@article {3407, title = {A Case for Synthesis of Recursive Quantum Unitary Programs}, journal = {Proceedings of the ACM on Programming Languages}, volume = {8}, year = {2024}, month = {12/5/2023}, pages = {1759{\textendash}1788}, abstract = {

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.

}, issn = {2475-1421}, doi = {10.1145/3632901}, url = {https://arxiv.org/abs/2311.11503}, author = {Deng, Haowei and Tao, Runzhou and Peng, Yuxiang and Wu, Xiaodi} } @article {3506, title = {Clifford-Deformed Surface Codes}, journal = {PRX Quantum}, volume = {5}, year = {2024}, month = {3/19/2024}, abstract = {

Various realizations of Kitaev\&$\#$39;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.

}, issn = {2691-3399}, doi = {http://dx.doi.org/10.1103/PRXQuantum.5.010347}, url = {https://arxiv.org/abs/2201.07802}, author = {Dua, Arpit and Kubica, Aleksander and Jiang, Liang and Flammia, Steven T. and Michael Gullans} } @article {3492, title = {Complexity-constrained quantum thermodynamics}, year = {2024}, month = {3/7/2024}, abstract = {

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\&$\#$39;s complexity is restricted. We focus on the prototypical task of information erasure, or Landauer erasure, wherein an n-qubit memory is reset to the all-zero state. We show that the minimum thermodynamic work required to reset an arbitrary state, via a complexity-constrained process, is quantified by the state\&$\#$39;s complexity entropy. The complexity entropy therefore quantifies a trade-off between the work cost and complexity cost of resetting a state. If the qubits have a nontrivial (but product) Hamiltonian, the optimal work cost is determined by the complexity relative entropy. The complexity entropy quantifies the amount of randomness a system appears to have to a computationally limited observer. Similarly, the complexity relative entropy quantifies such an observer\&$\#$39;s ability to distinguish two states. We prove elementary properties of the complexity (relative) entropy and determine the complexity entropy\&$\#$39;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.

}, url = {https://arxiv.org/abs/2403.04828}, author = {Anthony Munson and Naga Bhavya Teja Kothakonda and Jonas Haferkamp and Nicole Yunger Halpern and Jens Eisert and Philippe Faist} } @article {3460, title = {Complexity-constrained quantum thermodynamics}, year = {2024}, month = {3/7/2024}, abstract = {

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\&$\#$39;s complexity is restricted. We focus on the prototypical task of information erasure, or Landauer erasure, wherein an n-qubit memory is reset to the all-zero state. We show that the minimum thermodynamic work required to reset an arbitrary state, via a complexity-constrained process, is quantified by the state\&$\#$39;s complexity entropy. The complexity entropy therefore quantifies a trade-off between the work cost and complexity cost of resetting a state. If the qubits have a nontrivial (but product) Hamiltonian, the optimal work cost is determined by the complexity relative entropy. The complexity entropy quantifies the amount of randomness a system appears to have to a computationally limited observer. Similarly, the complexity relative entropy quantifies such an observer\&$\#$39;s ability to distinguish two states. We prove elementary properties of the complexity (relative) entropy and determine the complexity entropy\&$\#$39;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.

}, url = {https://arxiv.org/abs/2403.04828}, author = {Anthony Munson and Naga Bhavya Teja Kothakonda and Jonas Haferkamp and Nicole Yunger Halpern and Jens Eisert and Philippe Faist} } @article {3514, title = {Continuous-Variable Quantum State Designs: Theory and Applications}, journal = {Phys. Rev. X}, volume = {14}, year = {2024}, month = {2/8/2024}, pages = {011013}, abstract = {

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.

}, doi = {10.1103/PhysRevX.14.011013}, url = {https://link.aps.org/doi/10.1103/PhysRevX.14.011013}, author = {Iosue, Joseph T. and Sharma, Kunal and Michael Gullans and Albert, Victor V.} } @article {3258, title = {Candidate for a passively protected quantum memory in two dimensions}, year = {2023}, month = {3/2/2023}, abstract = {

An interesting problem in the field of quantum error correction involves finding a physical system that hosts a {\textquoteleft}{\textquoteleft}passively protected quantum memory,\&$\#$39;\&$\#$39; defined as an encoded qubit coupled to an environment that naturally wants to correct errors. To date, a quantum memory stable against finite-temperature effects is only known in four spatial dimensions or higher. Here, we take a different approach to realize a stable quantum memory by relying on a driven-dissipative environment. We propose a new model, the photonic-Ising model, which appears to passively correct against both bit-flip and phase-flip errors in two dimensions: A square lattice composed of photonic {\textquoteleft}{\textquoteleft}cat qubits\&$\#$39;\&$\#$39; 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.

}, url = {https://arxiv.org/abs/2205.09767}, author = {Simon Lieu and Yu-Jie Liu and Alexey V. Gorshkov} } @article {3410, title = {Clifford operations and homological codes for rotors and oscillators}, year = {2023}, month = {11/13/2023}, abstract = {

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].

}, url = {https://arxiv.org/abs/2311.07679}, author = {Yijia Xu and Yixu Wang and Victor V. Albert} } @article {3248, title = {Collision-resolved pressure sensing}, year = {2023}, month = {3/17/2023}, abstract = {

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 {\textquoteleft}{\textquoteleft}standard quantum limit\&$\#$39;\&$\#$39; 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.

}, url = {https://arxiv.org/abs/2303.09922}, author = {Daniel S. Barker and Daniel Carney and Thomas W. LeBrun and David C. Moore and Jacob M. Taylor} } @article {3317, title = {Colloquium: Advances in automation of quantum dot devices control}, journal = {Reviews of Modern Physics}, volume = {95}, year = {2023}, month = {2/17/2023}, abstract = {

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.

}, doi = {10.1103/revmodphys.95.011006}, url = {https://arxiv.org/abs/2112.09362}, author = {Justyna P. Zwolak and Jacob M. Taylor} } @article {3311, title = {Colloquium: Quantum and Classical Discrete Time Crystals}, year = {2023}, month = {5/15/2023}, abstract = {

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.

