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Exact entanglement cost of quantum states and channels under positive-partial-transpose-preserving operations

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Physical Review A 2023年第1期107卷 012429-012429页

作者： Xin Wang Mark M. Wilde Institute for Quantum Computing Baidu Research Beijing 100093 China Joint Center for Quantum Information and Computer Science University of Maryland College Park Maryland 20742 USA Hearne Institute for Theoretical Physics Department of Physics and Astronomy Center for Computation and Technology Louisiana State University Baton Rouge Louisiana 70803 USA School of Electrical and Computer Engineering Cornell University Ithaca New York 14850 USA

This paper establishes single-letter formulas for the exact entanglement cost of simulating quantum channels under free quantum operations that completely preserve positivity of the partial transpose (PPT). First, we introduce the κ-entanglement measure for point-to-point quantum channels, based on the idea of the κ entanglement of bipartite states, and we establish several fundamental properties for it, including amortization collapse, monotonicity under PPT superchannels, additivity, normalization, faithfulness, and nonconvexity. Second, we introduce and solve the exact entanglement cost for simulating quantum channels in both the parallel and sequential settings, along with the assistance of free PPT-preserving operations. In particular, we establish that the entanglement cost in both cases is given by the same single-letter formula, the κ-entanglement measure of a quantum channel. We further show that this cost is equal to the largest κ entanglement that can be shared or generated by the sender and receiver of the channel. This formula is calculable by a semidefinite program, thus allowing for an efficiently computable solution for general quantum channels. Noting that the sequential regime is more powerful than the parallel regime, another notable implication of our result is that both regimes have the same power for exact quantum channel simulation, when PPT superchannels are free. For several basic Gaussian quantum channels, we show that the exact entanglement cost is given by the Holevo-Werner formula [Holevo and Werner, Phys. Rev. A 63, 032312 (2001)], giving an operational meaning of the Holevo-Werner quantity for these channels.

关键词： Entanglement manipulation Entanglement measures quantum channels quantum communication quantum entanglement

Time-Energy Uncertainty Relation for Noisy quantum Metrology

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PRX quantum 2023年第4期4卷 040336-040336页

作者： Philippe Faist Mischa P. Woods Victor V. Albert Joseph M. Renes Jens Eisert John Preskill Dahlem Center for Complex Quantum Systems Freie Universität Berlin Berlin Germany Institute for Quantum Information and Matter Caltech Pasadena California USA Institute for Theoretical Physics ETH Zurich Zurich Switzerland University Grenoble Alpes Inria Grenoble 38000 France Joint Center for Quantum Information and Computer Science NIST and University of Maryland College Park Maryland USA Walter Burke Institute for Theoretical Physics Caltech Pasadena California USA AWS Center for Quantum Computing Caltech Pasadena California USA

Detection of very weak forces and precise measurement of time are two of the many applications of quantum metrology to science and technology. To sense an unknown physical parameter, one prepares an initial state of a probe system, allows the probe to evolve as governed by a Hamiltonian H for some time t, and then measures the probe. If H is known, we can estimate t by this method; if t is known, we can estimate classical parameters on which H depends. The accuracy of a quantum sensor can be limited by either intrinsic quantum noise or by noise arising from the interactions of the probe with its environment. In this work, we introduce and study a fundamental trade-off, which relates the amount by which noise reduces the accuracy of a quantum clock to the amount of information about the energy of the clock that leaks to the environment. Specifically, we consider an idealized scenario in which a party Alice prepares an initial pure state of the clock, allows the clock to evolve for a time that is not precisely known, and then transmits the clock through a noisy channel to a party Bob. Meanwhile, the environment (Eve) receives any information about the clock that is lost during transmission. We prove that Bob’s loss of quantum Fisher information about the elapsed time is equal to Eve’s gain of quantum Fisher information about a complementary energy parameter. We also prove a similar, but more general, trade-off that applies when Bob and Eve wish to estimate the values of parameters associated with two noncommuting observables. We derive the necessary and sufficient conditions for the accuracy of the clock to be unaffected by the noise, which form a subset of the Knill-Laflamme error-correction conditions. A state and its local time-evolution direction, if they satisfy these conditions, are said to form a metrological code. We provide a scheme to construct metrological codes in the stabilizer formalism. We show that there are metrological codes that cannot be written as

关键词： Metrology Noise quantum error correction quantum metrology quantum sensing Uncertainty relation quantum many-body systems

Approximation Algorithms for Noncommutative CSPs

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arXiv 2023年

作者： Culf, Eric Mousavi, Hamoon Spirig, Taro Faculty of Mathematics Institute for Quantum Computing University of Waterloo Canada Simons Institute for Theoretical Computer Science University of California at Berkeley United States QMATH Department of Mathematical Sciences University of Copenhagen Denmark

Noncommutative constraint satisfaction problems (NC-CSPs) are higher-dimensional operator extensions of classical CSPs. Despite their significance in quantum information, their approximability remains largely unexplored. A notable example of a noncommutative CSP that is not solvable in polynomial time is NC-Max-3-Cut. We present a 0.864-approximation algorithm for this problem. Our approach extends to a broader class of both classical and noncommutative CSPs. We introduce three key concepts: approximate isometry, relative distribution, and ∗-anticommutation, which may be of independent interest. © 2023, CC BY-SA.

