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Challenges and Opportunities in quantum Optimization

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arXiv 2023年

作者： Abbas, Amira Ambainis, Andris Augustino, Brandon Bärtschi, Andreas Buhrman, Harry Coffrin, Carleton Cortiana, Giorgio Dunjko, Vedran Egger, Daniel J. Elmegreen, Bruce G. Franco, Nicola Fratini, Filippo Fuller, Bryce Gacon, Julien Gonciulea, Constantin Gribling, Sander Gupta, Swati Hadfield, Stuart Heese, Raoul Kircher, Gerhard Kleinert, Thomas Koch, Thorsten Korpas, Georgios Lenk, Steve Marecek, Jakub Markov, Vanio Mazzola, Guglielmo Mensa, Stefano Mohseni, Naeimeh Nannicini, Giacomo O’Meara, Corey Tapia, Elena Peña Pokutta, Sebastian Proissl, Manuel Rebentrost, Patrick Sahin, Emre Symons, Benjamin C.B. Tornow, Sabine Valls, Víctor Woerner, Stefan Wolf-Bauwens, Mira L. Yard, Jon Yarkoni, Sheir Zechiel, Dirk Zhuk, Sergiy Zoufal, Christa QuSoft University of Amsterdam Netherlands University of Latvia Latvia Massachusetts Institute of Technology United States Los Alamos National Laboratory United States E.ON Digital Technology GmbH Germany Leiden University Netherlands IBM Quantum IBM Research Europe Zurich Switzerland IBM Research IBM T.J. Watson Research Center United States Fraunhofer IKS Germany Erste Group Bank Austria IBM Quantum IBM T.J. Watson Research Center United States École Polytechnique Fédérale de Lausanne Switzerland Wells Fargo United States Tilburg University Netherlands Quantum Artificial Intelligence Lab NASA Ames Research Center United States USRA Research Institute for Advanced Computer Science United States Fraunhofer ITWM Germany Quantagonia Zuse Institute Berlin Germany Technische Universität Berlin Germany HSBC Lab Innovation and Ventures HSBC London United Kingdom Czech Technical University in Prague Czech Republic Fraunhofer IOSB-AST Germany University of Zurich Switzerland The Hartree Centre STFC United Kingdom University of Southern California United States Centre for Quantum Technologies National University of Singapore Singapore University of the Bundeswehr Munich Germany IBM Quantum IBM Research Europe Dublin Ireland Institute for Quantum Computing Perimeter Institute for Theoretical Physics University of Waterloo Canada Volkswagen AG

Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization being one of the most pronounced domains. Across computer science and physics, there are a number of different approaches for major classes of optimization problems, such as combinatorial optimization, convex optimization, non-convex optimization, and stochastic extensions. This work draws on multiple approaches to study quantum optimization. Provably exact versus heuristic settings are first explained using computational complexity theory – highlighting where quantum advantage is possible in each context. Then, the core building blocks for quantum optimization algorithms are outlined to subsequently define prominent problem classes and identify key open questions that, if answered, will advance the field. The effects of scaling relevant problems on noisy quantum devices are also outlined in detail, alongside meaningful benchmarking problems. We underscore the importance of benchmarking by proposing clear metrics to conduct appropriate comparisons with classical optimization techniques. Lastly, we highlight two domains – finance and sustainability – as rich sources of optimization problems that could be used to benchmark, and eventually validate, the potential real-world impact of quantum optimization. © 2023, CC BY.

关键词： quantum computers

quantum Resource Theories beyond Convexity

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arXiv 2024年

作者： Salazar, Roberto Czartowski, Jakub Rodríguez, Ricard Ravell Rajchel-Mieldzioć, Grzegorz Horodecki, Pawel Życzkowski, Karol Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University Kraków30-348 Poland Doctoral School of Exact and Natural Sciences Jagiellonian University ul. Lojasiewicza 11 Kraków30-348 Poland Campus Universitat Illes Balears Palma de MallorcaE-07122 Spain NASK National Research Institute ul. Kolska 12 Warszawa01-045 Poland ICFO-Institut de Ciencies Fotoniques The Barcelona Institute of Science and Technology Av. Carl Friedrich Gauss 3 Castelldefels Barcelona08860 Spain International Centre for Theory of Quantum Technologies University of Gdańsk Wita Stwosza 63 Gdańsk80-308 Poland Center for Theoretical Physics Polish Academy of Sciences Warszawa02-668 Poland