}, url = {https://arxiv.org/abs/2305.08904}, author = {Michael P. Zaletel and Mikhail Lukin and Christopher Monroe and Chetan Nayak and Frank Wilczek and Norman Y. Yao} } @article {3353, title = {Complexity and order in approximate quantum error-correcting codes}, year = {2023}, month = {10/7/2023}, abstract = {

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 {\textquoteleft}{\textquoteleft}phases\&$\#$39;\&$\#$39; of codes. Based on our results, we propose O(k/n) as a boundary between subspaces that should and should not count as AQEC codes. This theory of AQEC provides a versatile framework for understanding the quantum complexity and order of many-body quantum systems, offering new insights for wide-ranging physical scenarios, in particular topological order and critical quantum systems which are of outstanding importance in many-body and high energy physics. We observe from various different perspectives that roughly O(1/n) represents a common, physically significant {\textquoteleft}{\textquoteleft}scaling threshold\&$\#$39;\&$\#$39; of subsystem variance for features associated with nontrivial quantum order.

}, url = {https://arxiv.org/abs/2310.04710}, author = {Jinmin Yi and Weicheng Ye and Daniel Gottesman and Zi-Wen Liu} } @article {3415, title = {Compressed gate characterization for quantum devices with time-correlated noise}, year = {2023}, month = {12/22/2023}, abstract = {

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.

}, url = {https://arxiv.org/abs/2307.14432}, author = {Michael Gullans and M. Caranti and A. R. Mills and J. R. Petta} } @article {3367, title = {Critical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits}, journal = {Physical Review B}, volume = {108}, year = {2023}, month = {8/17/2023}, abstract = {

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\&$\#$39;s non-Abelian nature, measuring qubit pairs allows for nontrivial entanglement scaling even in the measurement-only limit. We find a transition between a volume-law entangled phase and a critical phase whose diffusive purification dynamics emerge from the non-Abelian symmetry. Additionally, we numerically identify a \"spin-sharpening transition.\" On one side is a phase in which the measurements can efficiently identify the system\&$\#$39;s total spin quantum number; on the other side is a phase in which measurements cannot.

}, doi = {10.1103/physrevb.108.054307}, url = {https://arxiv.org/abs/2305.13356}, author = {Shayan Majidy and Utkarsh Agrawal and Sarang Gopalakrishnan and Andrew C. Potter and Romain Vasseur and Nicole Yunger Halpern} } @article {3073, title = {Candidate for a self-correcting quantum memory in two dimensions}, year = {2022}, month = {5/19/2022}, abstract = {

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.\ 

}, url = {https://arxiv.org/abs/2205.09767}, author = {Simon Lieu and Yu-Jie Liu and Alexey V. Gorshkov} } @article {3075, title = {Certifying Temporal Correlations}, year = {2022}, month = {6/13/2022}, abstract = {

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.\ 

}, url = {https://arxiv.org/abs/2206.06092}, author = {Harshank Shrotriya and Leong-Chuan Kwek, Kishor Bharti and Kishor Bharti} } @article {2945, title = {Chiral central charge from a single bulk wave function}, journal = {Phys. Rev. Lett. }, volume = {128}, year = {2022}, month = {4/28/2022}, pages = {176402}, abstract = {

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.

}, doi = {10.1103/PhysRevLett.128.176402}, url = {https://arxiv.org/abs/2110.06932}, author = {Isaac H. Kim and Bowen Shi and Kohtaro Kato and Victor V. Albert} } @article {2930, title = {Classification of (2+1)D invertible fermionic topological phases with symmetry}, journal = {Phys. Rev. B}, volume = {105}, year = {2022}, month = {5/30/2022}, abstract = {

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.\ 

}, doi = {https://doi.org/10.1103/PhysRevB.105.235143}, url = {https://arxiv.org/abs/2109.11039}, author = {Maissam Barkeshli and Yu-An Chen and Po-Shen Hsin and Naren Manjunath} } @article {3082, title = {Closing the Locality and Detection Loopholes in Multiparticle Entanglement Self-Testing}, journal = {Physical Review Letters}, volume = {128}, year = {2022}, month = {06/23/2022}, pages = {250401}, abstract = {

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.

}, doi = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.250401}, url = {https://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-Entangl}, author = {Dian Wu and Qi Zhao and Can Wang and Liang Huang and Yang-Fan Jiang and Bing Bai and You Zhou and Xue-Mei Gu and Feng-Ming Liu and Ying-Qiu Mao and Qi-Chao Sun and Ming-Cheng Chen and Jun Zhang and Cheng-Zhi Peng and Xiao-Bo Zhu and Qiang Zhang and Chao-Yang Lu and Jian-Wei Pan} } @article {3144, title = {Codimension-2 defects and higher symmetries in (3+1)D topological phases}, year = {2022}, month = {8/15/2022}, abstract = {

(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.

}, keywords = {FOS: Mathematics, FOS: Physical sciences, High Energy Physics - Theory (hep-th), Mathematical Physics (math-ph), Quantum Algebra (math.QA), Quantum Physics (quant-ph), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2208.07367}, url = {https://arxiv.org/abs/2208.07367}, author = {Barkeshli, Maissam and Chen, Yu-An and Huang, Sheng-Jie and Kobayashi, Ryohei and Tantivasadakarn, Nathanan and Zhu, Guanyu} } @article {3080, title = {Combining machine learning with physics: A framework for tracking and sorting multiple dark solitons}, journal = {Phys. Rev. Research}, volume = {4}, year = {2022}, month = {06/01/2022}, pages = {023163 }, abstract = {

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.

}, doi = {https://doi.org/10.1103/PhysRevResearch.4.023163}, url = {https://arxiv.org/abs/2111.04881}, author = {Shangjie Guo and Sophia M. Koh and Amilson R. Fritsch and I. B. Spielman and Justyna P. Zwolak} } @article {3066, title = {Computational advantage of quantum random sampling}, year = {2022}, month = {6/8/2022}, abstract = {

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.

}, url = {https://arxiv.org/abs/2206.04079}, author = {Dominik Hangleiter and Jens Eisert} } @article {3021, title = {Computational self-testing of multi-qubit states and measurements}, year = {2022}, month = {1/31/2022}, abstract = {

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.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2201.13430}, url = {https://arxiv.org/abs/2201.13430}, author = {Fu, Honghao and Daochen Wang and Zhao, Qi} } @article {2488, title = {Constant-sized correlations are sufficient to robustly self-test maximally entangled states with unbounded dimension}, journal = {Quantum}, volume = {6}, year = {2022}, month = {01/03/2022}, pages = {614}, abstract = {

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.