关键词： Constraint satisfaction problems

quantum Hamiltonian Descent for Non-smooth Optimization

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arXiv 2025年

作者： Leng, Jiaqi Zheng, Yufan Jia, Zhiyuan Fan, Lei Zhao, Chaoyue Peng, Yuxiang Wu, Xiaodi Simons Institute for the Theory of Computing University of California Berkeley United States Department of Mathematics 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 Department of Applied Mathematics University of Washington United States Department of Engineering Technology University of Houston United States Department of Electrical and Computer Engineering University of Houston United States Department of Industrial and Systems Engineering University of Washington United States Artephi Computing Inc United States

Non-smooth optimization models play a fundamental role in various disciplines, including engineering, science, management, and finance. However, classical algorithms for solving such models often struggle with convergence speed, scalability, and parameter tuning, particularly in high-dimensional and non-convex settings. In this paper, we explore how quantum mechanics can be leveraged to overcome these limitations. Specifically, we investigate the theoretical properties of the quantum Hamiltonian Descent (QHD) algorithm for non-smooth optimization in both continuous and discrete time. First, we propose continuous-time variants of the general QHD algorithm and establish their global convergence and convergence rate for non-smooth convex and strongly convex problems through a novel Lyapunov function design. Furthermore, we prove the finite-time global convergence of continuous-time QHD for non-smooth non-convex problems under mild conditions (i.e., locally Lipschitz). In addition, we propose discrete-time QHD, a fully digitized implementation of QHD via operator splitting (i.e., product formula). We find that discrete-time QHD exhibits similar convergence properties even with large time steps. Finally, numerical experiments validate our theoretical findings and demonstrate the computational advantages of QHD over classical non-smooth non-convex optimization algorithms. Copyright © 2025, The Authors. All rights reserved.

关键词： Continuous time systems

High-rate discretely-modulated continuous-variable quantum key distribution using quantum machine learning

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arXiv 2023年

作者： Liao, Qin Liu, Jieyu Huang, Anqi Huang, Lei Fei, Zhuoying Fu, Xiquan College of Computer Science and Electronic Engineering Hunan University Changsha410082 China Institute for Quantum Information State Key Laboratory of High Performance Computing College of Computer Science and Technology National University of Defense Technology Changsha410073 China

We propose a high-rate scheme for discretely-modulated continuous-variable quantum key distribution (DM CVQKD) using quantum machine learning technologies, which divides the whole CVQKD system into three parts, i.e., the initialization part that is used for training and estimating quantum classifier, the prediction part that is used for generating highly correlated raw keys, and the data-postprocessing part that generates the final secret key string shared by Alice and Bob. To this end, a low-complexity quantum k-nearest neighbor (QkNN) classifier is designed for predicting the lossy discretely-modulated coherent states (DMCSs) at Bob's side. The performance of the proposed QkNN-based CVQKD especially in terms of machine learning metrics and complexity is analyzed, and its theoretical security is proved by using semi-definite program (SDP) method. Numerical simulation shows that the secret key rate of our proposed scheme is explicitly superior to the existing DM CVQKD protocols, and it can be further enhanced with the increase of modulation variance. Copyright © 2023, The Authors. All rights reserved.

关键词： Nearest neighbor search

Shallow quantum circuits for efficient preparation of Slater determinants and correlated states on a quantum computer

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Physical Review A 2023年第2期108卷 022416-022416页

作者： Chong Hian Chee Daniel Leykam Adrian M. Mak Dimitris G. Angelakis Centre for Quantum Technologies National University of Singapore 3 Science Drive 2 Singapore 117543 Institute of High Performance Computing Agency for Science Technology & Research (A*STAR) 1 Fusionopolis Way 16-16 Connexis Singapore 138632 School of Electrical and Computer Engineering Technical University of Crete 73100 Chania Greece AngelQ Quantum Computing 531A Upper Cross Street 04-95 Hong Lim Complex Singapore 051531

Fermionic Ansatz state preparation is a critical subroutine in many quantum algorithms such as the variational quantum eigensolver for quantum chemistry and condensed-matter applications. The shallowest circuit depth needed to prepare Slater determinants and correlated states to date scales at least linearly with respect to the system size N. Inspired by data-loading circuits developed for quantum machine learning, we propose an alternate paradigm that provides shallower, yet scalable, O(dlog22N) two-qubit gate-depth circuits to prepare such states with d fermions, offering a subexponential reduction in N over existing approaches in second quantization, enabling high-accuracy studies of d≪O(N/log22N) fermionic systems with larger basis sets on near-term quantum devices.

