01576nas a2200181 4500008004100000022001400041245006300055210006100118260001400179300001600193490000600209520107500215100001701290700001701307700001801324700001501342856003701357 2024 eng d a2475-142100aA Case for Synthesis of Recursive Quantum Unitary Programs0 aCase for Synthesis of Recursive Quantum Unitary Programs c12/5/2023 a1759–17880 v83 a

Quantum programs are notoriously difficult to code and verify due to unintuitive quantum knowledge associated with quantum programming. Automated tools relieving the tedium and errors associated with low-level quantum details would hence be highly desirable. In this paper, we initiate the study of program synthesis for quantum unitary programs that recursively define a family of unitary circuits for different input sizes, which are widely used in existing quantum programming languages. Specifically, we present QSynth, the first quantum program synthesis framework, including a new inductive quantum programming language, its specification, a sound logic for reasoning, and an encoding of the reasoning procedure into SMT instances. By leveraging existing SMT solvers, QSynth successfully synthesizes ten quantum unitary programs including quantum adder circuits, quantum eigenvalue inversion circuits and Quantum Fourier Transformation, which can be readily transpiled to executable programs on major quantum platforms, e.g., Q#, IBM Qiskit, and AWS Braket.

1 aDeng, Haowei1 aTao, Runzhou1 aPeng, Yuxiang1 aWu, Xiaodi uhttps://arxiv.org/abs/2311.1150301807nas a2200181 4500008004100000022001400041245003600055210003500091260001400126490000600140520134200146100001501488700002301503700001701526700002401543700002101567856003701588 2024 eng d a2691-339900aClifford-Deformed Surface Codes0 aCliffordDeformed Surface Codes c3/19/20240 v53 a

Various realizations of Kitaev's surface code perform surprisingly well for biased Pauli noise. Attracted by these potential gains, we study the performance of Clifford-deformed surface codes (CDSCs) obtained from the surface code by applying single-qubit Clifford operators. We first analyze CDSCs on the 3×3 square lattice and find that, depending on the noise bias, their logical error rates can differ by orders of magnitude. To explain the observed behavior, we introduce the effective distance d′, which reduces to the standard distance for unbiased noise. To study CDSC performance in the thermodynamic limit, we focus on random CDSCs. Using the statistical mechanical mapping for quantum codes, we uncover a phase diagram that describes random CDSC families with 50% threshold at infinite bias. In the high-threshold region, we further demonstrate that typical code realizations outperform the thresholds and subthreshold logical error rates, at finite bias, of the best-known translationally invariant codes. We demonstrate the practical relevance of these random CDSC families by constructing a translation-invariant CDSC belonging to a high-performance random CDSC family. We also show that our translation-invariant CDSC outperforms well-known translation-invariant CDSCs such as the XZZX and XY codes.

1 aDua, Arpit1 aKubica, Aleksander1 aJiang, Liang1 aFlammia, Steven, T.1 aGullans, Michael uhttps://arxiv.org/abs/2201.0780202447nas a2200169 4500008004100000245005000041210004900091260001300140520194800153100002002101700003302121700002102154700002802175700001702203700002002220856003702240 2024 eng d00aComplexity-constrained quantum thermodynamics0 aComplexityconstrained quantum thermodynamics c3/7/20243 a

Quantum complexity measures the difficulty of realizing a quantum process, such as preparing a state or implementing a unitary. We present an approach to quantifying the thermodynamic resources required to implement a process if the process's complexity is restricted. We focus on the prototypical task of information erasure, or Landauer erasure, wherein an n-qubit memory is reset to the all-zero state. We show that the minimum thermodynamic work required to reset an arbitrary state, via a complexity-constrained process, is quantified by the state's complexity entropy. The complexity entropy therefore quantifies a trade-off between the work cost and complexity cost of resetting a state. If the qubits have a nontrivial (but product) Hamiltonian, the optimal work cost is determined by the complexity relative entropy. The complexity entropy quantifies the amount of randomness a system appears to have to a computationally limited observer. Similarly, the complexity relative entropy quantifies such an observer's ability to distinguish two states. We prove elementary properties of the complexity (relative) entropy and determine the complexity entropy's behavior under random circuits. Also, we identify information-theoretic applications of the complexity entropy. The complexity entropy quantifies the resources required for data compression if the compression algorithm must use a restricted number of gates. We further introduce a complexity conditional entropy, which arises naturally in a complexity-constrained variant of information-theoretic decoupling. Assuming that this entropy obeys a conjectured chain rule, we show that the entropy bounds the number of qubits that one can decouple from a reference system, as judged by a computationally bounded referee. Overall, our framework extends the resource-theoretic approach to thermodynamics to integrate a notion of time, as quantified by complexity.

1 aMunson, Anthony1 aKothakonda, Naga, Bhavya Tej1 aHaferkamp, Jonas1 aHalpern, Nicole, Yunger1 aEisert, Jens1 aFaist, Philippe uhttps://arxiv.org/abs/2403.0482802447nas a2200169 4500008004100000245005000041210004900091260001300140520194800153100002002101700003302121700002102154700002802175700001702203700002002220856003702240 2024 eng d00aComplexity-constrained quantum thermodynamics0 aComplexityconstrained quantum thermodynamics c3/7/20243 a

Quantum complexity measures the difficulty of realizing a quantum process, such as preparing a state or implementing a unitary. We present an approach to quantifying the thermodynamic resources required to implement a process if the process's complexity is restricted. We focus on the prototypical task of information erasure, or Landauer erasure, wherein an n-qubit memory is reset to the all-zero state. We show that the minimum thermodynamic work required to reset an arbitrary state, via a complexity-constrained process, is quantified by the state's complexity entropy. The complexity entropy therefore quantifies a trade-off between the work cost and complexity cost of resetting a state. If the qubits have a nontrivial (but product) Hamiltonian, the optimal work cost is determined by the complexity relative entropy. The complexity entropy quantifies the amount of randomness a system appears to have to a computationally limited observer. Similarly, the complexity relative entropy quantifies such an observer's ability to distinguish two states. We prove elementary properties of the complexity (relative) entropy and determine the complexity entropy's behavior under random circuits. Also, we identify information-theoretic applications of the complexity entropy. The complexity entropy quantifies the resources required for data compression if the compression algorithm must use a restricted number of gates. We further introduce a complexity conditional entropy, which arises naturally in a complexity-constrained variant of information-theoretic decoupling. Assuming that this entropy obeys a conjectured chain rule, we show that the entropy bounds the number of qubits that one can decouple from a reference system, as judged by a computationally bounded referee. Overall, our framework extends the resource-theoretic approach to thermodynamics to integrate a notion of time, as quantified by complexity.

1 aMunson, Anthony1 aKothakonda, Naga, Bhavya Tej1 aHaferkamp, Jonas1 aHalpern, Nicole, Yunger1 aEisert, Jens1 aFaist, Philippe uhttps://arxiv.org/abs/2403.0482801455nas a2200169 4500008004100000245007100041210006900112260001300181300001100194490000700205520093300212100002201145700001801167700002101185700002301206856005601229 2024 eng d00aContinuous-Variable Quantum State Designs: Theory and Applications0 aContinuousVariable Quantum State Designs Theory and Applications c2/8/2024 a0110130 v143 a

We generalize the notion of quantum state designs to infinite-dimensional spaces. We first prove that, under the definition of continuous-variable (CV) state t-designs from [Blume-Kohout et al., Commun. Math. Phys. 326, 755 (2014)], no state designs exist for t≥2. Similarly, we prove that no CV unitary t-designs exist for t≥2. We propose an alternative definition for CV state designs, which we call rigged t-designs, and provide explicit constructions for t = 2. As an application of rigged designs, we develop a design-based shadow-tomography protocol for CV states. Using energy-constrained versions of rigged designs, we define an average fidelity for CV quantum channels and relate this fidelity to the CV entanglement fidelity. As an additional result of independent interest, we establish a connection between torus 2-designs and complete sets of mutually unbiased bases.

1 aIosue, Joseph, T.1 aSharma, Kunal1 aGullans, Michael1 aAlbert, Victor, V. uhttps://link.aps.org/doi/10.1103/PhysRevX.14.01101301489nas a2200133 4500008004100000245007300041210006900114260001300183520106500196100001601261700001601277700002501293856003701318 2023 eng d00aCandidate for a passively protected quantum memory in two dimensions0 aCandidate for a passively protected quantum memory in two dimens c3/2/20233 a

An interesting problem in the field of quantum error correction involves finding a physical system that hosts a ``passively protected quantum memory,'' defined as an encoded qubit coupled to an environment that naturally wants to correct errors. To date, a quantum memory stable against finite-temperature effects is only known in four spatial dimensions or higher. Here, we take a different approach to realize a stable quantum memory by relying on a driven-dissipative environment. We propose a new model, the photonic-Ising model, which appears to passively correct against both bit-flip and phase-flip errors in two dimensions: A square lattice composed of photonic ``cat qubits'' coupled via dissipative terms which tend to fix errors locally. Inspired by the presence of two distinct Z2-symmetry-broken phases, our scheme relies on Ising-like dissipators to protect against bit flips and on a driven-dissipative photonic environment to protect against phase flips. We also discuss possible ways to realize the photonic-Ising model.

1 aLieu, Simon1 aLiu, Yu-Jie1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2205.0976701707nas a2200133 4500008004100000245007300041210006900114260001500183520128600198100001401484700001501498700002301513856003701536 2023 eng d00aClifford operations and homological codes for rotors and oscillators0 aClifford operations and homological codes for rotors and oscilla c11/13/20233 a

We develop quantum information processing primitives for the planar rotor, the state space of a particle on a circle. By interpreting rotor wavefunctions as periodically identified wavefunctions of a harmonic oscillator, we determine the group of bosonic Gaussian operations inherited by the rotor. This n-rotor Clifford group, U(1)n(n+1)/2⋊GLn(Z), is represented by continuous U(1) gates generated by polynomials quadratic in angular momenta, as well as discrete GLn(Z) momentum sign-flip and sum gates. We classify homological rotor error-correcting codes [arXiv:2303.13723] and various rotor states based on equivalence under Clifford operations.
Reversing direction, we map homological rotor codes and rotor Clifford operations back into oscillators by interpreting occupation-number states as rotor states of non-negative angular momentum. This yields new multimode homological bosonic codes protecting against dephasing and changes in occupation number, along with their corresponding encoding and decoding circuits. In particular, we show how to non-destructively measure the oscillator phase using conditional occupation-number addition and post selection. We also outline several rotor and oscillator varieties of the GKP-stabilizer codes [arXiv:1903.12615].

1 aXu, Yijia1 aWang, Yixu1 aAlbert, Victor, V. uhttps://arxiv.org/abs/2311.0767901210nas a2200157 4500008004100000245004000041210003900081260001400120520077300134100002300907700001900930700002300949700002100972700002200993856003701015 2023 eng d00aCollision-resolved pressure sensing0 aCollisionresolved pressure sensing c3/17/20233 a

Heat and pressure are ultimately transmitted via quantized degrees of freedom, like gas particles and phonons. While a continuous Brownian description of these noise sources is adequate to model measurements with relatively long integration times, sufficiently precise measurements can resolve the detailed time dependence coming from individual bath-system interactions. We propose the use of nanomechanical devices operated with impulse readout sensitivity around the ``standard quantum limit'' to sense ultra-low gas pressures by directly counting the individual collisions of gas particles on a sensor. We illustrate this in two paradigmatic model systems: an optically levitated nanobead and a tethered membrane system in a phononic bandgap shield.

1 aBarker, Daniel, S.1 aCarney, Daniel1 aLeBrun, Thomas, W.1 aMoore, David, C.1 aTaylor, Jacob, M. uhttps://arxiv.org/abs/2303.0992201798nas a2200133 4500008004100000245007100041210006900112260001400181490000700195520137900202100002401581700002201605856003701627 2023 eng d00aColloquium: Advances in automation of quantum dot devices control0 aColloquium Advances in automation of quantum dot devices control c2/17/20230 v953 a

Arrays of quantum dots (QDs) are a promising candidate system to realize scalable, coupled qubit systems and serve as a fundamental building block for quantum computers. In such semiconductor quantum systems, devices now have tens of individual electrostatic and dynamical voltages that must be carefully set to localize the system into the single-electron regime and to realize good qubit operational performance. The mapping of requisite QD locations and charges to gate voltages presents a challenging classical control problem. With an increasing number of QD qubits, the relevant parameter space grows sufficiently to make heuristic control unfeasible. In recent years, there has been considerable effort to automate device control that combines script-based algorithms with machine learning (ML) techniques. In this Colloquium, a comprehensive overview of the recent progress in the automation of QD device control is presented, with a particular emphasis on silicon- and GaAs-based QDs formed in two-dimensional electron gases. Combining physics-based modeling with modern numerical optimization and ML has proven effective in yielding efficient, scalable control. Further integration of theoretical, computational, and experimental efforts with computer science and ML holds vast potential in advancing semiconductor and other platforms for quantum computing.

1 aZwolak, Justyna, P.1 aTaylor, Jacob, M. uhttps://arxiv.org/abs/2112.0936201851nas a2200169 4500008004100000245006100041210006000102260001400162520134300176100002501519700001901544700002401563700001801587700001901605700002001624856003701644 2023 eng d00aColloquium: Quantum and Classical Discrete Time Crystals0 aColloquium Quantum and Classical Discrete Time Crystals c5/15/20233 a

The spontaneous breaking of time translation symmetry has led to the discovery of a new phase of matter - the discrete time crystal. Discrete time crystals exhibit rigid subharmonic oscillations, which result from a combination of many-body interactions, collective synchronization, and ergodicity breaking. This Colloquium reviews recent theoretical and experimental advances in the study of quantum and classical discrete time crystals. We focus on the breaking of ergodicity as the key to discrete time crystals and the delaying of ergodicity as the source of numerous phenomena that share many of the properties of discrete time crystals, including the AC Josephson effect, coupled map lattices, and Faraday waves. Theoretically, there exists a diverse array of strategies to stabilize time crystalline order in both closed and open systems, ranging from localization and prethermalization to dissipation and error correction. Experimentally, many-body quantum simulators provide a natural platform for investigating signatures of time crystalline order; recent work utilizing trapped ions, solid-state spin systems, and superconducting qubits will be reviewed. Finally, this Colloquium concludes by describing outstanding challenges in the field and a vision for new directions on both the experimental and theoretical fronts.

1 aZaletel, Michael, P.1 aLukin, Mikhail1 aMonroe, Christopher1 aNayak, Chetan1 aWilczek, Frank1 aYao, Norman, Y. uhttps://arxiv.org/abs/2305.0890401689nas a2200145 4500008004100000245007100041210006900112260001400181520124100195100001501436700001701451700002201468700001601490856003701506 2023 eng d00aComplexity and order in approximate quantum error-correcting codes0 aComplexity and order in approximate quantum errorcorrecting code c10/7/20233 a

We establish rigorous connections between quantum circuit complexity and approximate quantum error correction (AQEC) properties, covering both all-to-all and geometric scenarios including lattice systems. To this end, we introduce a type of code parameter that we call subsystem variance, which is closely related to the optimal AQEC precision. Our key finding is that if the subsystem variance is below an O(k/n) threshold then any state in the code subspace must obey certain circuit complexity lower bounds, which identify nontrivial ``phases'' of codes. Based on our results, we propose O(k/n) as a boundary between subspaces that should and should not count as AQEC codes. This theory of AQEC provides a versatile framework for understanding the quantum complexity and order of many-body quantum systems, offering new insights for wide-ranging physical scenarios, in particular topological order and critical quantum systems which are of outstanding importance in many-body and high energy physics. We observe from various different perspectives that roughly O(1/n) represents a common, physically significant ``scaling threshold'' of subsystem variance for features associated with nontrivial quantum order.

1 aYi, Jinmin1 aYe, Weicheng1 aGottesman, Daniel1 aLiu, Zi-Wen uhttps://arxiv.org/abs/2310.0471002370nas a2200145 4500008004100000245008400041210006900125260001500194520190500209100002102114700001602135700001802151700001802169856003702187 2023 eng d00aCompressed gate characterization for quantum devices with time-correlated noise0 aCompressed gate characterization for quantum devices with timeco c12/22/20233 a

As quantum devices make steady progress towards intermediate scale and fault-tolerant quantum computing, it is essential to develop rigorous and efficient measurement protocols that account for known sources of noise. Most existing quantum characterization protocols such as gate set tomography and randomized benchmarking assume the noise acting on the qubits is Markovian. However, this assumption is often not valid, as for the case of 1/f charge noise or hyperfine nuclear spin noise. Here, we present a general framework for quantum process tomography (QPT) in the presence of time-correlated noise. We further introduce fidelity benchmarks that quantify the relative strength of different sources of Markovian and non-Markovian noise. As an application of our method, we perform a comparative theoretical and experimental analysis of silicon spin qubits. We first develop a detailed noise model that accounts for the dominant sources of noise and validate the model against experimental data. Applying our framework for time-correlated QPT, we find that the number of independent parameters needed to characterize one and two-qubit gates can be compressed by 10x and 100x, respectively, when compared to the fully generic case. These compressions reduce the amount of tomographic measurements needed in experiment, while also significantly speeding up numerical simulations of noisy quantum circuit dynamics compared to time-dependent Hamiltonian simulation. Using this compressed noise model, we find good agreement between our theoretically predicted process fidelities and two qubit interleaved randomized benchmarking fidelities of 99.8% measured in recent experiments on silicon spin qubits. More broadly, our formalism can be directly extended to develop efficient and scalable tuning protocols for high-fidelity control of large-arrays of quantum devices with non-Markovian noise.

1 aGullans, Michael1 aCaranti, M.1 aMills, A., R.1 aPetta, J., R. uhttps://arxiv.org/abs/2307.1443201495nas a2200181 4500008004100000245008500041210006900126260001400195490000800209520092100217100001901138700002101157700002701178700002301205700002001228700002801248856003701276 2023 eng d00aCritical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits0 aCritical phase and spin sharpening in SU2symmetric monitored qua c8/17/20230 v1083 a

Monitored quantum circuits exhibit entanglement transitions at certain measurement rates. Such a transition separates phases characterized by how much information an observer can learn from the measurement outcomes. We study SU(2)-symmetric monitored quantum circuits, using exact numerics and a mapping onto an effective statistical-mechanics model. Due to the symmetry's non-Abelian nature, measuring qubit pairs allows for nontrivial entanglement scaling even in the measurement-only limit. We find a transition between a volume-law entangled phase and a critical phase whose diffusive purification dynamics emerge from the non-Abelian symmetry. Additionally, we numerically identify a "spin-sharpening transition." On one side is a phase in which the measurements can efficiently identify the system's total spin quantum number; on the other side is a phase in which measurements cannot.