}, doi = {https://doi.org/10.22331/q-2022-01-03-614}, url = {https://arxiv.org/abs/1911.01494}, author = {Honghao Fu} } @article {3184, title = {Continuous Symmetry Breaking in a Trapped-Ion Spin Chain}, year = {2022}, month = {11/2/2022}, abstract = {

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.

}, keywords = {FOS: Physical sciences, Quantum Gases (cond-mat.quant-gas), Quantum Physics (quant-ph), Statistical Mechanics (cond-mat.stat-mech), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2211.01275}, url = {https://arxiv.org/abs/2211.01275}, author = {Feng, Lei and Katz, Or and Haack, Casey and Maghrebi, Mohammad and Alexey V. Gorshkov and Gong, Zhexuan and Cetina, Marko and Monroe, Christopher} } @article {3182, title = {Continuous-Variable Shadow Tomography}, year = {2022}, month = {11/9/2022}, abstract = {

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.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2211.05149}, url = {https://arxiv.org/abs/2211.05149}, author = {Gandhari, Srilekha and Victor V. Albert and Gerrits, Thomas and Taylor, Jacob M. and Michael Gullans} } @article {3072, title = {A Convergence Theory for Over-parameterized Variational Quantum Eigensolvers}, year = {2022}, month = {5/25/2022}, abstract = {

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\&$\#$39;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

}, url = {https://arxiv.org/abs/2205.12481}, author = {Xuchen You and Shouvanik Chakrabarti and Xiaodi Wu} } @article {3007, title = {Convex optimization for non-equilibrium steady states on a hybrid quantum processor}, year = {2022}, month = {4/7/2022}, abstract = {

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.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {https://doi.org/10.48550/arXiv.2204.03203}, url = {https://arxiv.org/abs/2204.03203}, author = {Lau, Jonathan Wei Zhong and Lim, Kian Hwee and Bharti, Kishor and Kwek, Leong-Chuan and Vinjanampathy, Sai} } @article {3128, title = {CoVault: A Secure Analytics Platform}, year = {2022}, month = {8/7/2022}, abstract = {

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\&$\#$39; 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.

}, keywords = {and Cluster Computing (cs.DC), Cryptography and Security (cs.CR), Distributed, FOS: Computer and information sciences, Parallel}, doi = {10.48550/ARXIV.2208.03784}, url = {https://arxiv.org/abs/2208.03784}, author = {De Viti, Roberta and Sheff, Isaac and Glaeser, Noemi and Dinis, Baltasar and Rodrigues, Rodrigo and Katz, Jonathan and Bhattacharjee, Bobby and Hithnawi, Anwar and Garg, Deepak and Druschel, Peter} } @article {2307, title = {Can you sign a quantum state?}, journal = {v4: version for publication in Quantum, v5: CC license}, year = {2021}, month = {12/6/2021}, abstract = {

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.

}, url = {https://arxiv.org/abs/1811.11858}, author = {Gorjan Alagic and Tommaso Gagliardoni and Christian Majenz} } @article {2857, title = {Chiral transport of hot carriers in graphene in the quantum Hall regime}, year = {2021}, month = {10/3/2021}, abstract = {

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\&$\#$39; edges are observed. These oscillation amplitudes form an envelope which depends on the strength of the magnetic field, as does the PCs\&$\#$39; 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.\ 

}, url = {https://arxiv.org/abs/2110.01079}, author = {Bin Cao and Tobias Grass and Olivier Gazzano and Kishan Ashokbhai Patel and Jiuning Hu and Markus M{\"u}ller and Tobias Huber and Luca Anzi and Kenji Watanabe and Takashi Taniguchi and David Newell and Michael Gullans and Roman Sordan and Mohammad Hafezi and Glenn Solomon} } @article {2813, title = {Circuit Quantum Electrodynamics in Hyperbolic Space: From Photon Bound States to Frustrated Spin Models}, year = {2021}, month = {5/13/2021}, abstract = {

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 Poincar{\'e} 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.

}, url = {https://arxiv.org/abs/2105.06490}, author = {Przemyslaw Bienias and Igor Boettcher and Ron Belyansky and Alicia J. Koll{\'a}r and Alexey V. Gorshkov} } @article {2684, title = {Circulation by microwave-induced vortex transport for signal isolation}, journal = {PRX Quantum}, volume = {2}, year = {2021}, month = {6/14/2021}, pages = {030309}, abstract = {

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.

}, doi = {https://doi.org/10.1103/PRXQuantum.2.030309}, url = {https://arxiv.org/abs/2010.04118}, author = {Brittany Richman and J. M. Taylor} } @article {2920, title = {Clustering of steady-state correlations in open systems with long-range interactions}, year = {2021}, month = {10/28/2021}, abstract = {

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.

}, url = {https://arxiv.org/abs/2110.15368}, author = {Andrew Y. Guo and Simon Lieu and Minh C. Tran and Alexey V. Gorshkov} } @article {2914, title = {Comment on "Using an atom interferometer to infer gravitational entanglement generation{\textquoteright}{\textquoteright}}, year = {2021}, month = {11/8/2021}, abstract = {

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.

}, url = {https://arxiv.org/abs/2111.04667}, author = {Daniel Carney and Holger M{\"u}ller and Jacob M. Taylor} } @article {2867, title = {Complexity of Fermionic Dissipative Interactions and Applications to Quantum Computing}, journal = {PRX Quantum}, volume = {2}, year = {2021}, month = {9/17/2021}, abstract = {

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.\ 

}, issn = {2691-3399}, doi = {10.1103/prxquantum.2.030350}, url = {http://dx.doi.org/10.1103/PRXQuantum.2.030350}, author = {Shtanko, Oles and Deshpande, Abhinav and Julienne, Paul S. and Alexey V. Gorshkov} } @article {2807, title = {Compressed Sensing Measurement of Long-Range Correlated Noise}, year = {2021}, month = {5/26/2021}, abstract = {

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.

}, url = {https://arxiv.org/abs/2105.12589}, author = {Alireza Seif and Mohammad Hafezi and Yi-Kai Liu} } @article {2638, title = {Conformal field theories are magical}, journal = {Physical Review B}, volume = {103}, year = {2021}, month = {2/25/2021}, pages = {075145}, abstract = {

\"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\&$\#$39;s critical point, and that this mana resides in the system\&$\#$39;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.

}, doi = {https://journals.aps.org/prb/pdf/10.1103/PhysRevB.103.075145}, url = {https://arxiv.org/abs/2007.01303}, author = {Christopher David White and ChunJun Cao and Brian Swingle} } @article {2939, title = {Constructing quantum many-body scar Hamiltonians from Floquet automata}, year = {2021}, month = {12/22/2021}, abstract = {

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.

