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quantum-Informed Recursive Optimization Algorithms

PRX quantum 2024年第2期5卷 020327-020327页

作者： Jernej Rudi Finžgar Aron Kerschbaumer Martin J.A. Schuetz Christian B. Mendl Helmut G. Katzgraber BMW AG Munich Germany Department of Computer Science Technical University Munich School of CIT Garching Germany Amazon Quantum Solutions Lab Seattle Washington USA AWS Center for Quantum Computing Pasadena California USA Technical University of Munich Institute for Advanced Study Garching Germany

We propose and implement a family of quantum-informed recursive optimization (QIRO) algorithms for combinatorial optimization problems. Our approach leverages quantum resources to obtain information that is used in problem-specific classical reduction steps that recursively simplify the problem. These reduction steps address the limitations of the quantum component (e.g., locality) and ensure solution feasibility in constrained optimization problems. Additionally, we use backtracking techniques to further improve the performance of the algorithm without increasing the requirements on the quantum hardware. We showcase the capabilities of our approach by informing QIRO with correlations from classical simulations of shallow circuits of the quantum approximate optimization algorithm, solving instances of maximum independent set and maximum satisfiability problems with hundreds of variables. We also demonstrate how QIRO can be deployed on a neutral atom quantum processor to find large independent sets of graphs. In summary, our scheme achieves results comparable to classical heuristics even with relatively weak quantum resources. Furthermore, enhancing the quality of these quantum resources improves the performance of the algorithms. Notably, the modular nature of QIRO offers various avenues for modifications, positioning our work as a template for a broader class of hybrid quantum-classical algorithms for combinatorial optimization.

关键词： Adiabatic quantum optimization Optimization problems quantum algorithms quantum information with atoms & light

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Unconditional quantum Advantage for Sampling with Shallow Circuits

arXiv

引用

arXiv 2023年

作者： Watts, Adam Bene Parham, Natalie Institute for Quantum Computing University of Waterloo Canada Department of Computer Science Columbia University United States Perimeter Institute for Theoretical Physics Canada

Recent work by Bravyi, Gosset, and Koenig showed that there exists a search problem that a constant-depth quantum circuit can solve, but that any constant-depth classical circuit with bounded fan-in cannot. They also pose the question: Can we achieve a similar proof of separation for an input-independent sampling task? In this paper, we show that the answer to this question is yes when the number of random input bits given to the classical circuit is bounded. We introduce a distribution Dn over {0, 1}n and construct a constant-depth uniform quantum circuit family {Cn}n such that Cn samples from a distribution close to Dn in total variation distance. For any δ δ i.i.d. Bernouli random variables with entropy 1/k and produces output close to Dn in total variation distance has depth Ω(log log n). This gives an unconditional proof that constant-depth quantum circuits can sample from distributions that can’t be reproduced by constant-depth bounded fan-in classical circuits, even up to additive error. We also show a similar separation between constant-depth quantum circuits with advice and classical circuits with bounded fan-in and fan-out, but access to an unbounded number of i.i.d random inputs. The distribution Dn and classical circuit lower bounds are inspired by work of Viola, in which he shows a different (but related) distribution cannot be sampled from approximately by constant-depth bounded fan-in classical circuits. Copyright © 2023, The Authors. All rights reserved.

关键词： Timing circuits

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(Sub)Exponential quantum Speedup for Optimization

arXiv

引用

arXiv 2025年

作者： Leng, Jiaqi Wu, Kewen Wu, Xiaodi Zheng, Yufan Simons Institute for the Theory of Computing University of California Berkeley United States Department of Mathematics University of California Berkeley United States Department of EECS University of California Berkeley United States Department of Computer Science University of Maryland College Park United States Joint Center for Quantum Information and Computer Science University of Maryland United States

We demonstrate provable (sub)exponential quantum speedups in both discrete and continuous optimization, achieved through simple and natural quantum optimization algorithms, namely the quantum adiabatic algorithm for discrete optimization and quantum Hamiltonian descent for continuous optimization. Our result builds on the Gilyén–Hastings–Vazirani (sub)exponential oracle separation for adiabatic quantum computing. With a sequence of perturbative reductions, we compile their construction into two standalone objective functions, whose oracles can be directly leveraged by the plain adiabatic evolution and Schrödinger operator evolution for discrete and continuous optimization, respectively. Copyright © 2025, The Authors. All rights reserved.

关键词： quantum channel

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Clifford-Deformed Surface Codes

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PRX quantum 2024年第1期5卷 010347-010347页

作者： Arpit Dua Aleksander Kubica Liang Jiang Steven T. Flammia Michael J. Gullans Department of Physics and Institute for Quantum Information and Matter California Institute of Technology Pasadena California 91125 USA AWS Center for Quantum Computing Pasadena California 91125 USA California Institute of Technology Pasadena California 91125 USA Pritzker School of Molecular Engineering The University of Chicago Illinois 60637 USA Joint Center for Quantum Information and Computer Science NIST/University of Maryland College Park Maryland 20742 USA

Various realizations of Kitaev’s surface code perform surprisingly well for biased Pauli noise. Attracted by these potential gains, we study the performance of Clifford-deformed surface codes (CDSCs) obtained from the surface code by the application of 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.