1 aMajidy, Shayan1 aAgrawal, Utkarsh1 aGopalakrishnan, Sarang1 aPotter, Andrew, C.1 aVasseur, Romain1 aHalpern, Nicole, Yunger uhttps://arxiv.org/abs/2305.1335601388nas a2200133 4500008004100000245006900041210006800110260001400178520096800192100001601160700001601176700002501192856003701217 2022 eng d00aCandidate for a self-correcting quantum memory in two dimensions0 aCandidate for a selfcorrecting quantum memory in two dimensions c5/19/20223 a

An interesting problem in the field of quantum error correction involves finding a physical system that hosts a "self-correcting quantum memory," defined as an encoded qubit coupled to an environment that naturally wants to correct errors. To date, a quantum memory stable against finite-temperature effects is only known in four spatial dimensions or higher. Here, we take a different approach to realize a stable quantum memory by relying on a driven-dissipative environment. We propose a new model which appears to self correct against both bit-flip and phase-flip errors in two dimensions: A square lattice composed of photonic "cat qubits" coupled via dissipative terms which tend to fix errors locally. Inspired by the presence of two distinct Z2-symmetry-broken phases, our scheme relies on Ising-like dissipators to protect against bit flips and on a driven-dissipative photonic environment to protect against phase flips. 

1 aLieu, Simon1 aLiu, Yu-Jie1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2205.0976701438nas a2200133 4500008004100000245003700041210003700078260001400115520106600129100002401195700002901219700001901248856003701267 2022 eng d00aCertifying Temporal Correlations0 aCertifying Temporal Correlations c6/13/20223 a

Self-testing has been established as a major approach for quantum device certification based on experimental statistics under minimal assumptions. However, despite more than 20 years of research effort most of the self-testing protocols are restricted to spatial scenarios (Bell scenarios), without any temporal generalisations known. Under the scenario of sequential measurements performed on a single quantum system, we build upon previous works which used semi-definite programming (SDP) based methods to bound sequential measurement inequalities. For such SDPs, we show that the optimiser matrix is unique and moreover this uniqueness is robust to small deviations from the quantum bound. Further, we consider a generalised scenario in presence of quantum channels and draw analogies in the structure of Bell and sequential inequalities using the pseudo-density matrix formalism. These analogies allow us to show a practical use of maximal violations of sequential inequalities in the form of certification of quantum channels up to isometries. 

1 aShrotriya, Harshank1 aKwek, Kishor, Bharti Leo1 aBharti, Kishor uhttps://arxiv.org/abs/2206.0609201146nas a2200169 4500008004100000245005900041210005900100260001400159300001100173490000800184520067200192100001900864700001500883700001800898700002300916856003700939 2022 eng d00aChiral central charge from a single bulk wave function0 aChiral central charge from a single bulk wave function c4/28/2022 a1764020 v1283 a

A (2+1)-dimensional gapped quantum many-body system can have a topologically protected energy current at its edge. The magnitude of this current is determined entirely by the temperature and the chiral central charge, a quantity associated with the effective field theory of the edge. We derive a formula for the chiral central charge that, akin to the topological entanglement entropy, is completely determined by the many-body ground state wave function in the bulk. According to our formula, nonzero chiral central charge gives rise to a topological obstruction that prevents the ground state wave function from being real-valued in any local product basis.

1 aKim, Isaac, H.1 aShi, Bowen1 aKato, Kohtaro1 aAlbert, Victor, V. uhttps://arxiv.org/abs/2110.0693202117nas a2200157 4500008004100000245008300041210006900124260001400193490000800207520162900215100002301844700001601867700001801883700002101901856003701922 2022 eng d00aClassification of (2+1)D invertible fermionic topological phases with symmetry0 aClassification of 21D invertible fermionic topological phases wi c5/30/20220 v1053 a

We provide a classification of invertible topological phases of interacting fermions with symmetry in two spatial dimensions for general fermionic symmetry groups Gf and general values of the chiral central charge c−. Here Gf is a central extension of a bosonic symmetry group Gb by fermion parity, (−1)F, specified by a second cohomology class [ω2]∈H2(Gb,Z2). Our approach proceeds by gauging fermion parity and classifying the resulting Gb symmetry-enriched topological orders while keeping track of certain additional data and constraints. We perform this analysis through two perspectives, using G-crossed braided tensor categories and Spin(2c−)1 Chern-Simons theory coupled to a background G gauge field. These results give a way to characterize and classify invertible fermionic topological phases in terms of a concrete set of data and consistency equations, which is more physically transparent and computationally simpler than the more abstract methods using cobordism theory and spectral sequences. Our results also generalize and provide a different approach to the recent classification of fermionic symmetry-protected topological phases by Wang and Gu, which have chiral central charge c−=0. We show how the 10-fold way classification of topological insulators and superconductors fits into our scheme, along with general non-perturbative constraints due to certain choices of c− and Gf. Mathematically, our results also suggest an explicit general parameterization of deformation classes of (2+1)D invertible topological quantum field theories with Gf symmetry. 

1 aBarkeshli, Maissam1 aChen, Yu-An1 aHsin, Po-Shen1 aManjunath, Naren uhttps://arxiv.org/abs/2109.1103902045nas a2200337 4500008004100000245009200041210006900133260001500202300001100217490000800228520091000236100001301146700001301159700001401172700001701186700002001203700001401223700001401237700001601251700001901267700001801286700001701304700002101321700001501342700002001357700001701377700001701394700001801411700001801429856026001447 2022 eng d00aClosing the Locality and Detection Loopholes in Multiparticle Entanglement Self-Testing0 aClosing the Locality and Detection Loopholes in Multiparticle En c06/23/2022 a2504010 v1283 a

First proposed by Mayers and Yao, self-testing provides a certification method to infer the underlying physics of quantum experiments in a black-box scenario. Numerous demonstrations have been reported to self-test various types of entangled states. However, all the multiparticle self-testing experiments reported so far suffer from both detection and locality loopholes. Here, we report the first experimental realization of multiparticle entanglement self-testing closing the locality loophole in a photonic system, and the detection loophole in a superconducting system, respectively. We certify three-party and four-party GHZ states with at least 0.84 (1) and 0.86 (3) fidelities in a device-independent way. These results can be viewed as a meaningful advance in multiparticle loophole-free self-testing, and also significant progress on the foundations of quantum entanglement certification.

1 aWu, Dian1 aZhao, Qi1 aWang, Can1 aHuang, Liang1 aJiang, Yang-Fan1 aBai, Bing1 aZhou, You1 aGu, Xue-Mei1 aLiu, Feng-Ming1 aMao, Ying-Qiu1 aSun, Qi-Chao1 aChen, Ming-Cheng1 aZhang, Jun1 aPeng, Cheng-Zhi1 aZhu, Xiao-Bo1 aZhang, Qiang1 aLu, Chao-Yang1 aPan, Jian-Wei uhttps://www.researchgate.net/profile/Dian-Wu/publication/361497881_Closing_the_Locality_and_Detection_Loopholes_in_Multiparticle_Entanglement_Self-Testing/links/62b55a8c1010dc02cc57530c/Closing-the-Locality-and-Detection-Loopholes-in-Multiparticle-Entangl02685nas a2200253 4500008004100000245007700041210006900118260001400187520182700201653002102028653002702049653004202076653003502118653003002153653003102183653005202214100002302266700001602289700002102305700002202326700003002348700001602378856003702394 2022 eng d00aCodimension-2 defects and higher symmetries in (3+1)D topological phases0 aCodimension2 defects and higher symmetries in 31D topological ph c8/15/20223 a

(3+1)D topological phases of matter can host a broad class of non-trivial topological defects of codimension-1, 2, and 3, of which the well-known point charges and flux loops are special cases. The complete algebraic structure of these defects defines a higher category, and can be viewed as an emergent higher symmetry. This plays a crucial role both in the classification of phases of matter and the possible fault-tolerant logical operations in topological quantum error correcting codes. In this paper, we study several examples of such higher codimension defects from distinct perspectives. We mainly study a class of invertible codimension-2 topological defects, which we refer to as twist strings. We provide a number of general constructions for twist strings, in terms of gauging lower dimensional invertible phases, layer constructions, and condensation defects. We study some special examples in the context of Z2 gauge theory with fermionic charges, in Z2×Z2 gauge theory with bosonic charges, and also in non-Abelian discrete gauge theories based on dihedral (Dn) and alternating (A6) groups. The intersection between twist strings and Abelian flux loops sources Abelian point charges, which defines an H4 cohomology class that characterizes part of an underlying 3-group symmetry of the topological order. The equations involving background gauge fields for the 3-group symmetry have been explicitly written down for various cases. We also study examples of twist strings interacting with non-Abelian flux loops (defining part of a non-invertible higher symmetry), examples of non-invertible codimension-2 defects, and examples of interplay of codimension-2 defects with codimension-1 defects. We also find an example of geometric, not fully topological, twist strings in (3+1)D A6 gauge theory.

10aFOS: Mathematics10aFOS: Physical sciences10aHigh Energy Physics - Theory (hep-th)10aMathematical Physics (math-ph)10aQuantum Algebra (math.QA)10aQuantum Physics (quant-ph)10aStrongly Correlated Electrons (cond-mat.str-el)1 aBarkeshli, Maissam1 aChen, Yu-An1 aHuang, Sheng-Jie1 aKobayashi, Ryohei1 aTantivasadakarn, Nathanan1 aZhu, Guanyu uhttps://arxiv.org/abs/2208.0736701635nas a2200181 4500008004100000245010500041210006900146260001500215300001200230490000600242520106000248100001801308700002001326700002501346700002101371700002401392856003701416 2022 eng d00aCombining machine learning with physics: A framework for tracking and sorting multiple dark solitons0 aCombining machine learning with physics A framework for tracking c06/01/2022 a023163 0 v43 a

In ultracold-atom experiments, data often comes in the form of images which suffer information loss inherent in the techniques used to prepare and measure the system. This is particularly problematic when the processes of interest are complicated, such as interactions among excitations in Bose-Einstein condensates (BECs). In this paper, we describe a framework combining machine learning (ML) models with physics-based traditional analyses to identify and track multiple solitonic excitations in images of BECs. We use an ML-based object detector to locate the solitonic excitations and develop a physics-informed classifier to sort solitonic excitations into physically motivated subcategories. Lastly, we introduce a quality metric quantifying the likelihood that a specific feature is a longitudinal soliton. Our trained implementation of this framework, SolDet, is publicly available as an open-source python package. SolDet is broadly applicable to feature identification in cold-atom images when trained on a suitable user-provided dataset.

1 aGuo, Shangjie1 aKoh, Sophia, M.1 aFritsch, Amilson, R.1 aSpielman, I., B.1 aZwolak, Justyna, P. uhttps://arxiv.org/abs/2111.0488101130nas a2200121 4500008004100000245005500041210005500096260001300151520076600164100002400930700001700954856003700971 2022 eng d00aComputational advantage of quantum random sampling0 aComputational advantage of quantum random sampling c6/8/20223 a

Quantum random sampling is the leading proposal for demonstrating a computational advantage of quantum computers over classical computers. Recently, first large-scale implementations of quantum random sampling have arguably surpassed the boundary of what can be simulated on existing classical hardware. In this article, we comprehensively review the theoretical underpinning of quantum random sampling in terms of computational complexity and verifiability, as well as the practical aspects of its experimental implementation using superconducting and photonic devices and its classical simulation. We discuss in detail open questions in the field and provide perspectives for the road ahead, including potential applications of quantum random sampling.

1 aHangleiter, Dominik1 aEisert, Jens uhttps://arxiv.org/abs/2206.0407901667nas a2200157 4500008004100000245007000041210006800111260001400179520117400193653002701367653003101394100001601425700001801441700001301459856003701472 2022 eng d00aComputational self-testing of multi-qubit states and measurements0 aComputational selftesting of multiqubit states and measurements c1/31/20223 a

Self-testing is a fundamental technique within quantum information theory 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 standard computational assumptions. In this work, we generalize their techniques to give the first protocol that self-tests N EPR pairs and measurements 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, a simplified version of our protocol is the first that can efficiently certify an arbitrary number of qubits of a cloud quantum computer, on which we cannot enforce spatial separation, using only classical communication.

10aFOS: Physical sciences10aQuantum Physics (quant-ph)1 aFu, Honghao1 aWang, Daochen1 aZhao, Qi uhttps://arxiv.org/abs/2201.1343001123nas a2200133 4500008004100000245012100041210006900162260001500231300000800246490000600254520067600260100001600936856003700952 2022 eng d00aConstant-sized correlations are sufficient to robustly self-test maximally entangled states with unbounded dimension0 aConstantsized correlations are sufficient to robustly selftest m c01/03/2022 a6140 v63 a

We show that for any prime odd integer d, there exists a correlation of size Θ(r) that can robustly self-test a maximally entangled state of dimension 4d−4, where r is the smallest multiplicative generator of Z∗d. The construction of the correlation uses the embedding procedure proposed by Slofstra (Forum of Mathematics, Pi. Vol. 7, (2019)). Since there are infinitely many prime numbers whose smallest multiplicative generator is at most 5 (M. Murty The Mathematical Intelligencer 10.4 (1988)), our result implies that constant-sized correlations are sufficient for robust self-testing of maximally entangled states with unbounded local dimension.

1 aFu, Honghao uhttps://arxiv.org/abs/1911.0149401840nas a2200253 4500008004100000245006100041210006000102260001400162520102500176653002701201653003901228653003101267653004701298653005201345100001401397700001301411700001701424700002301441700002501464700001801489700001801507700002401525856003701549 2022 eng d00aContinuous Symmetry Breaking in a Trapped-Ion Spin Chain0 aContinuous Symmetry Breaking in a TrappedIon Spin Chain c11/2/20223 a

One-dimensional systems exhibiting a continuous symmetry can host quantum phases of matter with true long-range order only in the presence of sufficiently long-range interactions. In most physical systems, however, the interactions are short-ranged, hindering the emergence of such phases in one dimension. Here we use a one-dimensional trapped-ion quantum simulator to prepare states with long-range spin order that extends over the system size of up to 23 spins and is characteristic of the continuous symmetry-breaking phase of matter. Our preparation relies on simultaneous control over an array of tightly focused individual-addressing laser beams, generating long-range spin-spin interactions. We also observe a disordered phase with frustrated correlations. We further study the phases at different ranges of interaction and the out-of-equilibrium response to symmetry-breaking perturbations. This work opens an avenue to study new quantum phases and out-of-equilibrium dynamics in low-dimensional systems.

10aFOS: Physical sciences10aQuantum Gases (cond-mat.quant-gas)10aQuantum Physics (quant-ph)10aStatistical Mechanics (cond-mat.stat-mech)10aStrongly Correlated Electrons (cond-mat.str-el)1 aFeng, Lei1 aKatz, Or1 aHaack, Casey1 aMaghrebi, Mohammad1 aGorshkov, Alexey, V.1 aGong, Zhexuan1 aCetina, Marko1 aMonroe, Christopher uhttps://arxiv.org/abs/2211.0127501776nas a2200181 4500008004100000245004200041210004100083260001400124520125200138653002701390653003101417100002301448700002301471700002001494700002201514700002101536856003701557 2022 eng d00aContinuous-Variable Shadow Tomography0 aContinuousVariable Shadow Tomography c11/9/20223 a

Shadow tomography is a framework for constructing succinct descriptions of quantum states, called classical shadows, with powerful methods to bound the estimators used. We recast existing experimental protocols for continuous-variable tomography in the classical-shadow framework, obtaining rigorous bounds on the sample complexity 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(N5) 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.

10aFOS: Physical sciences10aQuantum Physics (quant-ph)1 aGandhari, Srilekha1 aAlbert, Victor, V.1 aGerrits, Thomas1 aTaylor, Jacob, M.1 aGullans, Michael uhttps://arxiv.org/abs/2211.0514901748nas a2200133 4500008004100000245008100041210006900122260001400191520131400205100001601519700002701535700001501562856003701577 2022 eng d00aA Convergence Theory for Over-parameterized Variational Quantum Eigensolvers0 aConvergence Theory for Overparameterized Variational Quantum Eig c5/25/20223 a

The Variational Quantum Eigensolver (VQE) is a promising candidate for quantum applications on near-term Noisy Intermediate-Scale Quantum (NISQ) computers. Despite a lot of empirical studies and recent progress in theoretical understanding of VQE's optimization landscape, the convergence for optimizing VQE is far less understood. We provide the first rigorous analysis of the convergence of VQEs in the over-parameterization regime. By connecting the training dynamics with the Riemannian Gradient Flow on the unit-sphere, we establish a threshold on the sufficient number of parameters for efficient convergence, which depends polynomially on the system dimension and the spectral ratio, a property of the problem Hamiltonian, and could be resilient to gradient noise to some extent. We further illustrate that this overparameterization threshold could be vastly reduced for specific VQE instances by establishing an ansatz-dependent threshold paralleling our main result. We showcase that our ansatz-dependent threshold could serve as a proxy of the trainability of different VQE ansatzes without performing empirical experiments, which hence leads to a principled way of evaluating ansatz design. Finally, we conclude with a comprehensive empirical study that supports our theoretical findings

1 aYou, Xuchen1 aChakrabarti, Shouvanik1 aWu, Xiaodi uhttps://arxiv.org/abs/2205.1248101282nas a2200181 4500008004100000245008800041210006900129260001300198520068100211653002700892653003100919100002900950700002000979700001900999700002201018700002301040856003701063 2022 eng d00aConvex optimization for non-equilibrium steady states on a hybrid quantum processor0 aConvex optimization for nonequilibrium steady states on a hybrid c4/7/20223 a

Finding the transient and steady state properties of open quantum systems is a central problem in various fields of quantum technologies. Here, we present a quantum-assisted algorithm to determine the steady states of open system dynamics. By reformulating the problem of finding the fixed point of Lindblad dynamics as a feasibility semi-definite program, we bypass several well known issues with variational quantum approaches to solving for steady states. We demonstrate that our hybrid approach allows us to estimate the steady states of higher dimensional open quantum systems and discuss how our method can find multiple steady states for systems with symmetries.