}, url = {https://arxiv.org/abs/2112.12153}, author = {Pierre-Gabriel Rozon and Michael Gullans and Kartiek Agarwal} } @article {2919, title = {Cross-Platform Comparison of Arbitrary Quantum Computations}, year = {2021}, month = {7/27/2021}, abstract = {

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.

}, url = {https://arxiv.org/abs/2107.11387}, author = {Daiwei Zhu and Ze-Pei Cian and Crystal Noel and Andrew Risinger and Debopriyo Biswas and Laird Egan and Yingyue Zhu and Alaina M. Green and Cinthia Huerta Alderete and Nhung H. Nguyen and Qingfeng Wang and Andrii Maksymov and Yunseong Nam and Marko Cetina and Norbert M. Linke and Mohammad Hafezi and Christopher Monroe} } @article {2815, title = {Crystallography of Hyperbolic Lattices}, year = {2021}, month = {5/3/2021}, abstract = {

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\&$\#$39;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.

}, url = {https://arxiv.org/abs/2105.01087}, author = {Igor Boettcher and Alexey V. Gorshkov and Alicia J. Koll{\'a}r and Joseph Maciejko and Steven Rayan and Ronny Thomale} } @article {2526, title = {Can graph properties have exponential quantum speedup?}, year = {2020}, month = {1/28/2020}, abstract = {

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.

}, url = {https://arxiv.org/abs/2001.10520}, author = {Andrew M. Childs and Daochen Wang} } @article {2575, title = {The Character of Motional Modes for Entanglement and Sympathetic Cooling of Mixed-Species Trapped Ion Chains}, year = {2020}, month = {4/16/2020}, abstract = {

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.

}, url = {https://arxiv.org/abs/2004.08045}, author = {Ksenia Sosnova and Allison Carter and Christopher Monroe} } @article {2364, title = {Circuit Complexity across a Topological Phase Transition}, journal = {Physical Review Research }, volume = {2}, year = {2020}, month = {03/16/2020}, pages = {013323}, abstract = {

We use Nielsen\&$\#$39;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.

}, doi = {https://doi.org/10.1103/PhysRevResearch.2.013323}, url = {https://arxiv.org/abs/1902.10720}, author = {Fangli Liu and Rex Lundgren and Paraj Titum and James R. Garrison and Alexey V. Gorshkov} } @article {2565, title = {Classical Models of Entanglement in Monitored Random Circuits}, year = {2020}, month = {4/14/2020}, abstract = {

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 R{\'e}nyi entropy and demonstrate that, in one dimension and in the limit of large local dimension, it coincides with the corresponding second-R{\'e}nyi-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.

}, url = {https://arxiv.org/abs/2004.06736}, author = {Oles Shtanko and Yaroslav A. Kharkov and Luis Pedro Garc{\'\i}a-Pintos and Alexey V. Gorshkov} } @article {2683, title = {Coherent transport of spin by adiabatic passage in quantum dot arrays}, journal = {Phys. Rev. B}, volume = {102}, year = {2020}, month = {9/17/2020}, abstract = {

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.

}, doi = {https://doi.org/10.1103/PhysRevB.102.155404}, url = {https://arxiv.org/abs/2007.10582}, author = {Michael Gullans and J. R. Petta} } @article {2779, title = {Coherent transport of spin by adiabatic passage in quantum dot arrays}, journal = {Physical Review B}, volume = {102}, year = {2020}, month = {9/17/2020}, abstract = {

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.

}, issn = {2469-9950}, doi = {10.1103/PhysRevB.102.155404}, url = {https://arxiv.org/abs/2007.10582}, author = {Michael Gullans and Petta, J. R.} } @article {2585, title = {Collisions of room-temperature helium with ultracold lithium and the van der Waals bound state of HeLi}, journal = {Phys. Rev. A }, volume = {101}, year = {2020}, month = {1/6/2020}, abstract = {

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 Schr{\"o}dinger 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 \…

}, doi = {https://doi.org/10.1103/PhysRevA.101.012702}, author = {Constantinos Makrides and Daniel S Barker and James A Fedchak and Julia Scherschligt and Stephen Eckel and Eite Tiesinga} } @article {2573, title = {Computations with Greater Quantum Depth Are Strictly More Powerful (Relative to an Oracle)}, journal = {Accepted to the Symposium on the Theory of Computing (STOC) 2020 conference}, year = {2020}, month = {4/23/2020}, abstract = {

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\&$\#$39;s oracle separation conjecture and provides a counterpoint to Jozsa\&$\#$39;s conjecture relative to the Welded Tree oracle problem. More precisely, we define two complexity classes, HQC and JC whose languages are decided by two different families of interleaved quantum-classical circuits. HQC contains BPPBQNC and is therefore relevant to Aaronson\&$\#$39;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.

}, doi = {https://doi.org/10.1145/3357713.3384269}, url = {https://arxiv.org/abs/1909.10503}, author = {Matthew Coudron and Sanketh Menda} } @article {2695, title = {Confronting lattice parton distributions with global QCD analysis}, year = {2020}, month = {10/1/2020}, abstract = {

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

}, url = {https://arxiv.org/abs/2010.00548}, author = {Jacob Bringewatt and N. Sato and W. Melnitchouk and Jian-Wei Qiu and F. Steffens and M. Constantinou} } @article {2723, title = {Constant-round Blind Classical Verification of Quantum Sampling}, year = {2020}, month = {12/8/2020}, abstract = {

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\&$\#$39;s input. It is a highly desirable property that has been intensively studied for the delegation of quantum computation. We provide a simple yet powerful generic compiler that transforms any CVQC protocol to a blind one while preserving its completeness and soundness errors as well as the number of rounds. Applying our compiler to (a parallel repetition of) Mahadev\&$\#$39;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.

}, url = {https://arxiv.org/abs/2012.04848}, author = {Kai-Min Chung and Yi Lee and Han-Hsuan Lin and Xiaodi Wu} } @article {2572, title = {Constructing Multipartite Bell inequalities from stabilizers}, year = {2020}, month = {2/5/2020}, abstract = {

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.

}, url = {https://arxiv.org/abs/2002.01843}, author = {Qi Zhao and You Zhou} } @article {2719, title = {Continuous symmetries and approximate quantum error correction}, journal = {Phys. Rev. X}, volume = {10}, year = {2020}, month = {10/26/2020}, abstract = {

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.