关键词： Classical statistical mechanics Critical phenomena Order parameters Percolation theory Phase diagrams Phase transitions by order quantum error correction quantum memories

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Measurement-Based quantum Approximate Optimization

Measurement-Based Quantum Approximate Optimization

引用

IEEE International Symposium on Parallel and Distributed Processing Workshops and Phd Forum (IPDPSW)

作者： Tobias Stollenwerk Stuart Hadfield Jülich Research Center Institute for Quantum Computing Analytics (PGI-12) Jülich Germany Quantum Artificial Intelligence Lab (QuAIL) USRA Research Institute for Advanced Computer Science NASA Ames Research Center CA

ISBN: (数字)9798350364606

ISBN: (纸本)9798350364613

Parameterized quantum circuits are attractive candidates for potential quantum advantage in the near term and beyond. At the same time, as quantum computing hardware not only continues to improve but also begins to incorporate new features such as mid-circuit measurement and adaptive control, opportunities arise for innovative algorithmic paradigms. In this work we focus on measurement-based quantum computing protocols for approximate optimization, in particular related to quantum alternating operator ansätze (QAOA), a popular quantum circuit model approach to combinatorial optimization. For the construction and analysis of our measurement-based protocols we demonstrate that diagrammatic approaches, specifically ZX-calculus and its extensions, are effective for adapting such algorithms to the measurement-based setting. In particular we derive measurement patterns for applying QAOA to the broad and important class of QUBO problems. We further outline how for constrained optimization, hard problem constraints may be directly incorporated into our protocol to guarantee the feasibility of the solution found and avoid the need for dealing with penalties. Finally we discuss the resource requirements and tradeoffs of our approach to that of more traditional quantum circuits.

关键词： Protocols quantum advantage Focusing Logic gates Approximation algorithms Time measurement Hardware

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Cryogenic Control and Readout Integrated Circuits for Solid-State quantum computing

arXiv

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arXiv 2024年

作者： Lei, Lingxiao Huang, Heng Chen, Pingxing Deng, Mingtang Institute for Quantum Information State Key Laboratory of High Performance Computing College of Computer Science and Technology National University of Defense Technology Changsha410073 China Institute for Quantum Science and Technology College of Sciences National University of Defense Technology Changsha410073 China

In the pursuit of quantum computing, solid-state quantum systems, particularly superconducting ones, have made remarkable advancements over the past two decades. However, achieving fault-tolerant quantum computing for next-generation applications necessitates the integration of several million qubits, which presents significant challenges in terms of interconnection complexity and latency that are currently unsolvable with state-of-the-art room-temperature control and readout electronics. Recently, cryogenic integrated circuits (ICs), including CMOS radio-frequency ICs and rapid-single-flux-quantum-logic ICs, have emerged as potential alternatives to room-temperature electronics. Unlike their room-temperature counterparts, these ICs are deployed within cryostats to enhance scalability by reducing the number and length of transmission lines. Additionally, operating at cryogenic temperatures can suppress electronic noise and improve qubit control fidelity. However, for CMOS ICs specifically, circuit design uncertainties arise due to a lack of reliable models for cryogenic field effect transistors as well as issues related to severe fickle noises and power dissipation at cryogenic temperatures. This paper provides a comprehensive review of recent research on both types of cryogenic control and readout ICs but primarily focuses on the more mature CMOS technology. The discussion encompasses principles underlying control and readout techniques employed in cryogenic CMOS ICs along with their architectural designs;characterization and modeling approaches for field effect transistors under cryogenic conditions;as well as fundamental concepts pertaining to rapid single flux quantum circuits. In conclusion, while prototypes of cryogenic ICs have been successfully fabricated recently, further studies are still necessary;we believe that rapid single-flux-quantum-based or hybrid ICs featuring enhanced digital components may represent the future direction in this emerging area. ©

关键词： CMOS integrated circuits

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Differentiable quantum computing for Large-scale Linear Control

arXiv

引用

arXiv 2024年

作者： Clayton, Connor Leng, Jiaqi Yang, Gengzhi Qiao, Yi-Ling Lin, Ming C. Wu, Xiaodi Joint Center for Quantum Information and Computer Science University of Maryland United States Department of Computer Science University of Maryland United States Department of Mathematics University of Maryland United States Center for Machine Learning University of Maryland United States Department of Mathematics Simons Institute The Theory of Computing UC Berkeley United States

As industrial models and designs grow increasingly complex, the demand for optimal control of large-scale dynamical systems has significantly increased. However, traditional methods for optimal control incur significant overhead as problem dimensions grow. In this paper, we introduce an end-to-end quantum algorithm for linear-quadratic control with provable speedups. Our algorithm, based on a policy gradient method, incorporates a novel quantum subroutine for solving the matrix Lyapunov equation. Specifically, we build a quantum-assisted differentiable simulator for efficient gradient estimation that is more accurate and robust than classical methods relying on stochastic approximation. Compared to the classical approaches, our method achieves a super-quadratic speedup. To the best of our knowledge, this is the first end-to-end quantum application to linear control problems with provable quantum advantage. Copyright © 2024, The Authors. All rights reserved.