10aFOS: Physical sciences10aQuantum Physics (quant-ph)1 aLau, Jonathan, Wei Zhong1 aLim, Kian, Hwee1 aBharti, Kishor1 aKwek, Leong-Chuan1 aVinjanampathy, Sai uhttps://arxiv.org/abs/2204.0320302302nas a2200277 4500008004100000245004100041210004000082260001300122520150700135653003401642653003801676653001601714653004301730653001301773100002101786700001701807700001901824700002001843700002301863700001901886700002501905700002001930700001701950700002001967856003701987 2022 eng d00aCoVault: A Secure Analytics Platform0 aCoVault A Secure Analytics Platform c8/7/20223 a

In a secure analytics platform, data sources consent to the exclusive use of their data for a pre-defined set of analytics queries performed by a specific group of analysts, and for a limited period. If the platform is secure under a sufficiently strong threat model, it can provide the missing link to enabling powerful analytics of sensitive personal data, by alleviating data subjects' concerns about leakage and misuse of data. For instance, many types of powerful analytics that benefit public health, mobility, infrastructure, finance, or sustainable energy can be made differentially private, thus alleviating concerns about privacy. However, no platform currently exists that is sufficiently secure to alleviate concerns about data leakage and misuse; as a result, many types of analytics that would be in the interest of data subjects and the public are not done. CoVault uses a new multi-party implementation of functional encryption (FE) for secure analytics, which relies on a unique combination of secret sharing, multi-party secure computation (MPC), and different trusted execution environments (TEEs). CoVault is secure under a very strong threat model that tolerates compromise and side-channel attacks on any one of a small set of parties and their TEEs. Despite the cost of MPC, we show that CoVault scales to very large data sizes using map-reduce based query parallelization. For example, we show that CoVault can perform queries relevant to epidemic analytics at scale.

10aand Cluster Computing (cs.DC)10aCryptography and Security (cs.CR)10aDistributed10aFOS: Computer and information sciences10aParallel1 aDe Viti, Roberta1 aSheff, Isaac1 aGlaeser, Noemi1 aDinis, Baltasar1 aRodrigues, Rodrigo1 aKatz, Jonathan1 aBhattacharjee, Bobby1 aHithnawi, Anwar1 aGarg, Deepak1 aDruschel, Peter uhttps://arxiv.org/abs/2208.0378402266nas a2200133 4500008004100000245003400041210003300075260001400108520190700122100001902029700002502048700002202073856003702095 2021 eng d00aCan you sign a quantum state?0 aCan you sign a quantum state c12/6/20213 a

Cryptography with quantum states exhibits a number of surprising and counterintuitive features. In a 2002 work, Barnum et al. argued informally that these strange features should imply that digital signatures for quantum states are impossible (Barnum et al., FOCS 2002). In this work, we perform the first rigorous study of the problem of signing quantum states. We first show that the intuition of Barnum et al. was correct, by proving an impossibility result which rules out even very weak forms of signing quantum states. Essentially, we show that any non-trivial combination of correctness and security requirements results in negligible security. This rules out all quantum signature schemes except those which simply measure the state and then sign the outcome using a classical scheme. In other words, only classical signature schemes exist. We then show a positive result: it is possible to sign quantum states, provided that they are also encrypted with the public key of the intended recipient. Following classical nomenclature, we call this notion quantum signcryption. Classically, signcryption is only interesting if it provides superior efficiency to simultaneous encryption and signing. Our results imply that, quantumly, it is far more interesting: by the laws of quantum mechanics, it is the only signing method available. We develop security definitions for quantum signcryption, ranging from a simple one-time two-user setting, to a chosen-ciphertext-secure many-time multi-user setting. We also give secure constructions based on post-quantum public-key primitives. Along the way, we show that a natural hybrid method of combining classical and quantum schemes can be used to "upgrade" a secure classical scheme to the fully-quantum setting, in a wide range of cryptographic settings including signcryption, authenticated encryption, and chosen-ciphertext security.

1 aAlagic, Gorjan1 aGagliardoni, Tommaso1 aMajenz, Christian uhttps://arxiv.org/abs/1811.1185801979nas a2200277 4500008004100000245007600041210006900117260001400186520117400200100001301374700001801387700002101405700002901426700001601455700002001471700001801491700001501509700002001524700002301544700001801567700002101585700001801606700002101624700001901645856003701664 2021 eng d00aChiral transport of hot carriers in graphene in the quantum Hall regime0 aChiral transport of hot carriers in graphene in the quantum Hall c10/3/20213 a

Photocurrent (PC) measurements can reveal the relaxation dynamics of photo-excited hot carriers beyond the linear response of conventional transport experiments, a regime important for carrier multiplication. In graphene subject to a magnetic field, PC measurements are able to probe the existence of Landau levels with different edge chiralities which is exclusive to relativistic electron systems. Here, we report the accurate measurement of PC in graphene in the quantum Hall regime. Prominent PC oscillations as a function of gate voltage on samples' edges are observed. These oscillation amplitudes form an envelope which depends on the strength of the magnetic field, as does the PCs' power dependence and their saturation behavior. We explain these experimental observations through a model using optical Bloch equations, incorporating relaxations through acoustic-, optical- phonons and Coulomb interactions. The simulated PC agrees with our experimental results, leading to a unified understanding of the chiral PC in graphene at various magnetic field strengths, and providing hints for the occurrence of a sizable carrier multiplication. 

1 aCao, Bin1 aGrass, Tobias1 aGazzano, Olivier1 aPatel, Kishan, Ashokbhai1 aHu, Jiuning1 aMüller, Markus1 aHuber, Tobias1 aAnzi, Luca1 aWatanabe, Kenji1 aTaniguchi, Takashi1 aNewell, David1 aGullans, Michael1 aSordan, Roman1 aHafezi, Mohammad1 aSolomon, Glenn uhttps://arxiv.org/abs/2110.0107901867nas a2200157 4500008004100000245010800041210006900149260001400218520132800232100002401560700002001584700001901604700002401623700002501647856003701672 2021 eng d00aCircuit Quantum Electrodynamics in Hyperbolic Space: From Photon Bound States to Frustrated Spin Models0 aCircuit Quantum Electrodynamics in Hyperbolic Space From Photon  c5/13/20213 a

Circuit quantum electrodynamics is one of the most promising platforms for efficient quantum simulation and computation. In recent groundbreaking experiments, the immense flexibility of superconducting microwave resonators was utilized to realize hyperbolic lattices that emulate quantum physics in negatively curved space. Here we investigate experimentally feasible settings in which a few superconducting qubits are coupled to a bath of photons evolving on the hyperbolic lattice. We compare our numerical results for finite lattices with analytical results for continuous hyperbolic space on the Poincaré disk. We find good agreement between the two descriptions in the long-wavelength regime. We show that photon-qubit bound states have a curvature-limited size. We propose to use a qubit as a local probe of the hyperbolic bath, for example by measuring the relaxation dynamics of the qubit. We find that, although the boundary effects strongly impact the photonic density of states, the spectral density is well described by the continuum theory. We show that interactions between qubits are mediated by photons propagating along geodesics. We demonstrate that the photonic bath can give rise to geometrically-frustrated hyperbolic quantum spin models with finite-range or exponentially-decaying interaction.

1 aBienias, Przemyslaw1 aBoettcher, Igor1 aBelyansky, Ron1 aKollár, Alicia, J.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2105.0649001456nas a2200145 4500008004100000245007500041210006900116260001400185300001100199490000600210520101600216100002201232700001901254856003701273 2021 eng d00aCirculation by microwave-induced vortex transport for signal isolation0 aCirculation by microwaveinduced vortex transport for signal isol c6/14/2021 a0303090 v23 a

Magnetic fields break time-reversal symmetry, which is leveraged in many settings to enable the nonreciprocal behavior of light. This is the core physics of circulators and other elements used in a variety of microwave and optical settings. Commercial circulators in the microwave domain typically use ferromagnetic materials and wave interference, requiring large devices and large fields. However, quantum information devices for sensing and computation require small sizes, lower fields, and better on-chip integration. Equivalences to ferromagnetic order---such as the XY model---can be realized at much lower magnetic fields by using arrays of superconducting islands connected by Josephson junctions. Here we show that the quantum-coherent motion of a single vortex in such an array suffices to induce nonreciprocal behavior, enabling a small-scale, moderate-bandwidth, and low insertion loss circulator at very low magnetic fields and at microwave frequencies relevant for experiments with qubits.

1 aRichman, Brittany1 aTaylor, J., M. uhttps://arxiv.org/abs/2010.0411801670nas a2200145 4500008004100000245008900041210006900130260001500199520119300214100002001407700001601427700001901443700002501462856003701487 2021 eng d00aClustering of steady-state correlations in open systems with long-range interactions0 aClustering of steadystate correlations in open systems with long c10/28/20213 a

Lieb-Robinson bounds are powerful analytical tools for constraining the dynamic and static properties of non-relativistic quantum systems. Recently, a complete picture for closed systems that evolve unitarily in time has been achieved. In experimental systems, however, interactions with the environment cannot generally be ignored, and the extension of Lieb-Robinson bounds to dissipative systems which evolve non-unitarily in time remains an open challenge. In this work, we prove two Lieb-Robinson bounds that constrain the dynamics of open quantum systems with long-range interactions that decay as a power-law in the distance between particles. Using a combination of these Lieb-Robinson bounds and mixing bounds which arise from "reversibility" -- naturally satisfied for thermal environments -- we prove the clustering of correlations in the steady states of open quantum systems with long-range interactions. Our work provides an initial step towards constraining the steady-state entanglement structure for a broad class of experimental platforms, and we highlight several open directions regarding the application of Lieb-Robinson bounds to dissipative systems.

1 aGuo, Andrew, Y.1 aLieu, Simon1 aTran, Minh, C.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2110.1536800790nas a2200133 4500008004100000245009400041210006900135260001400204520034000218100001900558700002000577700002200597856003700619 2021 eng d00aComment on "Using an atom interferometer to infer gravitational entanglement generation''0 aComment on Using an atom interferometer to infer gravitational e c11/8/20213 a

Our paper arXiv:2101.11629 contains a technical error which changes some of the conclusions. We thank Streltsov, Pedernales, and Plenio for bringing the essence of this error to our attention. Here we explain the error, examine its consequences, and suggest methods to overcome the resulting weakness in the proposed experiment.

1 aCarney, Daniel1 aMüller, Holger1 aTaylor, Jacob, M. uhttps://arxiv.org/abs/2111.0466701434nas a2200169 4500008004100000022001400041245009100055210006900146260001400215490000600229520089000235100001801125700002301143700002301166700002501189856005001214 2021 eng d a2691-339900aComplexity of Fermionic Dissipative Interactions and Applications to Quantum Computing0 aComplexity of Fermionic Dissipative Interactions and Application c9/17/20210 v23 a

Interactions between particles are usually a resource for quantum computing, making quantum many-body systems intractable by any known classical algorithm. In contrast, noise is typically considered as being inimical to quantum many-body correlations, ultimately leading the system to a classically tractable state. This work shows that noise represented by two-body processes, such as pair loss, plays the same role as many-body interactions and makes otherwise classically simulable systems universal for quantum computing. We analyze such processes in detail and establish a complexity transition between simulable and nonsimulable systems as a function of a tuning parameter. We determine important classes of simulable and nonsimulable two-body dissipation. Finally, we show how using resonant dissipation in cold atoms can enhance the performance of two-qubit gates. 

1 aShtanko, Oles1 aDeshpande, Abhinav1 aJulienne, Paul, S.1 aGorshkov, Alexey, V. uhttp://dx.doi.org/10.1103/PRXQuantum.2.03035002086nas a2200133 4500008004100000245006600041210006500107260001400172520167400186100001801860700002101878700001601899856003701915 2021 eng d00aCompressed Sensing Measurement of Long-Range Correlated Noise0 aCompressed Sensing Measurement of LongRange Correlated Noise c5/26/20213 a

Long-range correlated errors can severely impact the performance of NISQ (noisy intermediate-scale quantum) devices, and fault-tolerant quantum computation. Characterizing these errors is important for improving the performance of these devices, via calibration and error correction, and to ensure correct interpretation of the results. We propose a compressed sensing method for detecting two-qubit correlated dephasing errors, assuming only that the correlations are sparse (i.e., at most s pairs of qubits have correlated errors, where s << n(n-1)/2, and n is the total number of qubits). In particular, our method can detect long-range correlations between any two qubits in the system (i.e., the correlations are not restricted to be geometrically local).
Our method is highly scalable: it requires as few as m = O(s log n) measurement settings, and efficient classical postprocessing based on convex optimization. In addition, when m = O(s log^4(n)), our method is highly robust to noise, and has sample complexity O(max(n,s)^2 log^4(n)), which can be compared to conventional methods that have sample complexity O(n^3). Thus, our method is advantageous when the correlations are sufficiently sparse, that is, when s < O(n^(3/2) / log^2(n)). Our method also performs well in numerical simulations on small system sizes, and has some resistance to state-preparation-and-measurement (SPAM) errors. The key ingredient in our method is a new type of compressed sensing measurement, which works by preparing entangled Greenberger-Horne-Zeilinger states (GHZ states) on random subsets of qubits, and measuring their decay rates with high precision.

1 aSeif, Alireza1 aHafezi, Mohammad1 aLiu, Yi-Kai uhttps://arxiv.org/abs/2105.1258901258nas a2200157 4500008004100000245004100041210004100082260001400123300001100137490000800148520084100156100003000997700001701027700001901044856003701063 2021 eng d00aConformal field theories are magical0 aConformal field theories are magical c2/25/2021 a0751450 v1033 a

"Magic" is the degree to which a state cannot be approximated by Clifford gates. We study mana, a measure of magic, in the ground state of the Z3 Potts model, and argue that it is a broadly useful diagnostic for many-body physics. In particular we find that the q=3 ground state has large mana at the model's critical point, and that this mana resides in the system's correlations. We explain the form of the mana by a simple tensor-counting calculation based on a MERA representation of the state. Because mana is present at all length scales, we conclude that the conformal field theory describing the 3-state Potts model critical point is magical. These results control the difficulty of preparing the Potts ground state on an error-corrected quantum computer, and constrain tensor network models of AdS-CFT.

1 aWhite, Christopher, David1 aCao, ChunJun1 aSwingle, Brian uhttps://arxiv.org/abs/2007.0130301165nas a2200133 4500008004100000245007500041210006900116260001500185520072600200100002600926700002100952700002100973856003700994 2021 eng d00aConstructing quantum many-body scar Hamiltonians from Floquet automata0 aConstructing quantum manybody scar Hamiltonians from Floquet aut c12/22/20213 a

We provide a systematic approach for constructing approximate quantum many-body scars(QMBS) starting from two-layer Floquet automaton circuits that exhibit trivial many-body revivals. We do so by applying successively more restrictions that force local gates of the automaton circuit to commute concomitantly more accurately when acting on select scar states. With these rules in place, an effective local, Floquet Hamiltonian is seen to capture dynamics of the automata over a long prethermal window, and neglected terms can be used to estimate the relaxation of revivals. We provide numerical evidence for such a picture and use our construction to derive several QMBS models, including the celebrated PXP model.

1 aRozon, Pierre-Gabriel1 aGullans, Michael1 aAgarwal, Kartiek uhttps://arxiv.org/abs/2112.1215301894nas a2200301 4500008004100000245006400041210006300105260001400168520102800182100001601210700001701226700001801243700002101261700002201282700001601304700001701320700002201337700003001359700002201389700001901411700002101430700001801451700001801469700002301487700002101510700002401531856003701555 2021 eng d00aCross-Platform Comparison of Arbitrary Quantum Computations0 aCrossPlatform Comparison of Arbitrary Quantum Computations c7/27/20213 a

As we approach the era of quantum advantage, when quantum computers (QCs) can outperform any classical computer on particular tasks, there remains the difficult challenge of how to validate their performance. While algorithmic success can be easily verified in some instances such as number factoring or oracular algorithms, these approaches only provide pass/fail information for a single QC. On the other hand, a comparison between different QCs on the same arbitrary circuit provides a lower-bound for generic validation: a quantum computation is only as valid as the agreement between the results produced on different QCs. Such an approach is also at the heart of evaluating metrological standards such as disparate atomic clocks. In this paper, we report a cross-platform QC comparison using randomized and correlated measurements that results in a wealth of information on the QC systems. We execute several quantum circuits on widely different physical QC platforms and analyze the cross-platform fidelities.

1 aZhu, Daiwei1 aCian, Ze-Pei1 aNoel, Crystal1 aRisinger, Andrew1 aBiswas, Debopriyo1 aEgan, Laird1 aZhu, Yingyue1 aGreen, Alaina, M.1 aAlderete, Cinthia, Huerta1 aNguyen, Nhung, H.1 aWang, Qingfeng1 aMaksymov, Andrii1 aNam, Yunseong1 aCetina, Marko1 aLinke, Norbert, M.1 aHafezi, Mohammad1 aMonroe, Christopher uhttps://arxiv.org/abs/2107.1138702085nas a2200169 4500008004100000245004300041210004300084260001300127520161100140100002001751700002501771700002401796700002101820700001801841700001901859856003701878 2021 eng d00aCrystallography of Hyperbolic Lattices0 aCrystallography of Hyperbolic Lattices c5/3/20213 a

Hyperbolic lattices are a revolutionary platform for tabletop simulations of holography and quantum physics in curved space and facilitate efficient quantum error correcting codes. Their underlying geometry is non-Euclidean, and the absence of Bloch's theorem precludes a simple understanding of their band structure. Motivated by recent insights into hyperbolic band theory, we initiate a crystallography of hyperbolic lattices. We show that many hyperbolic lattices feature a hidden crystal structure characterized by unit cells, hyperbolic Bravais lattices, and associated symmetry groups. Using the mathematical framework of higher-genus Riemann surfaces and Fuchsian groups, we derive, for the first time, a list of example hyperbolic {p,q} lattices and their hyperbolic Bravais lattices, including five infinite families and several graphs relevant for experiments in circuit quantum electrodynamics and topolectrical circuits. Our results find application for both finite and infinite hyperbolic lattices. We describe a method to efficiently generate finite hyperbolic lattices of arbitrary size and explain why the present crystallography is the first step towards a complete band theory of hyperbolic lattices and apply it to construct Bloch wave Hamiltonians. This work lays the foundation for generalizing some of the most powerful concepts of solid state physics, such as crystal momentum and Brillouin zone, to the emerging field of hyperbolic lattices and tabletop simulations of gravitational theories, and reveals the connections to concepts from topology and algebraic geometry.