}, doi = {https://journals.aps.org/prx/abstract/10.1103/PhysRevX.10.041018}, url = {https://arxiv.org/abs/1902.07714}, author = {Philippe Faist and Sepehr Nezami and Victor V. Albert and Grant Salton and Fernando Pastawski and Patrick Hayden and John Preskill} } @article {2637, title = {Critical Theory for the Breakdown of Photon Blockade}, year = {2020}, month = {6/9/2020}, abstract = {

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.

}, url = {https://arxiv.org/abs/2006.05593}, author = {Jonathan B. Curtis and Igor Boettcher and Jeremy T. Young and Mohammad F. Maghrebi and Howard Carmichael and Alexey V. Gorshkov and Michael Foss-Feig} } @article {2271, title = {Canonical forms for single-qutrit Clifford+T operators}, journal = {Annals of Physics}, volume = {406}, year = {2019}, month = {8/19/2019}, pages = {54-70}, abstract = {

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.\ 

}, doi = {https://doi.org/10.1016/j.aop.2019.04.001}, url = {https://arxiv.org/abs/1803.05047}, author = {Andrew N. Glaudell and Neil J. Ross and J. M. Taylor} } @article {2374, title = {Chaos in a quantum rotor model}, year = {2019}, month = {01/29/2019}, abstract = {

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.\ 

}, url = {https://arxiv.org/abs/1901.10446}, author = {Gong Cheng and Brian Swingle} } @article {2372, title = {A characterization of quantum chaos by two-point correlation functions}, year = {2019}, month = {02/28/2019}, abstract = {

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).

}, url = {https://arxiv.org/abs/1902.11086}, author = {Hrant Gharibyan and Masanori Hanada and Brian Swingle and Masaki Tezuka} } @article {2361, title = {Circuit Transformations for Quantum Architectures}, journal = {Proceedings of TQC 2019, LIPIcs}, volume = {135 }, year = {2019}, month = {02/25/2019}, chapter = {1-3:24}, abstract = {

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.

}, doi = {https://doi.org/10.4230/LIPIcs.TQC.2019.3}, url = {https://arxiv.org/abs/1902.09102}, author = {Andrew M. Childs and Eddie Schoute and Cem M. Unsal} } @article {2451, title = {Classifying single-qubit noise using machine learning}, year = {2019}, month = {8/30/2019}, abstract = {

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.\ 

}, url = {https://arxiv.org/abs/1908.11762}, author = {Travis L. Scholten and Yi-Kai Liu and Kevin Young and Robin Blume-Kohout} } @article {2407, title = {Competing (Semi)-Selfish Miners in Bitcoin}, year = {2019}, month = {06/11/2019}, abstract = {

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.\ 

}, url = {https://arxiv.org/abs/1906.04502}, author = {Francisco J. Marmolejo-Coss{\'\i}o and Eric Brigham and Benjamin Sela and Jonathan Katz} } @article {2406, title = {Complexity phase diagram for interacting and long-range bosonic Hamiltonians}, year = {2019}, month = {06/10/2019}, abstract = {

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.\ 

}, url = {https://arxiv.org/abs/1906.04178}, author = {Nishad Maskara and Abhinav Deshpande and Minh C. Tran and Adam Ehrenberg and Bill Fefferman and Alexey V. Gorshkov} } @article {2264, title = {Confined Dynamics in Long-Range Interacting Quantum Spin Chains}, journal = {Phys. Rev. Lett.}, volume = {122 }, year = {2019}, month = {04/17/2019}, abstract = {

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.

}, doi = {https://doi.org/10.1103/PhysRevLett.122.150601}, url = {https://arxiv.org/abs/1810.02365}, author = {Fangli Liu and Rex Lundgren and Paraj Titum and Guido Pagano and Jiehang Zhang and Christopher Monroe and Alexey V. Gorshkov} } @conference {2129, title = {Capacity Approaching Codes for Low Noise Interactive Quantum Communication}, booktitle = {Annual ACM Symposium on the Theory of Computing STOC 2018}, year = {2018}, month = {2018/01/01}, abstract = {
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\&$\#$39;14].
Our work also improves over the best previously known quantum result
where the overhead is a non-explicit large constant [Brassard \emph{et
\  \  al.}, FOCS\&$\#$39;14] for low $\epsilon$.
}, url = {http://acm-stoc.org/stoc2018/STOC-2018-Accepted.html}, author = {Debbie Leung and Ashwin Nayak and Ala Shayeghi and Dave Touchette and Penghui Yao and Nengkun Yu} } @article {2272, title = {Circuit QED-based measurement of vortex lattice order in a Josephson junction array}, journal = {Phys. Rev. B 98, 060501}, year = {2018}, month = {2018/03/12}, abstract = {

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.\ 

}, doi = {https://doi.org/10.1103/PhysRevB.98.060501}, url = {https://arxiv.org/abs/1803.04113}, author = {R. Cosmic and Hiroki Ikegami and Zhirong Lin and Kunihiro Inomata and J. M. Taylor and Yasunobu Nakamura} } @article {2221, title = {Classical lower bounds from quantum upper bounds}, year = {2018}, abstract = {

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\&$\#$39;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.

}, url = {https://arxiv.org/abs/1807.06256}, author = {Shalev Ben-David and Adam Bouland and Ankit Garg and Robin Kothari} } @article {2216, title = {Coherent optical nano-tweezers for ultra-cold atoms}, year = {2018}, abstract = {

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.

}, url = {https://arxiv.org/abs/1808.02487}, author = {P. Bienias and S. Subhankar and Y. Wang and T-C Tsui and F. Jendrzejewski and T. Tiecke and G. Juzeliunas and L. Jiang and S. L. Rolston and J. V. Porto and Alexey V. Gorshkov} } @article {2283, title = {A Coherent Spin-Photon Interface in Silicon}, journal = {Nature }, volume = {555}, year = {2018}, month = {2018/03/29}, pages = {599-603}, abstract = {

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.

}, doi = {https://doi.org/10.1038/nature25769}, url = {https://arxiv.org/abs/1710.03265}, author = {X. Mi and M. Benito and S. Putz and D. M. Zajac and J. M. Taylor and Guido Burkard and J. R. Petta} } @article {2148, title = {A coherent spin{\textendash}photon interface in silicon}, journal = {Nature}, year = {2018}, month = {2018/02/14}, abstract = {

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.