关键词： Stochastic systems

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Distinguishability-based genuine nonlocality with genuine multipartite entanglement

引用

Physical Review A 2023年第2期108卷 022405-022405页

作者： Zong-Xing Xiong Mao-Sheng Li Zhu-Jun Zheng Lvzhou Li Institute of Quantum Computing and Software School of Computer Science and Engineering Sun Yat-Sen University Guangzhou 510006 China School of Mathematics South China University of Technology Guangzhou 510641 China

A set of orthogonal multipartite quantum states is said to be distinguishability-based genuinely nonlocal (also genuinely nonlocal, for abbreviation) if the states are locally indistinguishable across any bipartition of the subsystems. This form of multipartite nonlocality, although more naturally arising than the recently popular “strong nonlocality” in the context of local distinguishability, receives much less attention. In this work, we study the distinguishability-based genuine nonlocality of a typical type of genuine multipartite entangled states—the d-dimensional Greenberger-Horne-Zeilinger (GHZ) states, featuring systems with local dimension not limited to two. In the three-partite case, we find the existence of small genuinely nonlocal sets consisting of these states: we show that the cardinality can at least scale down to linear in the local dimension d, with the linear factor l=1. Specifically, the method we use is semidefinite programming and the GHZ states to construct these sets are special ones which we call “GHZ lattices”. This result might arguably suggest a significant gap between the strength of strong nonlocality and the distinguishability-based genuine nonlocality. Moreover, we put forward the notion of (s,n)-threshold distinguishability and, utilizing a similar method, we successfully construct (2,3)-threshold sets consisting of GHZ states in three-partite systems.

关键词： Nonlocality quantum correlations in quantum information quantum entanglement

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Phase error rate estimation in QKD with imperfect detectors

arXiv

引用

arXiv 2024年

作者： Tupkary, Devashish Nahar, Shlok Sinha, Pulkit Lütkenhaus, Norbert Institute for Quantum Computing Department of Physics and Astronomy University of Waterloo WaterlooONN2L 3G1 Canada Institute for Quantum Computing School of Computer Science University of Waterloo WaterlooONN2L 3G1 Canada

We present a finite-size security proof of the decoy-state BB84 QKD protocol against coherent attacks, using entropic uncertainty relations, for imperfect detectors. We apply this result to the case of detectors with imperfectly characterized basis-efficiency mismatch. Our proof works by obtaining a suitable bound on the phase error rate, without requiring any new modifications to the protocol steps or hardware. It is applicable to imperfectly characterized detectors, and only requires the maximum relative difference in detection efficiencies and dark count rates of the detectors to be characterized. Moreover, our proof allows Eve to choose detector efficiencies and dark count rates in their allowed ranges in each round, thereby addressing an important problem of detector side channels. We prove security in the variable-length framework, where users are allowed to adaptively determine the length of key to be produced, and number of bits to be used for error-correction, based on observations made during the protocol. We quantitatively demonstrate the effect of basis-efficiency mismatch by applying our results to the decoy-state BB84 protocol. © 2024, CC BY-NC-SA.

关键词： Quadrature phase shift keying

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quantum-Enhanced Simulation-Based Optimization for Newsvendor Problems

arXiv

引用

arXiv 2024年

作者： Sharma, Monit Lau, Hoong Chuin Raymond, Rudy School of Computing and Information Systems Singapore Management University Singapore Institute of High Performance Computing A*STAR Singapore IBM Quantum IBM Japan Japan Dept. of Computer Science The University of Tokyo Japan

Simulation-based optimization is a widely used method to solve stochastic optimization problems. This method aims to identify an optimal solution by maximizing the expected value of the objective function. However, due to its computational complexity, the function cannot be accurately evaluated directly, hence it is estimated through simulation. Exploiting the enhanced efficiency of quantum Amplitude Estimation (QAE) compared to classical Monte Carlo simulation, it frequently outpaces classical simulation-based optimization, resulting in notable performance enhancements in various scenarios. In this work, we make use of a quantum-enhanced algorithm for simulation-based optimization and apply it to solve a variant of the classical Newsvendor Problem which is known to be NP-hard. Such problems provide the building block for supply chain management, particularly in inventory management and procurement optimization under risks and uncertainty. © 2024, CC BY.

关键词： quantum efficiency

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