1 aBoettcher, Igor1 aGorshkov, Alexey, V.1 aKollár, Alicia, J.1 aMaciejko, Joseph1 aRayan, Steven1 aThomale, Ronny uhttps://arxiv.org/abs/2105.0108701616nas a2200121 4500008004100000245005900041210005800100260001400158520124400172100002301416700001801439856003701457 2020 eng d00aCan graph properties have exponential quantum speedup?0 aCan graph properties have exponential quantum speedup c1/28/20203 a

Quantum computers can sometimes exponentially outperform classical ones, but only for problems with sufficient structure. While it is well known that query problems with full permutation symmetry can have at most polynomial quantum speedup -- even for partial functions -- it is unclear how far this condition must be relaxed to enable exponential speedup. In particular, it is natural to ask whether exponential speedup is possible for (partial) graph properties, in which the input describes a graph and the output can only depend on its isomorphism class. We show that the answer to this question depends strongly on the input model. In the adjacency matrix model, we prove that the bounded-error randomized query complexity R of any graph property P has R(P)=O(Q(P)6), where Q is the bounded-error quantum query complexity. This negatively resolves an open question of Montanaro and de Wolf in the adjacency matrix model. More generally, we prove R(P)=O(Q(P)3l) for any l-uniform hypergraph property P in the adjacency matrix model. In direct contrast, in the adjacency list model for bounded-degree graphs, we exhibit a promise problem that shows an exponential separation between the randomized and quantum query complexities.

1 aChilds, Andrew, M.1 aWang, Daochen uhttps://arxiv.org/abs/2001.1052001526nas a2200133 4500008004100000245011300041210006900154260001400223520105400237100002001291700002001311700002401331856003701355 2020 eng d00aThe Character of Motional Modes for Entanglement and Sympathetic Cooling of Mixed-Species Trapped Ion Chains0 aCharacter of Motional Modes for Entanglement and Sympathetic Coo c4/16/20203 a

Modular mixed-species ion-trap networks are a promising framework for scalable quantum information processing, where one species acts as a memory qubit and another as a communication qubit. This architecture requires high-fidelity mixed-species entangling gates to transfer information from communication to memory qubits through their collective motion. We investigate the character of the motional modes of a mixed-species ion chain for entangling operations and also sympathetic cooling. We find that the laser power required for high-fidelity entangling gates based on transverse modes is at least an order of magnitude higher than that based on axial modes for widely different masses of the two species. We also find that for even moderate mass differences, the transverse modes are much harder to cool than the axial modes regardless of the ion chain configuration. Therefore, transverse modes conventionally used for operations in single-species ion chains may not be well suited for mixed-species chains with widely different masses.

1 aSosnova, Ksenia1 aCarter, Allison1 aMonroe, Christopher uhttps://arxiv.org/abs/2004.0804501525nas a2200181 4500008004100000245006100041210006100102260001500163300001100178490000600189520101100195100001601206700001801222700001701240700002401257700002501281856003701306 2020 eng d00aCircuit Complexity across a Topological Phase Transition0 aCircuit Complexity across a Topological Phase Transition c03/16/2020 a0133230 v23 a

We use Nielsen's approach to quantify the circuit complexity in the one-dimensional Kitaev model. In equilibrium, we find that the circuit complexity of ground states exhibits a divergent derivative at the critical point, signaling the presence of a topological phase transition. Out of equilibrium, we study the complexity dynamics after a sudden quench, and find that the steady-state complexity exhibits nonanalytical behavior when quenched across critical points. We generalize our results to the long-range interacting case, and demonstrate that the circuit complexity correctly predicts the critical point between regions with different semi-integer topological numbers. Our results establish a connection between circuit complexity and quantum phase transitions both in and out of equilibrium, and can be easily generalized to topological phase transitions in higher dimensions. Our study opens a new avenue to using circuit complexity as a novel quantity to understand many-body systems.

1 aLiu, Fangli1 aLundgren, Rex1 aTitum, Paraj1 aGarrison, James, R.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1902.1072001546nas a2200145 4500008004100000245006600041210006600107260001400173520107500187100001801262700002601280700003201306700002501338856003701363 2020 eng d00aClassical Models of Entanglement in Monitored Random Circuits0 aClassical Models of Entanglement in Monitored Random Circuits c4/14/20203 a

The evolution of entanglement entropy in quantum circuits composed of Haar-random gates and projective measurements shows versatile behavior, with connections to phase transitions and complexity theory. We reformulate the problem in terms of a classical Markov process for the dynamics of bipartition purities and establish a probabilistic cellular-automaton algorithm to compute entanglement entropy in monitored random circuits on arbitrary graphs. In one dimension, we further relate the evolution of the entropy to a simple classical spin model that naturally generalizes a two-dimensional lattice percolation problem. We also establish a Markov model for the evolution of the zeroth Rényi entropy and demonstrate that, in one dimension and in the limit of large local dimension, it coincides with the corresponding second-Rényi-entropy model. Finally, we extend the Markovian description to a more general setting that incorporates continuous-time dynamics, defined by stochastic Hamiltonians and weak local measurements continuously monitoring the system.

1 aShtanko, Oles1 aKharkov, Yaroslav, A.1 aGarcía-Pintos, Luis, Pedro1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2004.0673601446nas a2200133 4500008004100000245007400041210006900115260001400184490000800198520103000206100002101236700001801257856003701275 2020 eng d00aCoherent transport of spin by adiabatic passage in quantum dot arrays0 aCoherent transport of spin by adiabatic passage in quantum dot a c9/17/20200 v1023 a

We introduce an adiabatic transfer protocol for spin states in large quantum dot arrays that is based on time-dependent modulation of the Heisenberg exchange interaction in the presence of a magnetic field gradient. We refer to this protocol as spin-CTAP (coherent transport by adiabatic passage) in analogy to a related protocol developed for charge state transfer in quantum dot arrays. The insensitivity of this adiabatic protocol to pulse imperfections has potential advantages for reading out extended spin qubit arrays. When the static exchange interaction varies across the array, a quantum-controlled version of spin-CTAP is possible, where the transfer process is conditional on the spin states in the middle of the array. This conditional operation can be used to generate N-qubit entangled GHZ states. Using a realistic noise model, we analyze the robustness of the spin-CTAP operations and find that high-fidelity (>95%) spin eigenstate transfer and GHZ state preparation is feasible in current devices.

1 aGullans, Michael1 aPetta, J., R. uhttps://arxiv.org/abs/2007.1058201472nas a2200145 4500008004100000022001400041245007400055210006900129260001400198490000800212520103000220100002101250700001801271856003701289 2020 eng d a2469-995000aCoherent transport of spin by adiabatic passage in quantum dot arrays0 aCoherent transport of spin by adiabatic passage in quantum dot a c9/17/20200 v1023 a

We introduce an adiabatic transfer protocol for spin states in large quantum dot arrays that is based on time-dependent modulation of the Heisenberg exchange interaction in the presence of a magnetic field gradient. We refer to this protocol as spin-CTAP (coherent transport by adiabatic passage) in analogy to a related protocol developed for charge state transfer in quantum dot arrays. The insensitivity of this adiabatic protocol to pulse imperfections has potential advantages for reading out extended spin qubit arrays. When the static exchange interaction varies across the array, a quantum-controlled version of spin-CTAP is possible, where the transfer process is conditional on the spin states in the middle of the array. This conditional operation can be used to generate N-qubit entangled GHZ states. Using a realistic noise model, we analyze the robustness of the spin-CTAP operations and find that high-fidelity (>95%) spin eigenstate transfer and GHZ state preparation is feasible in current devices.

1 aGullans, Michael1 aPetta, J., R. uhttps://arxiv.org/abs/2007.1058201669nas a2200181 4500008004100000245010700041210006900148260001300217490000800230520098500238100002701223700002201250700002201272700002401294700001901318700001901337856013101356 2020 eng d00aCollisions of room-temperature helium with ultracold lithium and the van der Waals bound state of HeLi0 aCollisions of roomtemperature helium with ultracold lithium and  c1/6/20200 v1013 a

We have computed the thermally averaged total, elastic rate coefficient for the collision of a room-temperature helium atom with an ultracold lithium atom. This rate coefficient has been computed as part of the characterization of a cold-atom vacuum sensor based on laser-cooled Li 6 or Li 7 atoms that will operate in the ultrahigh-vacuum (p< 10− 6 Pa) and extreme-high-vacuum (p< 10− 10 Pa) regimes. The analysis involves computing the X 2 Σ+ HeLi Born-Oppenheimer potential followed by the numerical solution of the relevant radial Schrödinger equation. The potential is computed using a single-reference-coupled-cluster electronic-structure method with basis sets of different completeness in order to characterize our uncertainty budget. We predict that the rate coefficient for a 300 K helium gas and a 1 μ K Li gas is 1.467 (13)× 10− 9 cm 3/s for He 4+ Li 6 and 1.471 (13)× 10− 9 cm 3/s for He 4+ Li 7, where the …

1 aMakrides, Constantinos1 aBarker, Daniel, S1 aFedchak, James, A1 aScherschligt, Julia1 aEckel, Stephen1 aTiesinga, Eite uhttps://www.quics.umd.edu/publications/collisions-room-temperature-helium-ultracold-lithium-and-van-der-waals-bound-state-heli01895nas a2200121 4500008004100000245009500041210006900136260001400205520147700219100002101696700001901717856003701736 2020 eng d00aComputations with Greater Quantum Depth Are Strictly More Powerful (Relative to an Oracle)0 aComputations with Greater Quantum Depth Are Strictly More Powerf c4/23/20203 a

A conjecture of Jozsa [Jozsa06] states that any polynomial-time quantum computation can be simulated by polylogarithmic-depth quantum computation interleaved with polynomial-depth classical computation. Separately, Aaronson [Aaronson05, Aaronson11, Aaronson14] conjectured that there exists an oracle O such that BQPO≠(BPPBQNC)O. These conjectures are intriguing allusions to the unresolved potential of combining classical and low-depth quantum computation. In this work we show that the Welded Tree Problem, which is an oracle problem that can be solved in quantum polynomial time as shown by Childs et al. [ChildsCDFGS03], cannot be solved in BPPBQNC, nor can it be solved in the class that Jozsa describes. This proves Aaronson's oracle separation conjecture and provides a counterpoint to Jozsa's conjecture relative to the Welded Tree oracle problem. More precisely, we define two complexity classes, HQC and JC whose languages are decided by two different families of interleaved quantum-classical circuits. HQC contains BPPBQNC and is therefore relevant to Aaronson's conjecture, while JC captures the model of computation that Jozsa considers. We show that the Welded Tree Problem gives an oracle separation between either of {JC,HQC} and BQP. Therefore, even when interleaved with arbitrary polynomial-time classical computation, greater "quantum depth" leads to strictly greater computational ability in this relativized setting.

1 aCoudron, Matthew1 aMenda, Sanketh uhttps://arxiv.org/abs/1909.1050301342nas a2200169 4500008004100000245007000041210006900111260001400180520083000194100002201024700001301046700002001059700001801079700001701097700002101114856003701135 2020 eng d00aConfronting lattice parton distributions with global QCD analysis0 aConfronting lattice parton distributions with global QCD analysi c10/1/20203 a

We present the first Monte Carlo based global QCD analysis of spin-averaged and spin-dependent parton distribution functions (PDFs) that includes nucleon isovector matrix elements in coordinate space from lattice QCD. We investigate the degree of universality of the extracted PDFs when the lattice and experimental data are treated under the same conditions within the Bayesian likelihood analysis. For the unpolarized sector, we find rather weak constraints from the current lattice data on the phenomenological PDFs, and difficulties in describing the lattice matrix elements at large spatial distances. In contrast, for the polarized PDFs we find good agreement between experiment and lattice data, with the latter providing significant constraints on the spin-dependent isovector quark and antiquark distributions

1 aBringewatt, Jacob1 aSato, N.1 aMelnitchouk, W.1 aQiu, Jian-Wei1 aSteffens, F.1 aConstantinou, M. uhttps://arxiv.org/abs/2010.0054802263nas a2200145 4500008004100000245006800041210006700109260001400176520182500190100001902015700001202034700001902046700001502065856003702080 2020 eng d00aConstant-round Blind Classical Verification of Quantum Sampling0 aConstantround Blind Classical Verification of Quantum Sampling c12/8/20203 a

In a recent breakthrough, Mahadev constructed a classical verification of quantum computation (CVQC) protocol for a classical client to delegate decision problems in BQP to an untrusted quantum prover under computational assumptions. In this work, we explore further the feasibility of CVQC with the more general sampling problems in BQP and with the desirable blindness property. We contribute affirmative solutions to both as follows. (1) Motivated by the sampling nature of many quantum applications (e.g., quantum algorithms for machine learning and quantum supremacy tasks), we initiate the study of CVQC for quantum sampling problems (denoted by SampBQP). More precisely, in a CVQC protocol for a SampBQP problem, the prover and the verifier are given an input x∈{0,1}n and a quantum circuit C, and the goal of the classical client is to learn a sample from the output z←C(x) up to a small error, from its interaction with an untrusted prover. We demonstrate its feasibility by constructing a four-message CVQC protocol for SampBQP based on the quantum Learning With Error assumption. (2) The blindness of CVQC protocols refers to a property of the protocol where the prover learns nothing, and hence is blind, about the client's input. It is a highly desirable property that has been intensively studied for the delegation of quantum computation. We provide a simple yet powerful generic compiler that transforms any CVQC protocol to a blind one while preserving its completeness and soundness errors as well as the number of rounds. Applying our compiler to (a parallel repetition of) Mahadev's CVQC protocol for BQP and our CVQC protocol for SampBQP yields the first constant-round blind CVQC protocol for BQP and SampBQP respectively, with negligible completeness and soundness errors.

1 aChung, Kai-Min1 aLee, Yi1 aLin, Han-Hsuan1 aWu, Xiaodi uhttps://arxiv.org/abs/2012.0484801854nas a2200121 4500008004100000245006500041210006500106260001300171520148400184100001301668700001401681856003701695 2020 eng d00aConstructing Multipartite Bell inequalities from stabilizers0 aConstructing Multipartite Bell inequalities from stabilizers c2/5/20203 a

Bell inequality with self-testing property has played an important role in quantum information field with both fundamental and practical applications. However, it is generally challenging to find Bell inequalities with self-testing property for multipartite states and actually there are not many known candidates. In this work, we propose a systematical framework to construct Bell inequalities from stabilizers which are maximally violated by general stabilizer states, with two observables for each local party. We show that the constructed Bell inequalities can self-test any stabilizer state which is essentially device-independent, if and only if these stabilizers can uniquely determine the state in a device-dependent manner. This bridges the gap between device-independent and device-dependent verification methods. Our framework can provide plenty of Bell inequalities for self-testing stabilizer states. Among them, we give two families of Bell inequalities with different advantages: (1) a family of Bell inequalities with a constant ratio of quantum and classical bounds using 2N correlations, (2) Single pair inequalities improving on all previous robustness self-testing bounds using N+1 correlations, which are both efficient and suitable for realizations in multipartite systems. Our framework can not only inspire more fruitful multipartite Bell inequalities from conventional verification methods, but also pave the way for their practical applications.

1 aZhao, Qi1 aZhou, You uhttps://arxiv.org/abs/2002.0184302409nas a2200193 4500008004100000245006700041210006700108260001500175490000700190520183800197100002002035700001902055700002302074700001802097700002402115700002002139700001902159856003702178 2020 eng d00aContinuous symmetries and approximate quantum error correction0 aContinuous symmetries and approximate quantum error correction c10/26/20200 v103 a

Quantum error correction and symmetry arise in many areas of physics, including many-body systems, metrology in the presence of noise, fault-tolerant computation, and holographic quantum gravity. Here we study the compatibility of these two important principles. If a logical quantum system is encoded into n physical subsystems, we say that the code is covariant with respect to a symmetry group G if a G transformation on the logical system can be realized by performing transformations on the individual subsystems. For a G-covariant code with G a continuous group, we derive a lower bound on the error correction infidelity following erasure of a subsystem. This bound approaches zero when the number of subsystems n or the dimension d of each subsystem is large. We exhibit codes achieving approximately the same scaling of infidelity with n or d as the lower bound. Leveraging tools from representation theory, we prove an approximate version of the Eastin-Knill theorem: If a code admits a universal set of transversal gates and corrects erasure with fixed accuracy, then, for each logical qubit, we need a number of physical qubits per subsystem that is inversely proportional to the error parameter. We construct codes covariant with respect to the full logical unitary group, achieving good accuracy for large d (using random codes) or n (using codes based on W-states). We systematically construct codes covariant with respect to general groups, obtaining natural generalizations of qubit codes to, for instance, oscillators and rotors. In the context of the AdS/CFT correspondence, our approach provides insight into how time evolution in the bulk corresponds to time evolution on the boundary without violating the Eastin-Knill theorem, and our five-rotor code can be stacked to form a covariant holographic code.