}, doi = {10.1038/nature25769}, url = {https://www.nature.com/articles/nature25769$\#$author-information}, author = {X. Mi and M. Benito and S. Putz and D. M. Zajac and J. M. Taylor and Guido Burkard and J. R. Petta} } @article {2289, title = {Cryogenic Trapped-Ion System for Large Scale Quantum Simulation}, year = {2018}, abstract = {

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.

}, url = {https://arxiv.org/abs/1802.03118}, author = {G. Pagano and P. W. Hess and H. B. Kaplan and W. L. Tan and P. Richerme and P. Becker and A. Kyprianidis and J. Zhang and E. Birckelbaw and M. R. Hernandez and Y. Wu and C. Monroe} } @article {1971, title = {Complete 3-Qubit Grover Search on a Programmable Quantum Computer}, journal = {Nature Communications, accepted}, year = {2017}, month = {2017/03/30}, abstract = {

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.

}, url = {https://arxiv.org/abs/1703.10535}, author = {C. Figgatt and Dmitri Maslov and K. A. Landsman and N. M. Linke and S. Debnath and Christopher Monroe} } @article {1952, title = {Complexity of sampling as an order parameter}, year = {2017}, month = {2017/03/15}, abstract = {

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.

}, url = {https://arxiv.org/abs/1703.05332}, author = {Abhinav Deshpande and Bill Fefferman and Michael Foss-Feig and Alexey V. Gorshkov} } @article {2056, title = {Computational Notions of Quantum Min-Entropy}, year = {2017}, month = {2017/09/09}, abstract = {

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.

}, url = {https://arxiv.org/abs/1704.07309}, author = {Yi-Hsiu Chen and Kai-Min Chung and Ching-Yi Lai and Salil P. Vadhan and Xiaodi Wu} } @article {1820, title = {Cooling a harmonic oscillator by optomechanical modification of its bath}, journal = {Physical Review Letters}, volume = {118}, year = {2017}, month = {2017/05/31}, pages = {223602}, abstract = {

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.

}, doi = {doi.org/10.1103/PhysRevLett.118.223602}, url = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.223602}, author = {Xunnong Xu and Thomas Purdy and J. M. Taylor} } @article {1814, title = {Correlated Photon Dynamics in Dissipative Rydberg Media}, journal = {Physical Review Letters}, volume = {119}, year = {2017}, month = {2017/07/26}, pages = {043602}, abstract = {

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.

}, doi = {10.1103/PhysRevLett.119.043602}, url = {https://arxiv.org/abs/1608.06068}, author = {Emil Zeuthen and Michael Gullans and Mohammad F. Maghrebi and Alexey V. Gorshkov} } @article {1960, title = {Causality and quantum criticality in long-range lattice models}, journal = {Physical Review B}, volume = {93}, year = {2016}, month = {2016/03/17}, pages = {125128}, doi = {10.1103/PhysRevB.93.125128}, url = {http://link.aps.org/doi/10.1103/PhysRevB.93.125128}, author = {Mohammad F. Maghrebi and Zhe-Xuan Gong and Michael Foss-Feig and Alexey V. Gorshkov} } @article {1179, title = {Causality and quantum criticality with long-range interactions}, journal = {Physical Review B}, volume = {92}, year = {2016}, month = {2016/03/17}, pages = {125128}, abstract = { 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. }, doi = {10.1103/PhysRevB.93.125128}, url = {http://arxiv.org/abs/1508.00906}, author = {Mohammad F. Maghrebi and Zhe-Xuan Gong and Michael Foss-Feig and Alexey V. Gorshkov} } @article {1716, title = {Co-Designing a Scalable Quantum Computer with Trapped Atomic Ions}, year = {2016}, month = {2016/02/09}, abstract = {The 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.}, url = {http://arxiv.org/abs/1602.02840}, author = {Kenneth R. Brown and Jaewan Kim and Christopher Monroe} } @article {1737, title = {Collective phases of strongly interacting cavity photons}, journal = {Physical Review A}, volume = {94}, year = {2016}, month = {2016/09/01}, pages = {033801}, abstract = {

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.

}, doi = {http://dx.doi.org/10.1103/PhysRevA.94.033801}, url = {http://arxiv.org/abs/1601.06857}, author = {Ryan M. Wilson and Khan W. Mahmud and Anzi Hu and Alexey V. Gorshkov and Mohammad Hafezi and Michael Foss-Feig} } @article {1760, title = {A Complete Characterization of Unitary Quantum Space}, year = {2016}, month = {2016/04/05}, abstract = {We 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)){\texttimes}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{\texttimes}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.}, url = {http://arxiv.org/abs/1604.01384}, author = {Bill Fefferman and Cedric Yen-Yu Lin} } @article {1234, title = {Complexity of the XY antiferromagnet at fixed magnetization}, journal = {Quantum Information and Computation}, volume = {16}, year = {2016}, month = {2016/01/01}, pages = {1-18}, abstract = { 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. }, url = {http://arxiv.org/abs/1503.07083v1}, author = {Andrew M. Childs and David Gosset and Zak Webb} } @conference {1712, title = {Computational Security of Quantum Encryption}, booktitle = {Computational Security of Quantum Encryption. In: Nascimento A., Barreto P. (eds) Information Theoretic Security. }, year = {2016}, month = {2016/11/10}, abstract = {

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.

