eng d00aPreparation of Non-equilibrium Nuclear Spin States in Double Quantum Dots 0 aPreparation of Nonequilibrium Nuclear Spin States in Double Quan c2013/7/150 v883 a We theoretically study the dynamic polarization of lattice nuclear spins in GaAs double quantum dots containing two electrons. In our prior work [Phys. Rev. Lett. 104, 226807 (2010)] we identified three regimes of long-term dynamics, including the build up of a large difference in the Overhauser fields across the dots, the saturation of the nuclear polarization process associated with formation of so-called "dark states," and the elimination of the difference field. In particular, when the dots are different sizes we found that the Overhauser field becomes larger in the smaller dot. Here we present a detailed theoretical analysis of these problems including a model of the polarization dynamics and the development of a new numerical method to efficiently simulate semiclassical central-spin problems. When nuclear spin noise is included, the results agree with our prior work indicating that large difference fields and dark states are stable configurations, while the elimination of the difference field is unstable; however, in the absence of noise we find all three steady states are achieved depending on parameters. These results are in good agreement with dynamic nuclear polarization experiments in double quantum dots. 1 aGullans, Michael1 aKrich, J., J.1 aTaylor, J., M.1 aHalperin, B., I.1 aLukin, M., D. uhttp://arxiv.org/abs/1212.6953v301207nas a2200145 4500008004100000245008800041210006900129260001500198300001100213490000700224520075600231100001900987700001801006856003701024 2013 eng d00aPrethermalization and dynamical transition in an isolated trapped ion spin chain 0 aPrethermalization and dynamical transition in an isolated trappe c2013/11/26 a1130510 v153 a We propose an experimental scheme to observe prethermalization and dynamical transition in one-dimensional XY spin chain with long range interaction and inhomogeneous lattice spacing, which can be readily implemented with the recently developed trapped-ion quantum simulator. Local physical observables are found to relax to prethermal values at intermediate time scale, followed by complete relaxation to thermal values at much longer time. The physical origin of prethermalization is explained by spotting a non-trivial structure in lower half of the energy spectrum. The dynamical behavior of the system is shown to cross difference phases when the interaction range is continuously tuned, indicating the existence of dynamical phase transition. 1 aGong, Zhe-Xuan1 aDuan, L., -M. uhttp://arxiv.org/abs/1305.0985v101289nas a2200145 4500008004100000245005300041210005300094260001500147300001100162490000700173520088500180100002301065700001801088856003701106 2013 eng d00aProduct Formulas for Exponentials of Commutators0 aProduct Formulas for Exponentials of Commutators c2013/02/07 a0622020 v543 a We provide a recursive method for constructing product formula approximations to exponentials of commutators, giving the first approximations that are accurate to arbitrarily high order. Using these formulas, we show how to approximate unitary exponentials of (possibly nested) commutators using exponentials of the elementary operators, and we upper bound the number of elementary exponentials needed to implement the desired operation within a given error tolerance. By presenting an algorithm for quantum search using evolution according to a commutator, we show that the scaling of the number of exponentials in our product formulas with the evolution time is nearly optimal. Finally, we discuss applications of our product formulas to quantum control and to implementing anticommutators, providing new methods for simulating many-body interaction Hamiltonians. 1 aChilds, Andrew, M.1 aWiebe, Nathan uhttp://arxiv.org/abs/1211.4945v201592nas a2200205 4500008004100000245012500041210006900166260001500235520091800250100001801168700002001186700002601206700002001232700001901252700001901271700001801290700002101308700002001329856003701349 2012 eng d00aPhotonic quantum simulation of ground state configurations of Heisenberg square and checkerboard lattice spin systems 0 aPhotonic quantum simulation of ground state configurations of He c2012/05/123 a Photonic quantum simulators are promising candidates for providing insight into other small- to medium-sized quantum systems. The available photonic quantum technology is reaching the state where significant advantages arise for the quantum simulation of interesting questions in Heisenberg spin systems. Here we experimentally simulate such spin systems with single photons and linear optics. The effective Heisenberg-type interactions among individual single photons are realized by quantum interference at the tunable direction coupler followed by the measurement process. The effective interactions are characterized by comparing the entanglement dynamics using pairwise concurrence of a four-photon quantum system. We further show that photonic quantum simulations of generalized Heisenberg interactions on a four-site square lattice and a six-site checkerboard lattice are in reach of current technology. 1 aMa, Xiao-song1 aDakic, Borivoje1 aKropatsche, Sebastian1 aNaylor, William1 aChan, Yang-hao1 aGong, Zhe-Xuan1 aDuan, Lu-ming1 aZeilinger, Anton1 aWalther, Philip uhttp://arxiv.org/abs/1205.2801v101667nas a2200145 4500008004100000245006400041210006200105260001400167490000700181520123200188100002701420700001801447700001901465856003701484 2012 eng d00aPolymer-mediated entropic forces between scale-free objects0 aPolymermediated entropic forces between scalefree objects c2012/12/30 v863 a The number of configurations of a polymer is reduced in the presence of a barrier or an obstacle. The resulting loss of entropy adds a repulsive component to other forces generated by interaction potentials. When the obstructions are scale invariant shapes (such as cones, wedges, lines or planes) the only relevant length scales are the polymer size R_0 and characteristic separations, severely constraining the functional form of entropic forces. Specifically, we consider a polymer (single strand or star) attached to the tip of a cone, at a separation h from a surface (or another cone). At close proximity, such that h<