1 aFaist, Philippe1 aNezami, Sepehr1 aAlbert, Victor, V.1 aSalton, Grant1 aPastawski, Fernando1 aHayden, Patrick1 aPreskill, John uhttps://arxiv.org/abs/1902.0771401932nas a2200181 4500008004100000245005700041210005700098260001300155520138000168100002501548700002001573700002201593700002701615700002301642700002501665700002301690856003701713 2020 eng d00aCritical Theory for the Breakdown of Photon Blockade0 aCritical Theory for the Breakdown of Photon Blockade c6/9/20203 a

Photon blockade is the result of the interplay between the quantized nature of light and strong optical nonlinearities, whereby strong photon-photon repulsion prevents a quantum optical system from absorbing multiple photons. We theoretically study a single atom coupled to the light field, described by the resonantly driven Jaynes--Cummings model, in which case the photon blockade breaks down in a second order phase transition at a critical drive strength. We show that this transition is associated to the spontaneous breaking of an anti-unitary PT-symmetry. Within a semiclassical approximation we calculate the expectation values of observables in the steady state. We then move beyond the semiclassical approximation and approach the critical point from the disordered (blockaded) phase by reducing the Lindblad quantum master equation to a classical rate equation that we solve. The width of the steady-state distribution in Fock space is found to diverge as we approach the critical point with a simple power-law, allowing us to calculate the critical scaling of steady state observables without invoking mean-field theory. We propose a simple physical toy model for biased diffusion in the space of occupation numbers, which captures the universal properties of the steady state. We list several experimental platforms where this phenomenon may be observed.

1 aCurtis, Jonathan, B.1 aBoettcher, Igor1 aYoung, Jeremy, T.1 aMaghrebi, Mohammad, F.1 aCarmichael, Howard1 aGorshkov, Alexey, V.1 aFoss-Feig, Michael uhttps://arxiv.org/abs/2006.0559301389nas a2200157 4500008004100000245005900041210005700100260001400157300001000171490000800181520094200189100002501131700001901156700001901175856003701194 2019 eng d00aCanonical forms for single-qutrit Clifford+T operators0 aCanonical forms for singlequtrit CliffordT operators c8/19/2019 a54-700 v4063 a

We introduce canonical forms for single qutrit Clifford+T circuits and prove that every single-qutrit Clifford+T operator admits a unique such canonical form. We show that our canonical forms are T-optimal in the sense that among all the single-qutrit Clifford+T circuits implementing a given operator our canonical form uses the least number of T gates. Finally, we provide an algorithm which inputs the description of an operator (as a matrix or a circuit) and constructs the canonical form for this operator. The algorithm runs in time linear in the number of T gates. Our results provide a higher-dimensional generalization of prior work by Matsumoto and Amano who introduced similar canonical forms for single-qubit Clifford+T circuits. 

1 aGlaudell, Andrew, N.1 aRoss, Neil, J.1 aTaylor, J., M. uhttps://arxiv.org/abs/1803.0504701125nas a2200121 4500008004100000245003500041210003500076260001500111520080500126100001600931700001900947856003700966 2019 eng d00aChaos in a quantum rotor model0 aChaos in a quantum rotor model c01/29/20193 a

We study scrambling in a model consisting of a number N of M-component quantum rotors coupled by random infinite-range interactions. This model is known to have both a paramagnetic phase and a spin glass phase separated by second order phase transition. We calculate in perturbation theory the squared commutator of rotor fields at different sites in the paramagnetic phase, to leading non-trivial order at large N and large M. This quantity diagnoses the onset of quantum chaos in this system, and we show that the squared commutator grows exponentially with time, with a Lyapunov exponent proportional to 1M. At high temperature, the Lyapunov exponent limits to a value set by the microscopic couplings, while at low temperature, the exponent exhibits a T4 dependence on temperature T. 

1 aCheng, Gong1 aSwingle, Brian uhttps://arxiv.org/abs/1901.1044601228nas a2200145 4500008004100000245007500041210006900116260001500185520076500200100002100965700002100986700001901007700001901026856003701045 2019 eng d00aA characterization of quantum chaos by two-point correlation functions0 acharacterization of quantum chaos by twopoint correlation functi c02/28/20193 a

We propose a characterization of quantum many-body chaos: given a collection of simple operators, the set of all possible pair-correlations between these operators can be organized into a matrix with random-matrix-like spectrum. This approach is particularly useful for locally interacting systems, which do not generically show exponential Lyapunov growth of out-of-time-ordered correlators. We demonstrate the validity of this characterization by numerically studying the Sachdev-Ye-Kitaev model and a one-dimensional spin chain with random magnetic field (XXZ model).

1 aGharibyan, Hrant1 aHanada, Masanori1 aSwingle, Brian1 aTezuka, Masaki uhttps://arxiv.org/abs/1902.1108601730nas a2200145 4500008004100000245005400041210005400095260001500149490000900164520131300173100002301486700001901509700001901528856003701547 2019 eng d00aCircuit Transformations for Quantum Architectures0 aCircuit Transformations for Quantum Architectures c02/25/20190 v135 3 a

Quantum computer architectures impose restrictions on qubit interactions. We propose efficient circuit transformations that modify a given quantum circuit to fit an architecture, allowing for any initial and final mapping of circuit qubits to architecture qubits. To achieve this, we first consider the qubit movement subproblem and use the routing via matchings framework to prove tighter bounds on parallel routing. In practice, we only need to perform partial permutations, so we generalize routing via matchings to that setting. We give new routing procedures for common architecture graphs and for the generalized hierarchical product of graphs, which produces subgraphs of the Cartesian product. Secondly, for serial routing, we consider the token swapping framework and extend a 4-approximation algorithm for general graphs to support partial permutations. We apply these routing procedures to give several circuit transformations, using various heuristic qubit placement subroutines. We implement these transformations in software and compare their performance for large quantum circuits on grid and modular architectures, identifying strategies that work well in practice.

1 aChilds, Andrew, M.1 aSchoute, Eddie1 aUnsal, Cem, M. uhttps://arxiv.org/abs/1902.0910201696nas a2200145 4500008004100000245005800041210005700099260001400156520126100170100002501431700001601456700001701472700002401489856003701513 2019 eng d00aClassifying single-qubit noise using machine learning0 aClassifying singlequbit noise using machine learning c8/30/20193 a

Quantum characterization, validation, and verification (QCVV) techniques are used to probe, characterize, diagnose, and detect errors in quantum information processors (QIPs). An important component of any QCVV protocol is a mapping from experimental data to an estimate of a property of a QIP. Machine learning (ML) algorithms can help automate the development of QCVV protocols, creating such maps by learning them from training data. We identify the critical components of "machine-learned" QCVV techniques, and present a rubric for developing them. To demonstrate this approach, we focus on the problem of determining whether noise affecting a single qubit is coherent or stochastic (incoherent) using the data sets originally proposed for gate set tomography. We leverage known ML algorithms to train a classifier distinguishing these two kinds of noise. The accuracy of the classifier depends on how well it can approximate the "natural" geometry of the training data. We find GST data sets generated by a noisy qubit can reliably be separated by linear surfaces, although feature engineering can be necessary. We also show the classifier learned by a support vector machine (SVM) is robust under finite-sample noise. 

1 aScholten, Travis, L.1 aLiu, Yi-Kai1 aYoung, Kevin1 aBlume-Kohout, Robin uhttps://arxiv.org/abs/1908.1176201524nas a2200145 4500008004100000245004700041210004400088260001500132520110100147100003701248700001801285700001901303700001901322856003701341 2019 eng d00aCompeting (Semi)-Selfish Miners in Bitcoin0 aCompeting SemiSelfish Miners in Bitcoin c06/11/20193 a

The Bitcoin protocol prescribes certain behavior by the miners who are responsible for maintaining and extending the underlying blockchain; in particular, miners who successfully solve a puzzle, and hence can extend the chain by a block, are supposed to release that block immediately. Eyal and Sirer showed, however, that a selfish miner is incentivized to deviate from the protocol and withhold its blocks under certain conditions. The analysis by Eyal and Sirer, as well as in followup work, considers a \emph{single} deviating miner (who may control a large fraction of the hashing power in the network) interacting with a remaining pool of honest miners. Here, we extend this analysis to the case where there are \emph{multiple} (non-colluding) selfish miners. We find that with multiple strategic miners, specific deviations from honest mining by multiple strategic agents can outperform honest mining, even if individually miners would not be incentivised to be dishonest. This previous point effectively renders the Bitcoin protocol to be less secure than previously thought. 

1 aMarmolejo-Cossío, Francisco, J.1 aBrigham, Eric1 aSela, Benjamin1 aKatz, Jonathan uhttps://arxiv.org/abs/1906.0450201697nas a2200169 4500008004100000245008100041210006900122260001500191520115700206100002001363700002301383700001901406700002001425700002001445700002501465856003701490 2019 eng d00aComplexity phase diagram for interacting and long-range bosonic Hamiltonians0 aComplexity phase diagram for interacting and longrange bosonic H c06/10/20193 a

Recent years have witnessed a growing interest in topics at the intersection of many-body physics and complexity theory. Many-body physics aims to understand and classify emergent behavior of systems with a large number of particles, while complexity theory aims to classify computational problems based on how the time required to solve the problem scales as the problem size becomes large. In this work, we use insights from complexity theory to classify phases in interacting many-body systems. Specifically, we demonstrate a "complexity phase diagram" for the Bose-Hubbard model with long-range hopping. This shows how the complexity of simulating time evolution varies according to various parameters appearing in the problem, such as the evolution time, the particle density, and the degree of locality. We find that classification of complexity phases is closely related to upper bounds on the spread of quantum correlations, and protocols to transfer quantum information in a controlled manner. Our work motivates future studies of complexity in many-body systems and its interplay with the associated physical phenomena. 

1 aMaskara, Nishad1 aDeshpande, Abhinav1 aTran, Minh, C.1 aEhrenberg, Adam1 aFefferman, Bill1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1906.0417801746nas a2200193 4500008004100000245006800041210006700109260001500176490000900191520117800200100001601378700001801394700001701412700001801429700001901447700002401466700002501490856003701515 2019 eng d00aConfined Dynamics in Long-Range Interacting Quantum Spin Chains0 aConfined Dynamics in LongRange Interacting Quantum Spin Chains c04/17/20190 v122 3 a

We study the quasiparticle excitation and quench dynamics of the one-dimensional transverse-field Ising model with power-law (1/rα) interactions. We find that long-range interactions give rise to a confining potential, which couples pairs of domain walls (kinks) into bound quasiparticles, analogous to mesonic bound states in high-energy physics. We show that these bound states have dramatic consequences for the non-equilibrium dynamics following a global quantum quench, such as suppressed spreading of quantum information and oscillations of order parameters. The masses of these bound states can be read out from the Fourier spectrum of these oscillating order parameters. We then use a two-kink model to qualitatively explain the phenomenon of long-range-interaction-induced confinement. The masses of the bound states predicted by this model are in good quantitative agreement with exact diagonalization results. Moreover, we illustrate that these bound states lead to weak thermalization of local observables for initial states with energy near the bottom of the many-body energy spectrum. Our work is readily applicable to current trapped-ion experiments.

1 aLiu, Fangli1 aLundgren, Rex1 aTitum, Paraj1 aPagano, Guido1 aZhang, Jiehang1 aMonroe, Christopher1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1810.0236505095nas a2200169 4500008004100000245007900041210006900120260001500189520455700204100001804761700001804779700001804797700002004815700001704835700001604852856005704868 2018 eng d00aCapacity Approaching Codes for Low Noise Interactive Quantum Communication0 aCapacity Approaching Codes for Low Noise Interactive Quantum Com c2018/01/013 a
We consider the problem of implementing two-party interactive quantum
communication over noisy channels, a necessary endeavor if we wish to
fully reap quantum advantages for communication.  
 
For an arbitrary protocol with n messages, designed for
noiseless qudit channels, our main result is a simulation method that fails with probability less than
$2^{-\Theta(n\epsilon)}$ and uses a qudit channel $n(1 + \Theta
(\sqrt{\epsilon}))$ times, of which an $\epsilon$ fraction can be
corrupted adversarially.
 
The simulation is thus capacity achieving to leading order, and
we conjecture that it is optimal up to a constant factor in 
the $\sqrt{\epsilon}$ term.  
 
Furthermore, the simulation is in a model that does not require
pre-shared resources such as randomness or entanglement between the
communicating parties.
 
Surprisingly, this outperforms the best-known overhead of $1 +
O(\sqrt{\epsilon \log \log 1/\epsilon})$ in the corresponding
\emph{classical} model, which is also conjectured to be optimal
     [Haeupler, FOCS'14].
 
Our work also improves over the best previously known quantum result
where the overhead is a non-explicit large constant [Brassard \emph{et
    al.}, FOCS'14] for low $\epsilon$.
1 aLeung, Debbie1 aNayak, Ashwin1 aShayeghi, Ala1 aTouchette, Dave1 aYao, Penghui1 aYu, Nengkun uhttp://acm-stoc.org/stoc2018/STOC-2018-Accepted.html01718nas a2200169 4500008004100000245008800041210006900129260001500198520118200213100001501395700002001410700001701430700002201447700001901469700002301488856003701511 2018 eng d00aCircuit QED-based measurement of vortex lattice order in a Josephson junction array0 aCircuit QEDbased measurement of vortex lattice order in a Joseph c2018/03/123 a

Superconductivity provides a canonical example of a quantum phase of matter. When superconducting islands are connected by Josephson junctions in a lattice, the low temperature state of the system can map to the celebrated XY model and its associated universality classes. This has been used to experimentally implement realizations of Mott insulator and Berezinskii--Kosterlitz--Thouless (BKT) transitions to vortex dynamics analogous to those in type-II superconductors. When an external magnetic field is added, the effective spins of the XY model become frustrated, leading to the formation of topological defects (vortices). Here we observe the many-body dynamics of such an array, including frustration, via its coupling to a superconducting microwave cavity. We take the design of the transmon qubit, but replace the single junction between two antenna pads with the complete array. This allows us to probe the system at 10 mK with minimal self-heating by using weak coherent states at the single (microwave) photon level to probe the resonance frequency of the cavity. We observe signatures of ordered vortex lattice at rational flux fillings of the array. 

1 aCosmic, R.1 aIkegami, Hiroki1 aLin, Zhirong1 aInomata, Kunihiro1 aTaylor, J., M.1 aNakamura, Yasunobu uhttps://arxiv.org/abs/1803.0411302454nas a2200133 4500008004100000245005300041210005300094520206100147100002202208700001802230700001602248700001902264856003702283 2018 eng d00aClassical lower bounds from quantum upper bounds0 aClassical lower bounds from quantum upper bounds3 a

We prove lower bounds on complexity measures, such as the approximate degree of a Boolean function and the approximate rank of a Boolean matrix, using quantum arguments. We prove these lower bounds using a quantum query algorithm for the combinatorial group testing problem. 
We show that for any function f, the approximate degree of computing the OR of n copies of f is Omega(sqrt{n}) times the approximate degree of f, which is optimal. No such general result was known prior to our work, and even the lower bound for the OR of ANDs function was only resolved in 2013. 
We then prove an analogous result in communication complexity, showing that the logarithm of the approximate rank (or more precisely, the approximate gamma_2 norm) of F: X x Y -> {0,1} grows by a factor of Omega~(sqrt{n}) when we take the OR of n copies of F, which is also essentially optimal. As a corollary, we give a new proof of Razborov's celebrated Omega(sqrt{n}) lower bound on the quantum communication complexity of the disjointness problem. 
Finally, we generalize both these results from composition with the OR function to composition with arbitrary symmetric functions, yielding nearly optimal lower bounds in this setting as well.

1 aBen-David, Shalev1 aBouland, Adam1 aGarg, Ankit1 aKothari, Robin uhttps://arxiv.org/abs/1807.0625601379nas a2200217 4500008004100000245005600041210005400097520077800151100001600929700001800945700001300963700001400976700002200990700001501012700002001027700001401047700002001061700001801081700002501099856003701124 2018 eng d00aCoherent optical nano-tweezers for ultra-cold atoms0 aCoherent optical nanotweezers for ultracold atoms3 a

There has been a recent surge of interest and progress in creating subwavelength free-space optical potentials for ultra-cold atoms. A key open question is whether geometric potentials, which are repulsive and ubiquitous in the creation of subwavelength free-space potentials, forbid the creation of narrow traps with long lifetimes. Here, we show that it is possible to create such traps. We propose two schemes for realizing subwavelength traps and demonstrate their superiority over existing proposals. We analyze the lifetime of atoms in such traps and show that long-lived bound states are possible. This work opens a new frontier for the subwavelength control and manipulation of ultracold matter, with applications in quantum chemistry and quantum simulation.

1 aBienias, P.1 aSubhankar, S.1 aWang, Y.1 aTsui, T-C1 aJendrzejewski, F.1 aTiecke, T.1 aJuzeliūnas, G.1 aJiang, L.1 aRolston, S., L.1 aPorto, J., V.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1808.0248701523nas a2200205 4500008004100000245004800041210004500089260001500134300001200149490000800161520099800169100001101167700001501178700001301193700001801206700001901224700001901243700001801262856003701280 2018 eng d00aA Coherent Spin-Photon Interface in Silicon0 aCoherent SpinPhoton Interface in Silicon c2018/03/29 a599-6030 v5553 a

Electron spins in silicon quantum dots are attractive systems for quantum computing due to their long coherence times and the promise of rapid scaling using semiconductor fabrication techniques. While nearest neighbor exchange coupling of two spins has been demonstrated, the interaction of spins via microwave frequency photons could enable long distance spin-spin coupling and "all-to-all" qubit connectivity. Here we demonstrate strong-coupling between a single spin in silicon and a microwave frequency photon with spin-photon coupling rates g_s/(2π) > 10 MHz. The mechanism enabling coherent spin-photon interactions is based on spin-charge hybridization in the presence of a magnetic field gradient. In addition to spin-photon coupling, we demonstrate coherent control of a single spin in the device and quantum non-demolition spin state readout using cavity photons. These results open a direct path toward entangling single spins using microwave frequency photons.