}, url = {https://link.springer.com/chapter/10.1007\%2F978-3-319-49175-2_3}, author = {Gorjan Alagic and Anne Broadbent and Bill Fefferman and Tommaso Gagliardoni and Christian Schaffner and Michael St. Jules} } @article {1336, title = {Capacitively coupled singlet-triplet qubits in the double charge resonant regime}, journal = {Physical Review B}, volume = {92}, year = {2015}, month = {2015/12/01}, pages = {235301}, abstract = {We 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. }, url = {http://arxiv.org/abs/1408.4740v2}, author = {V. Srinivasa and J. M. Taylor} } @article {1338, title = {A chemical potential for light}, journal = {Physical Review B}, volume = {92}, year = {2015}, month = {2014/05/22}, pages = {174305}, abstract = {Photons 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. }, doi = {10.1103/PhysRevB.92.174305}, url = {http://arxiv.org/abs/1405.5821v2}, author = {M. Hafezi and P. Adhikari and J. M. Taylor} } @article {1696, title = {Continuous symmetry breaking and a new universality class in 1D long-range interacting quantum systems}, year = {2015}, month = {2015/10/05}, abstract = {Continuous 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.}, url = {http://arxiv.org/abs/1510.01325}, author = {Mohammad F. Maghrebi and Zhe-Xuan Gong and Alexey V. Gorshkov} } @article {1507, title = {Coulomb bound states of strongly interacting photons}, journal = {Physical Review Letters}, volume = {115}, year = {2015}, month = {2015/09/16}, pages = {123601}, abstract = { 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. }, doi = {10.1103/PhysRevLett.115.123601}, url = {http://arxiv.org/abs/1505.03859v1}, author = {Mohammad F. Maghrebi and Michael Gullans and P. Bienias and S. Choi and I. Martin and O. Firstenberg and M. D. Lukin and H. P. B{\"u}chler and Alexey V. Gorshkov} } @article {1340, title = {A classical channel model for gravitational decoherence}, journal = {New Journal of Physics}, volume = {16}, year = {2014}, month = {2014/06/26}, pages = {065020}, abstract = {We 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. }, doi = {10.1088/1367-2630/16/6/065020}, url = {http://arxiv.org/abs/1401.0946v1}, author = {D. Kafri and J. M. Taylor and G. J. Milburn} } @article {1391, title = {Classical simulation of Yang-Baxter gates}, journal = {9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)}, volume = {27}, year = {2014}, month = {2014/07/05}, pages = {161-175}, abstract = { 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. }, doi = {10.4230/LIPIcs.TQC.2014.161}, url = {http://arxiv.org/abs/1407.1361v1}, author = {Gorjan Alagic and Aniruddha Bapat and Stephen P. Jordan} } @article {1230, title = {The computational power of matchgates and the XY interaction on arbitrary graphs}, journal = {Quantum Information and Computation}, volume = {14}, year = {2014}, month = {2014/09/01}, pages = {901-916}, abstract = { 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. }, url = {http://arxiv.org/abs/1308.1463v1}, author = {Daniel J. Brod and Andrew M. Childs} } @article {1518, title = {The computational power of normalizer circuits over black-box groups}, year = {2014}, month = {2014/09/16}, abstract = { This work presents a precise connection between Clifford circuits, Shor{\textquoteright}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. }, url = {http://arxiv.org/abs/1409.4800v1}, author = {Juan Bermejo-Vega and Cedric Yen-Yu Lin and Maarten Van den Nest} } @article {1226, title = {Constructing elliptic curve isogenies in quantum subexponential time}, journal = {Journal of Mathematical Cryptology}, volume = {8}, year = {2014}, month = {2014/01/01}, pages = {1 - 29}, abstract = { 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{\textquoteright}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. }, doi = {10.1515/jmc-2012-0016}, url = {http://arxiv.org/abs/1012.4019v2}, author = {Andrew M. Childs and David Jao and Vladimir Soukharev} } @article {1186, title = {Controllable quantum spin glasses with magnetic impurities embedded in quantum solids }, journal = {Physical Review B}, volume = {88}, year = {2013}, month = {2013/7/24}, abstract = { 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. }, doi = {10.1103/PhysRevB.88.014426}, url = {http://arxiv.org/abs/1307.1130v1}, author = {Mikhail Lemeshko and Norman Y. Yao and Alexey V. Gorshkov and Hendrik Weimer and Steven D. Bennett and Takamasa Momose and Sarang Gopalakrishnan} } @article {1272, title = {Controlling the group velocity of colliding atomic Bose-Einstein condensates with Feshbach resonances }, journal = {Physical Review A}, volume = {87}, year = {2013}, month = {2013/5/10}, abstract = { 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. }, doi = {10.1103/PhysRevA.87.053608}, url = {http://arxiv.org/abs/1301.4234v2}, author = {Ranchu Mathew and Eite Tiesinga} } @article {1844, title = {Cavity QED with atomic mirrors}, journal = {New J. Phys.}, volume = {14}, year = {2012}, pages = {063003}, url = {http://iopscience.iop.org/1367-2630/14/6/063003/}, author = {D E Chang and Jiang, L and Alexey V. Gorshkov and H J Kimble} } @article {1458, title = {Comment on some results of Erdahl and the convex structure of reduced density matrices}, journal = {Journal of Mathematical Physics}, volume = {53}, year = {2012}, month = {2012/05/16}, pages = {072203}, abstract = { 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{\textquoteright}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. }, doi = {10.1063/1.4736842}, url = {http://arxiv.org/abs/1205.3682v1}, author = {Jianxin Chen and Zhengfeng Ji and Mary Beth Ruskai and Bei Zeng and Duan-Lu Zhou} } @article {1443, title = {Correlations in excited states of local Hamiltonians}, journal = {Physical Review A}, volume = {85}, year = {2012}, month = {2012/4/9}, abstract = { 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). }, doi = {10.1103/PhysRevA.85.040303}, url = {http://arxiv.org/abs/1106.1373v2}, author = {Jianxin Chen and Zhengfeng Ji and Zhaohui Wei and Bei Zeng} } @article {1531, title = {Casimir force between sharp-shaped conductors}, journal = {Proceedings of the National Academy of Sciences}, volume = {108}, year = {2011}, month = {2011/04/11}, pages = {6867 - 6871}, abstract = { 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. }, doi = {10.1073/pnas.1018079108}, url = {http://arxiv.org/abs/1010.3223v1}, author = {Mohammad F. Maghrebi and Sahand Jamal Rahi and Thorsten Emig and Noah Graham and Robert L. Jaffe and Mehran Kardar} } @article {1412, title = {Chern numbers hiding in time-of-flight images}, journal = {Physical Review A}, volume = {84}, year = {2011}, month = {2011/12/21}, abstract = { 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{\textquoteright} 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. }, doi = {10.1103/PhysRevA.84.063629}, url = {http://arxiv.org/abs/1105.3100v3}, author = {Erhai Zhao and Noah