关键词： quantum algorithms for chemical calculations

Giant Stokes shift for charged vacancies in monolayer SnS

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Physical Review Materials 2022年第4期6卷 044003-044003页

作者： Anne Marie Z. Tan Maria A. Garcia Richard G. Hennig Institute of High Performance Computing A*STAR Singapore 138632 Singapore Department of Materials Science and Engineering University of Florida Gainesville Florida 32611 USA Quantum Theory Project University of Florida Gainesville Florida 32611 USA

We perform first-principles density-functional theory calculations to determine the equilibrium defect structures, formation energies, charge transition levels, and electronic structures of Sn and S vacancies in monolayer SnS. Both Sn and S vacancies exhibit multiple charge transition levels and in-gap defect states, indicating that they may be stable in different charge states depending on the Fermi level in the system. Depending on the charge state of the vacancy, the easily distorted SnS lattice undergoes different relaxations, and in some cases, symmetry-breaking reconstructions, creating defect states within the gap that electrons can occupy at a lower energetic cost. Due to significant atomic relaxations between the equilibrium defect structures in different charge states, optical charge transitions involving both types of vacancies exhibit significant Stokes shifts of over 1 eV, which may provide opportunities for increased efficiency in light emission diode, solar cell, and solar concentrator applications.

关键词： Point defects 2-dimensional systems Density functional theory First-principles calculations

Edge Connectivity Augmentation in Near-Linear Time

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arXiv 2022年

作者： Cen, Ruoxu Li, Jason Panigrahi, Debmalya Department of Computer Science Duke University United States Simons Institute for Theory of Computing University of California Berkeley United States

We give an Õ(m)-time algorithm for the edge connectivity augmentation problem and the closely related edge splitting-off problem. This is optimal up to lower order terms and closes the long line of work on these ...

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Application of quantum Machine Learning to HEP Analysis at LHC using quantum computer Simulators and quantum computer Hardware

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Application of Quantum Machine Learning to HEP Analysis at L...

2021 European Physical Society Conference on High Energy Physics, EPS-HEP 2021

作者： Wu, S.L. Chan, J. Cheng, A. Guan, W. Sun, S.J. Zhang, R. Zhou, C. Livny, M. Meglio, A.D. Li, A.C.Y. Lykken, J. Spentzouris, P. Chen, S.Y.-C. Yoo, S. Wei, T.-C. Lougovski, P. Padhi, S. Severini, S. Walker, D. Physics Department of University of Wisconsin-Madison United States Computer Sciences Department of University of Wisconsin-Madison United States CERN Quantum Technology Initiative Switzerland Quantum Institute Fermilab United States Computational Science Initiative BNL United States C.N. Yang Institute for Theoretical Physics State University of New York Stony Brook United States Quantum Computing and AI Research Amazon Web Services United States

Machine learning enjoys widespread success in High Energy Physics (HEP) analyses at LHC. However the ambitious HL-LHC program will require much more computing resources in the next two decades. quantum computing may offer speed-up for HEP physics analyses at HL-LHC, and can be a new computational paradigm for big data analyses in High Energy Physics. We have successfully employed three methods (1) Variational quantum Classifier (VQC) method, (2) quantum Support Vector Machine Kernel (QSVM-kernel) method and (3) quantum Neural Network (QNN) method for two LHC flagship analyses: ttH (Higgs production in association with two top quarks) and H->mumu (Higgs decay to two muons, the second generation fermions). We shall address the progressive improvements in performance from method (1) to method (3). We will present our experiences and results of a study on LHC High Energy Physics data analyses with IBM quantum Simulator and quantum Hardware (using IBM Qiskit framework), Google quantum Simulator (using Google Cirq framework), and Amazon quantum Simulator (using Amazon Braket cloud service). The work is in the context of a Qubit platform (a gate-model quantum computer). Taking into account the present limitation of hardware access, different quantum machine learning methods are studied on simulators and the results are compared with classical machine learning methods (BDT, classical Support Vector Machine and classical Neural Network). Furthermore, we do apply quantum machine learning on IBM quantum hardware to compare performance between quantum simulator and quantum hardware. The work is performed by an international and interdisciplinary collaboration with the Department of Physics and Department of computer sciences of University of Wisconsin, CERN quantum Technology Initiative, IBM Research Zurich, IBM T.J. Watson Research Center, Fermilab quantum institute, BNL Computational science Initiative, State University of New York at Stony Brook, and quantum computing and AI

关键词： High energy physics