1 aMi, X.1 aBenito, M.1 aPutz, S.1 aZajac, D., M.1 aTaylor, J., M.1 aBurkard, Guido1 aPetta, J., R. uhttps://arxiv.org/abs/1710.0326501974nas a2200181 4500008004100000245005000041210004800091260001500139520145800154100001101612700001501623700001301638700001801651700001901669700001901688700001801707856006701725 2018 eng d00aA coherent spin–photon interface in silicon0 acoherent spin–photon interface in silicon c2018/02/143 a

Electron spins in silicon quantum dots are attractive systems for quantum computing owing to their long coherence times and the promise of rapid scaling of the number of dots in a system using semiconductor fabrication techniques. Although nearest-neighbour exchange coupling of two spins has been demonstrated, the interaction of spins via microwave-frequency photons could enable long-distance spin–spin coupling and connections between arbitrary pairs of qubits (‘all-to-all’ connectivity) in a spin-based quantum processor. Realizing coherent spin–photon coupling is challenging because of the small magnetic-dipole moment of a single spin, which limits magnetic-dipole coupling rates to less than 1 kilohertz. Here we demonstrate strong coupling between a single spin in silicon and a single microwave-frequency photon, with spin–photon coupling rates of more than 10 megahertz. The mechanism that enables the coherent spin–photon interactions is based on spin–charge hybridization in the presence of a magnetic-field gradient. In addition to spin–photon coupling, we demonstrate coherent control and dispersive readout of a single spin. These results open up a direct path to entangling single spins using microwave-frequency photons.

1 aMi, X.1 aBenito, M.1 aPutz, S.1 aZajac, D., M.1 aTaylor, J., M.1 aBurkard, Guido1 aPetta, J., R. uhttps://www.nature.com/articles/nature25769#author-information01463nas a2200229 4500008004100000245006800041210006700109520082000176100001500996700001701011700001901028700001601047700001701063700001501080700002001095700001401115700001901129700002201148700001101170700001501181856003701196 2018 eng d00aCryogenic Trapped-Ion System for Large Scale Quantum Simulation0 aCryogenic TrappedIon System for Large Scale Quantum Simulation3 a

We present a cryogenic ion trapping system designed for large scale quantum simulation of spin models. Our apparatus is based on a segmented-blade ion trap enclosed in a 4 K cryostat, which enables us to routinely trap over 100 171Yb+ ions in a linear configuration for hours due to a low background gas pressure from differential cryo-pumping. We characterize the cryogenic vacuum by using trapped ion crystals as a pressure gauge, measuring both inelastic and elastic collision rates with the molecular background gas. We demonstrate nearly equidistant ion spacing for chains of up to 44 ions using anharmonic axial potentials. This reliable production and lifetime enhancement of large linear ion chains will enable quantum simulation of spin models that are intractable with classical computer modelling.

1 aPagano, G.1 aHess, P., W.1 aKaplan, H., B.1 aTan, W., L.1 aRicherme, P.1 aBecker, P.1 aKyprianidis, A.1 aZhang, J.1 aBirckelbaw, E.1 aHernandez, M., R.1 aWu, Y.1 aMonroe, C. uhttps://arxiv.org/abs/1802.0311802065nas a2200169 4500008004100000245007000041210006900111260001500180520154900195100001601744700001901760700002101779700001801800700001601818700002401834856003701858 2017 eng d00aComplete 3-Qubit Grover Search on a Programmable Quantum Computer0 aComplete 3Qubit Grover Search on a Programmable Quantum Computer c2017/03/303 a

Searching large databases is an important problem with broad applications. The Grover search algorithm provides a powerful method for quantum computers to perform searches with a quadratic speedup in the number of required database queries over classical computers. It is an optimal search algorithm for a quantum computer, and has further applications as a subroutine for other quantum algorithms. Searches with two qubits have been demonstrated on a variety of platforms and proposed for others, but larger search spaces have only been demonstrated on a non-scalable NMR system. Here, we report results for a complete three-qubit Grover search algorithm using the scalable quantum computing technology of trapped atomic ions, with better-than-classical performance. The algorithm is performed for all 8 possible single-result oracles and all 28 possible two-result oracles. Two methods of state marking are used for the oracles: a phase-flip method employed by other experimental demonstrations, and a Boolean method requiring an ancilla qubit that is directly equivalent to the state-marking scheme required to perform a classical search. All quantum solutions are shown to outperform their classical counterparts. We also report the first implementation of a Toffoli-4 gate, which is used along with Toffoli-3 gates to construct the algorithms; these gates have process fidelities of 70.5% and 89.6%, respectively.

1 aFiggatt, C.1 aMaslov, Dmitri1 aLandsman, K., A.1 aLinke, N., M.1 aDebnath, S.1 aMonroe, Christopher uhttps://arxiv.org/abs/1703.1053505805nas a2200145 4500008004100000245004900041210004900090260001500139520537700154100002305531700002005554700002305574700002505597856003705622 2017 eng d00aComplexity of sampling as an order parameter0 aComplexity of sampling as an order parameter c2017/03/153 a

We consider the classical complexity of approximately simulating time evolution under spatially local quadratic bosonic Hamiltonians for time t. We obtain upper and lower bounds on the scaling of twith the number of bosons, n, for which simulation, cast as a sampling problem, is classically efficient and provably hard, respectively. We view these results in the light of classifying phases of physical systems based on parameters in the Hamiltonian and conjecture a link to dynamical phase transitions. In doing so, we combine ideas from mathematical physics and computational complexity to gain insight into the behavior of condensed matter systems.

1 aDeshpande, Abhinav1 aFefferman, Bill1 aFoss-Feig, Michael1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1703.0533201895nas a2200157 4500008004100000245004900041210004800090260001500138520145500153100001801608700001901626700001801645700002201663700001501685856003701700 2017 eng d00aComputational Notions of Quantum Min-Entropy0 aComputational Notions of Quantum MinEntropy c2017/09/093 a

We initiate the study of computational entropy in the quantum setting. We investigate to what extent the classical notions of computational entropy generalize to the quantum setting, and whether quantum analogues of classical theorems hold. Our main results are as follows. (1) The classical Leakage Chain Rule for pseudoentropy can be extended to the case that the leakage information is quantum (while the source remains classical). Specifically, if the source has pseudoentropy at least k, then it has pseudoentropy at least k − ℓ conditioned on an ℓ- qubit leakage. (2) As an application of the Leakage Chain Rule, we construct the first quantum leakage-resilient stream-cipher in the bounded-quantum-storage model, assuming the existence of a quantum-secure pseudorandom generator. (3) We show that the general form of the classical Dense Model Theorem (interpreted as the equivalence between two definitions of pseudo-relativemin-entropy) does not extend to quantum states. Along the way, we develop quantum analogues of some classical techniques (e.g., the Leakage Simulation Lemma, which is proven by a Nonuniform Min-Max Theorem or Boosting). On the other hand, we also identify some classical techniques (e.g., Gap Amplification) that do not work in the quantum setting. Moreover, we introduce a variety of notions that combine quantum information and quantum complexity, and this raises several directions for future work.

1 aChen, Yi-Hsiu1 aChung, Kai-Min1 aLai, Ching-Yi1 aVadhan, Salil, P.1 aWu, Xiaodi uhttps://arxiv.org/abs/1704.0730901983nas a2200157 4500008004100000245007700041210006900118260001500187300001100202490000800213520147800221100001601699700001801715700001901733856007301752 2017 eng d00aCooling a harmonic oscillator by optomechanical modification of its bath0 aCooling a harmonic oscillator by optomechanical modification of  c2017/05/31 a2236020 v1183 a

Optomechanical systems show tremendous promise for high sensitivity sensing of forces and modification of mechanical properties via light. For example, similar to neutral atoms and trapped ions, laser cooling of mechanical motion by radiation pressure can take single mechanical modes to their ground state. Conventional optomechanical cooling is able to introduce additional damping channel to mechanical motion, while keeping its thermal noise at the same level, and as a consequence, the effective temperature of the mechanical mode is lowered. However, the ratio of temperature to quality factor remains roughly constant, preventing dramatic advances in quantum sensing using this approach. Here we propose an approach for simultaneously reducing the thermal load on a mechanical resonator while improving its quality factor. In essence, we use the optical interaction to dynamically modify the dominant damping mechanism, providing an optomechanically-induced effect analogous to a phononic band gap. The mechanical mode of interest is assumed to be weakly coupled to its heat bath but strongly coupled to a second mechanical mode, which is cooled by radiation pressure coupling to a red detuned cavity field. We also identify a realistic optomechanical design that has the potential to realize this novel cooling scheme.

1 aXu, Xunnong1 aPurdy, Thomas1 aTaylor, J., M. uhttps://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.22360201698nas a2200169 4500008004100000245006000041210006000101260001500161300001100176490000800187520120500195100001801400700002101418700002701439700002501466856003701491 2017 eng d00aCorrelated Photon Dynamics in Dissipative Rydberg Media0 aCorrelated Photon Dynamics in Dissipative Rydberg Media c2017/07/26 a0436020 v1193 a

Rydberg blockade physics in optically dense atomic media under the conditions of electromagnetically induced transparency (EIT) leads to strong dissipative interactions between single photons. We introduce a new approach to analyzing this challenging many-body problem in the limit of large optical depth per blockade radius. In our approach, we separate the single-polariton EIT physics from Rydberg-Rydberg interactions in a serialized manner while using a hard-sphere model for the latter, thus capturing the dualistic particle-wave nature of light as it manifests itself in dissipative Rydberg-EIT media. Using this approach, we analyze the saturation behavior of the transmission through one-dimensional Rydberg-EIT media in the regime of non-perturbative dissipative interactions relevant to current experiments. Our model is in good agreement with experimental data. We also analyze a scheme for generating regular trains of single photons from continuous-wave input and derive its scaling behavior in the presence of imperfect single-photon EIT.

1 aZeuthen, Emil1 aGullans, Michael1 aMaghrebi, Mohammad, F.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1608.0606800514nas a2200157 4500008004100000245006700041210006600108260001500174300001100189490000700200100002700207700001900234700002300253700002500276856005500301 2016 eng d00aCausality and quantum criticality in long-range lattice models0 aCausality and quantum criticality in longrange lattice models c2016/03/17 a1251280 v931 aMaghrebi, Mohammad, F.1 aGong, Zhe-Xuan1 aFoss-Feig, Michael1 aGorshkov, Alexey, V. uhttp://link.aps.org/doi/10.1103/PhysRevB.93.12512801582nas a2200169 4500008004100000245006700041210006600108260001500174300001100189490000700200520107500207100002701282700001901309700002301328700002501351856003601376 2016 eng d00aCausality and quantum criticality with long-range interactions0 aCausality and quantum criticality with longrange interactions c2016/03/17 a1251280 v923 a Quantum lattice systems with long-range interactions often exhibit drastically different behavior than their short-range counterparts. In particular, because they do not satisfy the conditions for the Lieb-Robinson theorem, they need not have an emergent relativistic structure in the form of a light cone. Adopting a field-theoretic approach, we study the one-dimensional transverse-field Ising model and a fermionic model with long-range interactions, explore their critical and near-critical behavior, and characterize their response to local perturbations. We deduce the dynamic critical exponent, up to the two-loop order within the renormalization group theory, which we then use to characterize the emergent causal behavior. We show that beyond a critical value of the power-law exponent of long-range interactions, the dynamics effectively becomes relativistic. Various other critical exponents describing correlations in the ground state, as well as deviations from a linear causal cone, are deduced for a wide range of the power-law exponent. 1 aMaghrebi, Mohammad, F.1 aGong, Zhe-Xuan1 aFoss-Feig, Michael1 aGorshkov, Alexey, V. uhttp://arxiv.org/abs/1508.0090601522nas a2200133 4500008004100000245007000041210006900111260001500180520109400195100002301289700001601312700002401328856003601352 2016 eng d00aCo-Designing a Scalable Quantum Computer with Trapped Atomic Ions0 aCoDesigning a Scalable Quantum Computer with Trapped Atomic Ions c2016/02/093 aThe first generation of quantum computers are on the horizon, fabricated from quantum hardware platforms that may soon be able to tackle certain tasks that cannot be performed or modelled with conventional computers. These quantum devices will not likely be universal or fully programmable, but special-purpose processors whose hardware will be tightly co-designed with particular target applications. Trapped atomic ions are a leading platform for first generation quantum computers, but are also fundamentally scalable to more powerful general purpose devices in future generations. This is because trapped ion qubits are atomic clock standards that can be made identical to a part in 10^15, and their quantum circuit connectivity can be reconfigured through the use of external fields, without modifying the arrangement or architecture of the qubits themselves. In this article we show how a modular quantum computer of any size can be engineered from ion crystals, and how the wiring between ion trap qubits can be tailored to a variety of applications and quantum computing protocols.1 aBrown, Kenneth, R.1 aKim, Jaewan1 aMonroe, Christopher uhttp://arxiv.org/abs/1602.0284001682nas a2200193 4500008004100000245006100041210006100102260001500163300001100178490000700189520113200196100002101328700002101349700001301370700002501383700002101408700002301429856003601452 2016 eng d00aCollective phases of strongly interacting cavity photons0 aCollective phases of strongly interacting cavity photons c2016/09/01 a0338010 v943 a

We study a coupled array of coherently driven photonic cavities, which maps onto a driven-dissipative XY spin-12 model with ferromagnetic couplings in the limit of strong optical nonlinearities. Using a site-decoupled mean-field approximation, we identify steady state phases with canted antiferromagnetic order, in addition to limit cycle phases, where oscillatory dynamics persist indefinitely. We also identify collective bistable phases, where the system supports two steady states among spatially uniform, antiferromagnetic, and limit cycle phases. We compare these mean-field results to exact quantum trajectories simulations for finite one-dimensional arrays. The exact results exhibit short-range antiferromagnetic order for parameters that have significant overlap with the mean-field phase diagram. In the mean-field bistable regime, the exact quantum dynamics exhibits real-time collective switching between macroscopically distinguishable states. We present a clear physical picture for this dynamics, and establish a simple relationship between the switching times and properties of the quantum Liouvillian.

1 aWilson, Ryan, M.1 aMahmud, Khan, W.1 aHu, Anzi1 aGorshkov, Alexey, V.1 aHafezi, Mohammad1 aFoss-Feig, Michael uhttp://arxiv.org/abs/1601.0685701705nas a2200121 4500008004100000245005700041210005500098260001500153520133500168100002001503700002401523856003601547 2016 eng d00aA Complete Characterization of Unitary Quantum Space0 aComplete Characterization of Unitary Quantum Space c2016/04/053 aWe give two complete characterizations of unitary quantum space-bounded classes. The first is based on the Matrix Inversion problem for well-conditioned matrices. We show that given the size-n efficient encoding of a 2O(k(n))×2O(k(n)) well-conditioned matrix H, approximating a particular entry of H−1 is complete for the class of problems solvable by a quantum algorithm that uses O(k(n)) space and performs all quantum measurements at the end of the computation. In particular, the problem of computing entries of H−1 for an explicit well-conditioned n×n matrix H is complete for unitary quantum logspace. We then show that the problem of approximating to high precision the least eigenvalue of a positive semidefinite matrix H, encoded as a circuit, gives a second characterization of unitary quantum space complexity. In the process we also establish an equivalence between unitary quantum space-bounded classes and certain QMA proof systems. As consequences, we establish that QMA with exponentially small completeness-soundness gap is equal to PSPACE, that determining whether a local Hamiltonian is frustration-free is PSPACE-complete, and give a provable setting in which the ability to prepare PEPS states gives less computational power than the ability to prepare the ground state of a generic local Hamiltonian.1 aFefferman, Bill1 aLin, Cedric, Yen-Yu uhttp://arxiv.org/abs/1604.0138400953nas a2200157 4500008004100000245006400041210006400105260001500169300000900184490000700193520050200200100002300702700001800725700001400743856003800757 2016 eng d00aComplexity of the XY antiferromagnet at fixed magnetization0 aComplexity of the XY antiferromagnet at fixed magnetization c2016/01/01 a1-180 v163 a We prove that approximating the ground energy of the antiferromagnetic XY model on a simple graph at fixed magnetization (given as part of the instance specification) is QMA-complete. To show this, we strengthen a previous result by establishing QMA-completeness for approximating the ground energy of the Bose-Hubbard model on simple graphs. Using a connection between the XY and Bose-Hubbard models that we exploited in previous work, this establishes QMA-completeness of the XY model. 1 aChilds, Andrew, M.1 aGosset, David1 aWebb, Zak uhttp://arxiv.org/abs/1503.07083v101599nas a2200169 4500008004100000245004900041210004900090260001500139520107400154100001901228700002001247700002001267700002501287700002501312700002401337856006801361 2016 eng d00aComputational Security of Quantum Encryption0 aComputational Security of Quantum Encryption c2016/11/103 a

Quantum-mechanical devices have the potential to transform cryptography. Most research in this area has focused either on the information-theoretic advantages of quantum protocols or on the security of classical cryptographic schemes against quantum attacks. In this work, we initiate the study of another relevant topic: the encryption of quantum data in the computational setting. In this direction, we establish quantum versions of several fundamental classical results. First, we develop natural definitions for private-key and public-key encryption schemes for quantum data. We then define notions of semantic security and indistinguishability, and, in analogy with the classical work of Goldwasser and Micali, show that these notions are equivalent. Finally, we construct secure quantum encryption schemes from basic primitives. In particular, we show that quantum-secure one-way functions imply IND-CCA1-secure symmetric-key quantum encryption, and that quantum-secure trapdoor one-way permutations imply semantically-secure public-key quantum encryption.