Bray-Ali and Carl J. Williams and I. B. Spielman and Indubala I. Satija} } @article {1484, title = {Comment on "Foundation of Statistical Mechanics under Experimentally Realistic Conditions" }, year = {2011}, month = {2011/09/22}, abstract = { 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. }, url = {http://arxiv.org/abs/1109.4696v1}, author = {Zhe-Xuan Gong and L. -M. Duan} } @article {1433, title = {Continuous-variable quantum compressed sensing}, year = {2011}, month = {2011/11/03}, abstract = { 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. }, url = {http://arxiv.org/abs/1111.0853v3}, author = {Matthias Ohliger and Vincent Nesme and David Gross and Yi-Kai Liu and Jens Eisert} } @article {1242, title = {Characterization of universal two-qubit Hamiltonians}, year = {2010}, month = {2010/04/09}, abstract = { 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. }, url = {http://arxiv.org/abs/1004.1645v2}, author = {Andrew M. Childs and Debbie Leung and Laura Mancinska and Maris Ozols} } @article {1325, title = {Contextuality in Quantum Mechanics: Testing the Klyachko Inequality}, year = {2010}, month = {2010/06/02}, abstract = { 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. }, url = {http://arxiv.org/abs/1006.0500v2}, author = {Jeffrey Bub and Allen Stairs} } @article {1286, title = {Creation and manipulation of Feshbach resonances with radio-frequency radiation }, journal = {New Journal of Physics}, volume = {12}, year = {2010}, month = {2010/08/12}, pages = {083031}, abstract = { 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. }, doi = {10.1088/1367-2630/12/8/083031}, url = {http://arxiv.org/abs/1004.0636v1}, author = {Thomas M. Hanna and Eite Tiesinga and Paul S. Julienne} } @article {1293, title = {Collisional cooling of ultra-cold atom ensembles using Feshbach resonances }, journal = {Physical Review A}, volume = {80}, year = {2009}, month = {2009/9/8}, abstract = { 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. }, doi = {10.1103/PhysRevA.80.030702}, url = {http://arxiv.org/abs/0903.2568v1}, author = {L. Mathey and Eite Tiesinga and Paul S. Julienne and Charles W. Clark} } @article {1324, title = {Contextuality and nonlocality in {\textquoteright}no signaling{\textquoteright} theories}, journal = {Foundations of Physics}, volume = {39}, year = {2009}, month = {2009/4/21}, pages = {690 - 711}, abstract = { We define a family of {\textquoteright}no signaling{\textquoteright} 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 {\textquoteleft}no signaling{\textquoteright} 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 {\textquoteright}no signaling{\textquoteright} theories. }, doi = {10.1007/s10701-009-9307-8}, url = {http://arxiv.org/abs/0903.1462v2}, author = {Jeffrey Bub and Allen Stairs} } @article {1299, title = {Counterflow and paired superfluidity in one-dimensional Bose mixtures in optical lattices }, journal = {Physical Review A}, volume = {80}, year = {2009}, month = {2009/8/24}, abstract = { 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. }, doi = {10.1103/PhysRevA.80.023619}, url = {http://arxiv.org/abs/0906.2150v1}, author = {Anzi Hu and L. Mathey and Ippei Danshita and Eite Tiesinga and Carl J. Williams and Charles W. Clark} } @article {1355, title = {Coherence of an optically illuminated single nuclear spin qubit}, journal = {Physical Review Letters}, volume = {100}, year = {2008}, month = {2008/2/19}, abstract = {We 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. }, doi = {10.1103/PhysRevLett.100.073001}, url = {http://arxiv.org/abs/0707.1341v2}, author = {Liang Jiang and M. V. Gurudev Dutt and Emre Togan and Lily Childress and Paola Cappellaro and J. M. Taylor and Mikhail D. Lukin} } @article {1173, title = {Coherent Quantum Optical Control with Subwavelength Resolution}, journal = {Physical Review Letters}, volume = {100}, year = {2008}, month = {2008/3/7}, abstract = { 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. }, doi = {10.1103/PhysRevLett.100.093005}, url = {http://arxiv.org/abs/0706.3879v2}, author = {Alexey V. Gorshkov and Liang Jiang and Markus Greiner and Peter Zoller and Mikhail D. Lukin} } @article {1277, title = {Coherent, adiabatic and dissociation regimes in coupled atomic-molecular Bose-Einstein condensates }, year = {2007}, month = {2007/11/02}, abstract = { 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. }, url = {http://arxiv.org/abs/0711.0397v2}, author = {Pascal Naidon and Eite Tiesinga and Paul S. Julienne} } @article {1424, title = {The Complexity of the Consistency and N-representability Problems for Quantum States}, year = {2007}, month = {2007/12/18}, type = {PhD Thesis, Univ. of California, San Diego}, abstract = { QMA (Quantum Merlin-Arthur) is the quantum analogue of the class NP. There are a few QMA-complete problems, most notably the {\textquoteleft}{\textquoteleft}Local Hamiltonian{\textquoteright}{\textquoteright} problem introduced by Kitaev. In this dissertation we show some new QMA-complete problems. The first one is {\textquoteleft}{\textquoteleft}Consistency of Local Density Matrices{\textquoteright}{\textquoteright}: 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, {\textquoteleft}{\textquoteleft}Fermionic Local Hamiltonian{\textquoteright}{\textquoteright} and {\textquoteleft}{\textquoteleft}N-representability,{\textquoteright}{\textquoteright} 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{\textquoteright}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 {\textquoteleft}{\textquoteleft}stoquastic{\textquoteright}{\textquoteright} 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. }, url = {http://arxiv.org/abs/0712.3041v1}, author = {Yi-Kai Liu} } @article {1360, title = {Cavity quantum electrodynamics with semiconductor double-dot molecules on a chip}, year = {2006}, month = {2006/05/05}, abstract = {We 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. }, url = {http://arxiv.org/abs/cond-mat/0605144v1}, author = {J. M. Taylor and M. D. Lukin} } @article {1422, title = {Consistency of Local Density Matrices is QMA-complete}, journal = {Proc. RANDOM }, year = {2006}, month = {2006/04/21}, pages = {438-449}, abstract = { 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 {\textquoteleft}{\textquoteleft}consistent{\textquoteright}{\textquoteright} 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. }, url = {http://arxiv.org/abs/quant-ph/0604166v3}, author = {Yi-Kai Liu} } @article {1322, title = {Conditionalizing and commutativity: a note on Malley}, year = {2005}, month = {2005/06/19}, abstract = { This paper has been withdrawn. }, url = {http://arxiv.org/abs/quant-ph/0506159v2}, author = {Allen Stairs and Jeffrey Bub} } @article {1372, title = {Criteria for Exact Qudit Universality}, journal = {Physical Review A}, volume = {71}, year = {2005}, month = {2005/5/16}, abstract = { 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>