1 aAlagic, Gorjan1 aBroadbent, Anne1 aFefferman, Bill1 aGagliardoni, Tommaso1 aSchaffner, Christian1 aJules, Michael, St. uhttps://link.springer.com/chapter/10.1007%2F978-3-319-49175-2_302139nas a2200145 4500008004100000245008500041210006900126260001500195300001100210490000700221520169100228100001801919700001901937856003701956 2015 eng d00aCapacitively coupled singlet-triplet qubits in the double charge resonant regime0 aCapacitively coupled singlettriplet qubits in the double charge  c2015/12/01 a2353010 v923 aWe investigate a method for entangling two singlet-triplet qubits in adjacent double quantum dots via capacitive interactions. In contrast to prior work, here we focus on a regime with strong interactions between the qubits. The interplay of the interaction energy and simultaneous large detunings for both double dots gives rise to the double charge resonant regime, in which the unpolarized (1111) and fully polarized (0202) four-electron states in the absence of interqubit tunneling are near degeneracy, while being energetically well-separated from the partially polarized (0211 and 1102) states. A controlled-phase gate may be realized by combining time evolution in this regime in the presence of intraqubit tunneling and the interqubit Coulomb interaction with refocusing {\pi} pulses that swap the singly occupied singlet and triplet states of the two qubits via, e.g., magnetic gradients. We calculate the fidelity of this entangling gate, incorporating models for two types of noise - classical, Gaussian-distributed charge fluctuations in the single-qubit detunings and charge relaxation within the low-energy subspace via electron-phonon interaction - and identify parameter regimes that optimize the fidelity. The rates of phonon-induced decay for pairs of GaAs or Si double quantum dots vary with the sizes of the dipolar and quadrupolar contributions and are several orders of magnitude smaller for Si, leading to high theoretical gate fidelities for coupled singlet-triplet qubits in Si dots. We also consider the dependence of the capacitive coupling on the relative orientation of the double dots and find that a linear geometry provides the fastest potential gate. 1 aSrinivasa, V.1 aTaylor, J., M. uhttp://arxiv.org/abs/1408.4740v201437nas a2200157 4500008004100000245003500041210003300076260001500109300001100124490000700135520104900142100001501191700001701206700001901223856003701242 2015 eng d00aA chemical potential for light0 achemical potential for light c2014/05/22 a1743050 v923 aPhotons are not conserved in interactions with other matter. Consequently, when understanding the equation of state and thermodynamics of photons, while we have a concept of temperature for energy conservation, there is no equivalent chemical potential for particle number conservation. However, the notion of a chemical potential is crucial in understanding a wide variety of single- and many-body effects, from transport in conductors and semi-conductors to phase transitions in electronic and atomic systems. Here we show how a direct modification of the system-bath coupling via parametric oscillation creates an effective chemical potential for photons even in the thermodynamic limit. Specific implementations, using circuit-QED or optomechanics, are feasible using current technologies, and we show a detailed example demonstrating the emergence of Mott Insulator-superfluid transition in a lattice of nonlinear oscillators. Our approach paves the way for quantum simulation, quantum sources and even electron-like circuits with light. 1 aHafezi, M.1 aAdhikari, P.1 aTaylor, J., M. uhttp://arxiv.org/abs/1405.5821v201576nas a2200133 4500008004100000245010700041210006900148260001500217520110300232100002701335700001901362700002501381856003601406 2015 eng d00aContinuous symmetry breaking and a new universality class in 1D long-range interacting quantum systems0 aContinuous symmetry breaking and a new universality class in 1D  c2015/10/053 aContinuous symmetry breaking (CSB) in low-dimensional systems, forbidden by the Mermin-Wagner theorem for short-range interactions, may take place in the presence of slowly decaying long-range interactions. Nevertheless, there is no stringent bound on how slowly interactions should decay to give rise to CSB in 1D quantum systems at zero temperature. Here, we study a long-range interacting spin chain with U(1) symmetry and power-law interactions V(r)∼1/rα, directly relevant to ion-trap experiments. Using bosonization and renormalization group theory, we find CSB for α smaller than a critical exponent αc(≤3) depending on the microscopic parameters of the model. Furthermore, the transition from the gapless XY phase to the gapless CSB phase is mediated by the breaking of conformal symmetry due to long-range interactions, and is described by a new universality class akin to the Berezinskii-Kosterlitz-Thouless transition. Our analytical findings are in good agreement with a numerical calculation. Signatures of the CSB phase should be accessible in existing trapped-ion experiments.1 aMaghrebi, Mohammad, F.1 aGong, Zhe-Xuan1 aGorshkov, Alexey, V. uhttp://arxiv.org/abs/1510.0132501507nas a2200229 4500008004100000245005700041210005700098260001500155300001100170490000800181520087400189100002701063700002101090700001601111700001301127700001501140700002001155700001801175700002101193700002501214856003801239 2015 eng d00aCoulomb bound states of strongly interacting photons0 aCoulomb bound states of strongly interacting photons c2015/09/16 a1236010 v1153 a We show that two photons coupled to Rydberg states via electromagnetically induced transparency can interact via an effective Coulomb potential. This interaction gives rise to a continuum of two-body bound states. Within the continuum, metastable bound states are distinguished in analogy with quasi-bound states tunneling through a potential barrier. We find multiple branches of metastable bound states whose energy spectrum is governed by the Coulomb potential, thus obtaining a photonic analogue of the hydrogen atom. Under certain conditions, the wavefunction resembles that of a diatomic molecule in which the two polaritons are separated by a finite "bond length." These states propagate with a negative group velocity in the medium, allowing for a simple preparation and detection scheme, before they slowly decay to pairs of bound Rydberg atoms. 1 aMaghrebi, Mohammad, F.1 aGullans, Michael1 aBienias, P.1 aChoi, S.1 aMartin, I.1 aFirstenberg, O.1 aLukin, M., D.1 aBüchler, H., P.1 aGorshkov, Alexey, V. uhttp://arxiv.org/abs/1505.03859v101005nas a2200157 4500008004100000245006000041210005800101260001500159300001100174490000700185520056500192100001400757700001900771700002000790856003700810 2014 eng d00aA classical channel model for gravitational decoherence0 aclassical channel model for gravitational decoherence c2014/06/26 a0650200 v163 aWe show that, by treating the gravitational interaction between two mechanical resonators as a classical measurement channel, a gravitational decoherence model results that is equivalent to a model first proposed by Diosi. The resulting decoherence model implies that the classically mediated gravitational interaction between two gravitationally coupled resonators cannot create entanglement. The gravitational decoherence rate ( and the complementary heating rate) is of the order of the gravitationally induced normal mode splitting of the two resonators. 1 aKafri, D.1 aTaylor, J., M.1 aMilburn, G., J. uhttp://arxiv.org/abs/1401.0946v101280nas a2200157 4500008004100000245004600041210004500087260001500132300001200147490000700159520085500166100001901021700002101040700002401061856003701085 2014 eng d00aClassical simulation of Yang-Baxter gates0 aClassical simulation of YangBaxter gates c2014/07/05 a161-1750 v273 a A unitary operator that satisfies the constant Yang-Baxter equation immediately yields a unitary representation of the braid group B n for every $n \ge 2$. If we view such an operator as a quantum-computational gate, then topological braiding corresponds to a quantum circuit. A basic question is when such a representation affords universal quantum computation. In this work, we show how to classically simulate these circuits when the gate in question belongs to certain families of solutions to the Yang-Baxter equation. These include all of the qubit (i.e., $d = 2$) solutions, and some simple families that include solutions for arbitrary $d \ge 2$. Our main tool is a probabilistic classical algorithm for efficient simulation of a more general class of quantum circuits. This algorithm may be of use outside the present setting. 1 aAlagic, Gorjan1 aBapat, Aniruddha1 aJordan, Stephen, P. uhttp://arxiv.org/abs/1407.1361v101064nas a2200145 4500008004100000245008600041210006900127260001500196300001200211490000700223520060700230100002100837700002300858856003700881 2014 eng d00aThe computational power of matchgates and the XY interaction on arbitrary graphs0 acomputational power of matchgates and the XY interaction on arbi c2014/09/01 a901-9160 v143 a Matchgates are a restricted set of two-qubit gates known to be classically simulable when acting on nearest-neighbor qubits on a path, but universal for quantum computation when the qubits are arranged on certain other graphs. Here we characterize the power of matchgates acting on arbitrary graphs. Specifically, we show that they are universal on any connected graph other than a path or a cycle, and that they are classically simulable on a cycle. We also prove the same dichotomy for the XY interaction, a proper subset of matchgates related to some implementations of quantum computing. 1 aBrod, Daniel, J.1 aChilds, Andrew, M. uhttp://arxiv.org/abs/1308.1463v102194nas a2200133 4500008004100000245007300041210006800114260001500182520175300197100002301950700002401973700002601997856003702023 2014 eng d00aThe computational power of normalizer circuits over black-box groups0 acomputational power of normalizer circuits over blackbox groups c2014/09/163 a This work presents a precise connection between Clifford circuits, Shor's factoring algorithm and several other famous quantum algorithms with exponential quantum speed-ups for solving Abelian hidden subgroup problems. We show that all these different forms of quantum computation belong to a common new restricted model of quantum operations that we call \emph{black-box normalizer circuits}. To define these, we extend the previous model of normalizer circuits [arXiv:1201.4867v1,arXiv:1210.3637,arXiv:1409.3208], which are built of quantum Fourier transforms, group automorphism and quadratic phase gates associated to an Abelian group $G$. In previous works, the group $G$ is always given in an explicitly decomposed form. In our model, we remove this assumption and allow $G$ to be a black-box group. While standard normalizer circuits were shown to be efficiently classically simulable [arXiv:1201.4867v1,arXiv:1210.3637,arXiv:1409.3208], we find that normalizer circuits are powerful enough to factorize and solve classically-hard problems in the black-box setting. We further set upper limits to their computational power by showing that decomposing finite Abelian groups is complete for the associated complexity class. In particular, solving this problem renders black-box normalizer circuits efficiently classically simulable by exploiting the generalized stabilizer formalism in [arXiv:1201.4867v1,arXiv:1210.3637,arXiv:1409.3208]. Lastly, we employ our connection to draw a few practical implications for quantum algorithm design: namely, we give a no-go theorem for finding new quantum algorithms with black-box normalizer circuits, a universality result for low-depth normalizer circuits, and identify two other complete problems. 1 aBermejo-Vega, Juan1 aLin, Cedric, Yen-Yu1 aVan den Nest, Maarten uhttp://arxiv.org/abs/1409.4800v101598nas a2200157 4500008004100000245007300041210006900114260001500183300001100198490000600209520112600215100002301341700001501364700002401379856003701403 2014 eng d00aConstructing elliptic curve isogenies in quantum subexponential time0 aConstructing elliptic curve isogenies in quantum subexponential  c2014/01/01 a1 - 290 v83 a Given two elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit an isogeny between them, but finding such an isogeny is believed to be computationally difficult. The fastest known classical algorithm takes exponential time, and prior to our work no faster quantum algorithm was known. Recently, public-key cryptosystems based on the presumed hardness of this problem have been proposed as candidates for post-quantum cryptography. In this paper, we give a subexponential-time quantum algorithm for constructing isogenies, assuming the Generalized Riemann Hypothesis (but with no other assumptions). Our algorithm is based on a reduction to a hidden shift problem, together with a new subexponential-time algorithm for evaluating isogenies from kernel ideals (under only GRH), and represents the first nontrivial application of Kuperberg's quantum algorithm for the hidden shift problem. This result suggests that isogeny-based cryptosystems may be uncompetitive with more mainstream quantum-resistant cryptosystems such as lattice-based cryptosystems. 1 aChilds, Andrew, M.1 aJao, David1 aSoukharev, Vladimir uhttp://arxiv.org/abs/1012.4019v201262nas a2200193 4500008004100000245009300041210006900134260001400203490000700217520064800224100002200872700002000894700002500914700002000939700002400959700002100983700002701004856003701031 2013 eng d00aControllable quantum spin glasses with magnetic impurities embedded in quantum solids 0 aControllable quantum spin glasses with magnetic impurities embed c2013/7/240 v883 a Magnetic impurities embedded in inert solids can exhibit long coherence times and interact with one another via their intrinsic anisotropic dipolar interaction. We argue that, as a consequence of these properties, disordered ensembles of magnetic impurities provide an effective platform for realizing a controllable, tunable version of the dipolar quantum spin glass seen in LiHo$_x$Y$_{1-x}$F$_4$. Specifically, we propose and analyze a system composed of dysprosium atoms embedded in solid helium. We describe the phase diagram of the system and discuss the realizability and detectability of the quantum spin glass and antiglass phases. 1 aLemeshko, Mikhail1 aYao, Norman, Y.1 aGorshkov, Alexey, V.1 aWeimer, Hendrik1 aBennett, Steven, D.1 aMomose, Takamasa1 aGopalakrishnan, Sarang uhttp://arxiv.org/abs/1307.1130v101734nas a2200133 4500008004100000245010900041210006900150260001400219490000700233520128500240100001901525700001901544856003701563 2013 eng d00aControlling the group velocity of colliding atomic Bose-Einstein condensates with Feshbach resonances 0 aControlling the group velocity of colliding atomic BoseEinstein  c2013/5/100 v873 a We report on a proposal to change the group velocity of a small Bose Einstein Condensate (BEC) upon collision with another BEC in analogy to slowing of light passing through dispersive media. We make use of ultracold collisions near a magnetic Feshbach resonance, which gives rise to a sharp variation in scattering length with collision energy and thereby changes the group velocity. A generalized Gross-Pitaveskii equation is derived for a small BEC moving through a larger stationary BEC. We denote the two condensates by laser and medium BEC, respectively, to highlight the analogy to a laser pulse travelling through a medium. We derive an expression for the group velocity in a homogeneous medium as well as for the difference in distance, $\delta$, covered by the laser BEC in the presence and absence of a finite-sized medium BEC with a Thomas-Fermi density distribution. For a medium and laser of the same isotopic species, the shift $\delta$ has an upper bound of twice the Thomas-Fermi radius of the medium. For typical narrow Feshbach resonances and a medium with number density $10^{15}$ cm$^{-3}$ up to 85% of the upper bound can be achieved, making the effect experimentally observable. We also derive constraints on the experimental realization of our proposal. 1 aMathew, Ranchu1 aTiesinga, Eite uhttp://arxiv.org/abs/1301.4234v200399nas a2200145 4500008004100000245003500041210003500076300001100111490000700122100001600129700001300145700002500158700001700183856005300200 2012 eng d00aCavity QED with atomic mirrors0 aCavity QED with atomic mirrors a0630030 v141 aChang, D, E1 aJiang, L1 aGorshkov, Alexey, V.1 aKimble, H, J uhttp://iopscience.iop.org/1367-2630/14/6/063003/01351nas a2200181 4500008004100000245009200041210006900133260001500202300001100217490000700228520080600235100001801041700001801059700002301077700001401100700001801114856003701132 2012 eng d00aComment on some results of Erdahl and the convex structure of reduced density matrices0 aComment on some results of Erdahl and the convex structure of re c2012/05/16 a0722030 v533 a In J. Math. Phys. 13, 1608-1621 (1972), Erdahl considered the convex structure of the set of $N$-representable 2-body reduced density matrices in the case of fermions. Some of these results have a straightforward extension to the $m$-body setting and to the more general quantum marginal problem. We describe these extensions, but can not resolve a problem in the proof of Erdahl's claim that every extreme point is exposed in finite dimensions. Nevertheless, we can show that when $2m \geq N$ every extreme point of the set of $N$-representable $m$-body reduced density matrices has a unique pre-image in both the symmetric and anti-symmetric setting. Moreover, this extends to the quantum marginal setting for a pair of complementary $m$-body and $(N-m)$-body reduced density matrices. 1 aChen, Jianxin1 aJi, Zhengfeng1 aRuskai, Mary, Beth1 aZeng, Bei1 aZhou, Duan-Lu uhttp://arxiv.org/abs/1205.3682v101936nas a2200157 4500008004100000245005700041210005700098260001300155490000700168520149900175100001801674700001801692700001701710700001401727856003701741 2012 eng d00aCorrelations in excited states of local Hamiltonians0 aCorrelations in excited states of local Hamiltonians c2012/4/90 v853 a Physical properties of the ground and excited states of a $k$-local Hamiltonian are largely determined by the $k$-particle reduced density matrices ($k$-RDMs), or simply the $k$-matrix for fermionic systems---they are at least enough for the calculation of the ground state and excited state energies. Moreover, for a non-degenerate ground state of a $k$-local Hamiltonian, even the state itself is completely determined by its $k$-RDMs, and therefore contains no genuine ${>}k$-particle correlations, as they can be inferred from $k$-particle correlation functions. It is natural to ask whether a similar result holds for non-degenerate excited states. In fact, for fermionic systems, it has been conjectured that any non-degenerate excited state of a 2-local Hamiltonian is simultaneously a unique ground state of another 2-local Hamiltonian, hence is uniquely determined by its 2-matrix. And a weaker version of this conjecture states that any non-degenerate excited state of a 2-local Hamiltonian is uniquely determined by its 2-matrix among all the pure $n$-particle states. We construct explicit counterexamples to show that both conjectures are false. It means that correlations in excited states of local Hamiltonians could be dramatically different from those in ground states. We further show that any non-degenerate excited state of a $k$-local Hamiltonian is a unique ground state of another $2k$-local Hamiltonian, hence is uniquely determined by its $2k$-RDMs (or $2k$-matrix). 1 aChen, Jianxin1 aJi, Zhengfeng1 aWei, Zhaohui1 aZeng, Bei uhttp://arxiv.org/abs/1106.1373v201641nas a2200193 4500008004100000245005000041210004900091260001500140300001600155490000800171520110300179100002701282700002401309700001901333700001701352700002201369700001901391856003701410 2011 eng d00aCasimir force between sharp-shaped conductors0 aCasimir force between sharpshaped conductors c2011/04/11 a6867 - 68710 v1083 a Casimir forces between conductors at the sub-micron scale cannot be ignored in the design and operation of micro-electromechanical (MEM) devices. However, these forces depend non-trivially on geometry, and existing formulae and approximations cannot deal with realistic micro-machinery components with sharp edges and tips. Here, we employ a novel approach to electromagnetic scattering, appropriate to perfect conductors with sharp edges and tips, specifically to wedges and cones. The interaction of these objects with a metal plate (and among themselves) is then computed systematically by a multiple-scattering series. For the wedge, we obtain analytical expressions for the interaction with a plate, as functions of opening angle and tilt, which should provide a particularly useful tool for the design of MEMs. Our result for the Casimir interactions between conducting cones and plates applies directly to the force on the tip of a scanning tunneling probe; the unexpectedly large temperature dependence of the force in these configurations should attract immediate experimental interest. 1 aMaghrebi, Mohammad, F.1 aRahi, Sahand, Jamal1 aEmig, Thorsten1 aGraham, Noah1 aJaffe, Robert, L.1 aKardar, Mehran uhttp://arxiv.org/abs/1010.3223v101229nas a2200169 4500008004100000245005000041210004800091260001500139490000700154520075700161100001600918700001900934700002300953700002100976700002500997856003701022 2011 eng d00aChern numbers hiding in time-of-flight images0 aChern numbers hiding in timeofflight images c2011/12/210 v843 a We present a technique for detecting topological invariants -- Chern numbers -- from time-of-flight images of ultra-cold atoms. We show that the Chern numbers of integer quantum Hall states of lattice fermions leave their fingerprints in the atoms' momentum distribution. We analytically demonstrate that the number of local maxima in the momentum distribution is equal to the Chern number in two limiting cases, for large hopping anisotropy and in the continuum limit. In addition, our numerical simulations beyond these two limits show that these local maxima persist for a range of parameters. Thus, an everyday observable in cold atom experiments can serve as a useful tool to characterize and visualize quantum states with non-trivial topology. 1 aZhao, Erhai1 aBray-Ali, Noah1 aWilliams, Carl, J.1 aSpielman, I., B.1 aSatija, Indubala, I. uhttp://arxiv.org/abs/1105.3100v300744nas a2200121 4500008004100000245009800041210006900139260001500208520032500223100001900548700001800567856003700585 2011 eng d00aComment on "Foundation of Statistical Mechanics under Experimentally Realistic Conditions" 0 aComment on Foundation of Statistical Mechanics under Experimenta c2011/09/223 a Reimann [Phys. Rev. Lett. 101, 190403 (2008)] claimed that generic isolated macroscopic quantum system will equilibrate under experimentally realistic conditions by proving a theorem. We here show that the proof is invalid for most many-body systems and is unable to demonstrate equilibration in realistic experiment. 1 aGong, Zhe-Xuan1 aDuan, L., -M. uhttp://arxiv.org/abs/1109.4696v101526nas a2200157 4500008004100000245005100041210005000092260001500142520108300157100002201240700001901262700001701281700001601298700001701314856003701331 2011 eng d00aContinuous-variable quantum compressed sensing0 aContinuousvariable quantum compressed sensing c2011/11/033 a We significantly extend recently developed methods to faithfully reconstruct unknown quantum states that are approximately low-rank, using only a few measurement settings. Our new method is general enough to allow for measurements from a continuous family, and is also applicable to continuous-variable states. As a technical result, this work generalizes quantum compressed sensing to the situation where the measured observables are taken from a so-called tight frame (rather than an orthonormal basis) --- hence covering most realistic measurement scenarios. As an application, we discuss the reconstruction of quantum states of light from homodyne detection and other types of measurements, and we present simulations that show the advantage of the proposed compressed sensing technique over present methods. Finally, we introduce a method to construct a certificate which guarantees the success of the reconstruction with no assumption on the state, and we show how slightly more measurements give rise to "universal" state reconstruction that is highly robust to noise. 1 aOhliger, Matthias1 aNesme, Vincent1 aGross, David1 aLiu, Yi-Kai1 aEisert, Jens uhttp://arxiv.org/abs/1111.0853v301458nas a2200145 4500008004100000245005700041210005600098260001500154520102700169100002301196700001801219700002101237700001701258856003701275 2010 eng d00aCharacterization of universal two-qubit Hamiltonians0 aCharacterization of universal twoqubit Hamiltonians c2010/04/093 a Suppose we can apply a given 2-qubit Hamiltonian H to any (ordered) pair of qubits. We say H is n-universal if it can be used to approximate any unitary operation on n qubits. While it is well known that almost any 2-qubit Hamiltonian is 2-universal (Deutsch, Barenco, Ekert 1995; Lloyd 1995), an explicit characterization of the set of non-universal 2-qubit Hamiltonians has been elusive. Our main result is a complete characterization of 2-non-universal 2-qubit Hamiltonians. In particular, there are three ways that a 2-qubit Hamiltonian H can fail to be universal: (1) H shares an eigenvector with the gate that swaps two qubits, (2) H acts on the two qubits independently (in any of a certain family of bases), or (3) H has zero trace. A 2-non-universal 2-qubit Hamiltonian can still be n-universal for some n >= 3. We give some partial results on 3-universality. Finally, we also show how our characterization of 2-universal Hamiltonians implies the well-known result that almost any 2-qubit unitary is universal. 1 aChilds, Andrew, M.1 aLeung, Debbie1 aMancinska, Laura1 aOzols, Maris uhttp://arxiv.org/abs/1004.1645v201025nas a2200121 4500008004100000245007200041210006900113260001500182520063400197100001700831700001800848856003700866 2010 eng d00aContextuality in Quantum Mechanics: Testing the Klyachko Inequality0 aContextuality in Quantum Mechanics Testing the Klyachko Inequali c2010/06/023 a The Klyachko inequality is an inequality for the probabiities of the values of five observables of a spin-1 particle, which is satisfied by any noncontextual assignment of values to this set of observables, but is violated by the probabilities defined by a certain quantum state. We describe an experiment between two entangled spin-1 particles to test contextuality via a related inequality. We point out that a test of contextuality by measurements on a single particle to confirm the Klyachko inequality requires an assumption of non-disturbance by the measuring instrument, which is avoided in the two-particle experiment. 1 aBub, Jeffrey1 aStairs, Allen uhttp://arxiv.org/abs/1006.0500v201723nas a2200157 4500008004100000245008700041210006900128260001500197300001100212490000700223520123400230100002201464700001901486700002301505856003701528 2010 eng d00aCreation and manipulation of Feshbach resonances with radio-frequency radiation 0 aCreation and manipulation of Feshbach resonances with radiofrequ c2010/08/12 a0830310 v123 a We present a simple technique for studying collisions of ultracold atoms in the presence of a magnetic field and radio-frequency radiation (rf). Resonant control of scattering properties can be achieved by using rf to couple a colliding pair of atoms to a bound state. We show, using the example of 6Li, that in some ranges of rf frequency and magnetic field this can be done without giving rise to losses. We also show that halo molecules of large spatial extent require much less rf power than deeply bound states. Another way to exert resonant control is with a set of rf-coupled bound states, linked to the colliding pair through the molecular interactions that give rise to magnetically tunable Feshbach resonances. This was recently demonstrated for 87Rb [Kaufman et al., Phys. Rev. A 80:050701(R), 2009]. We examine the underlying atomic and molecular physics which made this possible. Lastly, we consider the control that may be exerted over atomic collisions by placing atoms in superpositions of Zeeman states, and suggest that it could be useful where small changes in scattering length are required. We suggest other species for which rf and magnetic field control could together provide a useful tuning mechanism. 1 aHanna, Thomas, M.1 aTiesinga, Eite1 aJulienne, Paul, S. uhttp://arxiv.org/abs/1004.0636v101137nas a2200157 4500008004100000245008200041210006900123260001300192490000700205520065000212100001500862700001900877700002300896700002300919856003700942 2009 eng d00aCollisional cooling of ultra-cold atom ensembles using Feshbach resonances 0 aCollisional cooling of ultracold atom ensembles using Feshbach r c2009/9/80 v803 a We propose a new type of cooling mechanism for ultra-cold fermionic atom ensembles, which capitalizes on the energy dependence of inelastic collisions in the presence of a Feshbach resonance. We first discuss the case of a single magnetic resonance, and find that the final temperature and the cooling rate is limited by the width of the resonance. A concrete example, based on a p-wave resonance of $^{40}$K, is given. We then improve upon this setup by using both a very sharp optical or radio-frequency induced resonance and a very broad magnetic resonance and show that one can improve upon temperatures reached with current technologies. 1 aMathey, L.1 aTiesinga, Eite1 aJulienne, Paul, S.1 aClark, Charles, W. uhttp://arxiv.org/abs/0903.2568v101445nas a2200145 4500008004100000245006100041210005900102260001400161300001400175490000700189520103100196100001701227700001801244856003701262 2009 eng d00aContextuality and nonlocality in 'no signaling' theories0 aContextuality and nonlocality in no signaling theories c2009/4/21 a690 - 7110 v393 a We define a family of 'no signaling' bipartite boxes with arbitrary inputs and binary outputs, and with a range of marginal probabilities. The defining correlations are motivated by the Klyachko version of the Kochen-Specker theorem, so we call these boxes Kochen-Specker-Klyachko boxes or, briefly, KS-boxes. The marginals cover a variety of cases, from those that can be simulated classically to the superquantum correlations that saturate the Clauser-Horne-Shimony-Holt inequality, when the KS-box is a generalized PR-box (hence a vertex of the `no signaling' polytope). We show that for certain marginal probabilities a KS-box is classical with respect to nonlocality as measured by the Clauser-Horne-Shimony-Holt correlation, i.e., no better than shared randomness as a resource in simulating a PR-box, even though such KS-boxes cannot be perfectly simulated by classical or quantum resources for all inputs. We comment on the significance of these results for contextuality and nonlocality in 'no signaling' theories. 1 aBub, Jeffrey1 aStairs, Allen uhttp://arxiv.org/abs/0903.1462v201819nas a2200181 4500008004100000245009700041210006900138260001400207490000700221520125900228100001301487700001501500700002001515700001901535700002301554700002301577856003701600 2009 eng d00aCounterflow and paired superfluidity in one-dimensional Bose mixtures in optical lattices 0 aCounterflow and paired superfluidity in onedimensional Bose mixt c2009/8/240 v803 a We study the quantum phases of mixtures of ultra-cold bosonic atoms held in an optical lattice that confines motion or hopping to one spatial dimension. The phases are found by using Tomonaga-Luttinger liquid theory as well as the numerical method of time evolving block decimation (TEBD). We consider a binary mixture with repulsive intra-species interactions, and either repulsive or attractive inter-species interaction. For a homogeneous system, we find paired- and counterflow-superfluid phases at different filling and hopping energies. We also predict parameter regions in which these types of superfluid order coexist with charge density wave order. We show that the Tomonaga-Luttinger liquid theory and TEBD qualitatively agree on the location of the phase boundary to superfluidity. We then describe how these phases are modified and can be detected when an additional harmonic trap is present. In particular, we show how experimentally measurable quantities, such as time-of-flight images and the structure factor, can be used to distinguish the quantum phases. Finally, we suggest applying a Feshbach ramp to detect the paired superfluid state, and a $\pi/2$ pulse followed by Bragg spectroscopy to detect the counterflow superfluid phase. 1 aHu, Anzi1 aMathey, L.1 aDanshita, Ippei1 aTiesinga, Eite1 aWilliams, Carl, J.1 aClark, Charles, W. uhttp://arxiv.org/abs/0906.2150v101409nas a2200193 4500008004100000245006800041210006800109260001400177490000800191520083700199100001701036700002501053700001601078700002001094700002201114700001901136700002301155856003701178 2008 eng d00aCoherence of an optically illuminated single nuclear spin qubit0 aCoherence of an optically illuminated single nuclear spin qubit c2008/2/190 v1003 aWe investigate the coherence properties of individual nuclear spin quantum bits in diamond [Dutt et al., Science, 316, 1312 (2007)] when a proximal electronic spin associated with a nitrogen-vacancy (NV) center is being interrogated by optical radiation. The resulting nuclear spin dynamics are governed by time-dependent hyperfine interaction associated with rapid electronic transitions, which can be described by a spin-fluctuator model. We show that due to a process analogous to motional averaging in nuclear magnetic resonance, the nuclear spin coherence can be preserved after a large number of optical excitation cycles. Our theoretical analysis is in good agreement with experimental results. It indicates a novel approach that could potentially isolate the nuclear spin system completely from the electronic environment. 1 aJiang, Liang1 aDutt, M., V. Gurudev1 aTogan, Emre1 aChildress, Lily1 aCappellaro, Paola1 aTaylor, J., M.1 aLukin, Mikhail, D. uhttp://arxiv.org/abs/0707.1341v201158nas a2200169 4500008004100000245006700041210006700108260001300175490000800188520065200196100002500848700001700873700002000890700001800910700002300928856003700951 2008 eng d00aCoherent Quantum Optical Control with Subwavelength Resolution0 aCoherent Quantum Optical Control with Subwavelength Resolution c2008/3/70 v1003 a We suggest a new method for quantum optical control with nanoscale resolution. Our method allows for coherent far-field manipulation of individual quantum systems with spatial selectivity that is not limited by the wavelength of radiation and can, in principle, approach a few nanometers. The selectivity is enabled by the nonlinear atomic response, under the conditions of Electromagnetically Induced Transparency, to a control beam with intensity vanishing at a certain location. Practical performance of this technique and its potential applications to quantum information science with cold atoms, ions, and solid-state qubits are discussed. 1 aGorshkov, Alexey, V.1 aJiang, Liang1 aGreiner, Markus1 aZoller, Peter1 aLukin, Mikhail, D. uhttp://arxiv.org/abs/0706.3879v201051nas a2200133 4500008004100000245010600041210006900147260001500216520058800231100001900819700001900838700002300857856003700880 2007 eng d00aCoherent, adiabatic and dissociation regimes in coupled atomic-molecular Bose-Einstein condensates 0 aCoherent adiabatic and dissociation regimes in coupled atomicmol c2007/11/023 a We discuss the dynamics of a Bose-Einstein condensate of atoms which is suddenly coupled to a condensate of molecules by an optical or magnetic Feshbach resonance. Three limiting regimes are found and can be understood from the transient dynamics occuring for each pair of atoms. This transient dynamics can be summarised into a time-dependent shift and broadening of the molecular state. A simple Gross-Pitaevskii picture including this shift and broadening is proposed to describe the system in the three regimes. Finally, we suggest how to explore these regimes experimentally. 1 aNaidon, Pascal1 aTiesinga, Eite1 aJulienne, Paul, S. uhttp://arxiv.org/abs/0711.0397v201885nas a2200109 4500008004100000245009000041210006900131260001500200520150700215100001601722856003701738 2007 eng d00aThe Complexity of the Consistency and N-representability Problems for Quantum States0 aComplexity of the Consistency and Nrepresentability Problems for c2007/12/183 a QMA (Quantum Merlin-Arthur) is the quantum analogue of the class NP. There are a few QMA-complete problems, most notably the ``Local Hamiltonian'' problem introduced by Kitaev. In this dissertation we show some new QMA-complete problems. The first one is ``Consistency of Local Density Matrices'': given several density matrices describing different (constant-size) subsets of an n-qubit system, decide whether these are consistent with a single global state. This problem was first suggested by Aharonov. We show that it is QMA-complete, via an oracle reduction from Local Hamiltonian. This uses algorithms for convex optimization with a membership oracle, due to Yudin and Nemirovskii. Next we show that two problems from quantum chemistry, ``Fermionic Local Hamiltonian'' and ``N-representability,'' are QMA-complete. These problems arise in calculating the ground state energies of molecular systems. N-representability is a key component in recently developed numerical methods using the contracted Schrodinger equation. Although these problems have been studied since the 1960's, it is only recently that the theory of quantum computation has allowed us to properly characterize their complexity. Finally, we study some special cases of the Consistency problem, pertaining to 1-dimensional and ``stoquastic'' systems. We also give an alternative proof of a result due to Jaynes: whenever local density matrices are consistent, they are consistent with a Gibbs state. 1 aLiu, Yi-Kai uhttp://arxiv.org/abs/0712.3041v100966nas a2200121 4500008004100000245008500041210006900126260001500195520055300210100001900763700001800782856004400800 2006 eng d00aCavity quantum electrodynamics with semiconductor double-dot molecules on a chip0 aCavity quantum electrodynamics with semiconductor doubledot mole c2006/05/053 aWe describe a coherent control technique for coupling electron spin states associated with semiconductor double-dot molecule to a microwave stripline resonator on a chip. We identify a novel regime of operation in which strong interaction between a molecule and a resonator can be achieved with minimal decoherence, reaching the so-called strong coupling regime of cavity QED. We describe potential applications of such a system, including low-noise coherent electrical control, fast QND measurements of spin states, and long-range spin coupling. 1 aTaylor, J., M.1 aLukin, M., D. uhttp://arxiv.org/abs/cond-mat/0605144v101241nas a2200121 4500008004100000245005800041210005700099260001500156300001200171520087600183100001601059856004401075 2006 eng d00aConsistency of Local Density Matrices is QMA-complete0 aConsistency of Local Density Matrices is QMAcomplete c2006/04/21 a438-4493 a Suppose we have an n-qubit system, and we are given a collection of local density matrices rho_1,...,rho_m, where each rho_i describes a subset C_i of the qubits. We say that the rho_i are ``consistent'' if there exists some global state sigma (on all n qubits) that matches each of the rho_i on the subsets C_i. This generalizes the classical notion of the consistency of marginal probability distributions. We show that deciding the consistency of local density matrices is QMA-complete (where QMA is the quantum analogue of NP). This gives an interesting example of a hard problem in QMA. Our proof is somewhat unusual: we give a Turing reduction from Local Hamiltonian, using a convex optimization algorithm by Bertsimas and Vempala, which is based on random sampling. Unlike in the classical case, simple mapping reductions do not seem to work here. 1 aLiu, Yi-Kai uhttp://arxiv.org/abs/quant-ph/0604166v300408nas a2200121 4500008004100000245005700041210005600098260001500154520003800169100001800207700001700225856004400242 2005 eng d00aConditionalizing and commutativity: a note on Malley0 aConditionalizing and commutativity a note on Malley c2005/06/193 a This paper has been withdrawn. 1 aStairs, Allen1 aBub, Jeffrey uhttp://arxiv.org/abs/quant-ph/0506159v201715nas a2200145 4500008004100000245004200041210004200083260001400125490000700139520130700146100002301453700002401476700002501500856004401525 2005 eng d00aCriteria for Exact Qudit Universality0 aCriteria for Exact Qudit Universality c2005/5/160 v713 a We describe criteria for implementation of quantum computation in qudits. A qudit is a d-dimensional system whose Hilbert space is spanned by states |0>, |1>,... |d-1>. An important earlier work of Mathukrishnan and Stroud [1] describes how to exactly simulate an arbitrary unitary on multiple qudits using a 2d-1 parameter family of single qudit and two qudit gates. Their technique is based on the spectral decomposition of unitaries. Here we generalize this argument to show that exact universality follows given a discrete set of single qudit Hamiltonians and one two-qudit Hamiltonian. The technique is related to the QR-matrix decomposition of numerical linear algebra. We consider a generic physical system in which the single qudit Hamiltonians are a small collection of H_{jk}^x=\hbar\Omega (|k>k iff H_{jk}^{x,y} are allowed Hamiltonians. One qudit exact universality follows iff this graph is connected, and complete universality results if the two-qudit Hamiltonian H=-\hbar\Omega |d-1,d-1>