A class of quantum resource theories, based on non-convex star-shape sets, presented in this work captures the key quantum properties that cannot be studied by standard convex theories. We provide operational interpretations for a resource of this class and demonstrate its advantage to improve performance of correlated quantum discrimination tasks and testing of quantum combs. Proposed techniques provide useful tools to describe quantum discord, total correlations in composite quantum systems and to estimate the degree of non-Markovianity of an analyzed quantum dynamics. Other applications include the problem of unistochasticity of a given bistochastic matrix, with relevance for quantization of classical dynamics and studies of violation of CP-symmetry in high energy physics. In all these cases, the non-linear witnesses introduced here outperform the standard linear witnesses. Importance of our findings for quantum information theory is also emphasized. Copyright © 2024, The Authors. All rights reserved.

关键词： quantum optics

Provably Efficient Simulation of 1D Long-Range Interacting Systems at Any Temperature

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Physical Review Letters 2025年第19期134卷 190404-190404页

作者： Rakesh Achutha Donghoon Kim Yusuke Kimura Tomotaka Kuwahara Analytical quantum complexity RIKEN Hakubi Research Team RIKEN Center for Quantum Computing (RQC) Wako Saitama 351-0198 Japan Department of Computer Science and Engineering Indian Institute of Technology (Banaras Hindu University) Varanasi 221005 India PRESTO Japan Science and Technology (JST) Kawaguchi Saitama 332-0012 Japan RIKEN Cluster for Pioneering Research (CPR) Wako Saitama 351-0198 Japan

We introduce a method that ensures efficient computation of one-dimensional quantum systems with long-range interactions across all temperatures. Our algorithm operates within a quasipolynomial run-time for inverse temperatures up to β=poly(ln(n)). At the core of our approach is the density matrix renormalization group algorithm, which typically does not guarantee efficiency. We have created a new truncation scheme for the matrix product operator of the quantum Gibbs states, which allows us to control the error analytically. Additionally, our method can be applied to simulate the time evolution of systems with long-range interactions, achieving significantly better precision than that offered by the Lieb-Robinson bound.

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Variational quantum algorithm for generalized eigenvalue problems and its application to the finite-element method

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Physical Review A 2023年第2期108卷 022429-022429页

作者： Yuki Sato Hiroshi C. Watanabe Rudy Raymond Ruho Kondo Kaito Wada Katsuhiro Endo Michihiko Sugawara Naoki Yamamoto Toyota Central R&D Labs. Inc. 41-1 Yokomichi Nagakute Aichi 480-1192 Japan Quantum Computing Center Keio University 3-14-1 Hiyoshi Kohoku-ku Yokohama Kanagawa 223-8522 Japan Department of Chemistry Graduate School of Science Kyushu University 744 Motooka Nishi-ku Fukuoka 819-0395 Japan IBM Quantum IBM Japan 19-21 Nihonbashi Hakozaki-cho Chuo-ku Tokyo 103-8510 Japan Department of Computer Science The University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo 113-0033 Japan Department of Applied Physics and Physico-Informatics Keio University Hiyoshi 3-14-1 Kohoku-ku Yokohama 223-8522 Japan Research Center for Computational Design of Advanced Functional Materials National Institute of Advanced Industrial Science and Technology (AIST) 1-1-1 Umezono Tsukuba Ibaraki 305-8568 Japan

Generalized eigenvalue problems (GEPs) play an important role in the variety of fields including engineering, machine learning, and quantum chemistry. Especially, many problems in these fields can be reduced to finding the minimum or maximum eigenvalue of GEPs. One of the key problems to handle GEPs is that the memory usage and computational complexity explode as the size of the system of interest grows. This paper aims at extending sequential quantum optimizers for GEPs. Sequential quantum optimizers are a family of algorithms that iteratively solve the analytical optimization of single-qubit gates in a coordinate descent manner. The contribution of this paper is as follows. First, we formulate the GEP as the minimization or maximization problem of the fractional form of the expectations of two Hermitians. We then show that the fractional objective function can be analytically minimized or maximized with respect to a single-qubit gate by solving a GEP of a 4×4 matrix. Second, we show that a system of linear equations characterized by a positive-definite Hermitian can be formulated as a GEP and thus be attacked using the proposed method. Finally, we demonstrate two applications to important engineering problems formulated with the finite-element method. Through the demonstration, we have the following bonus finding; a problem having a real-valued solution can be solved more effectively using quantum gates generating a complex-valued state vector, which demonstrates the effectiveness of the proposed method.

关键词： quantum algorithms

quantum linear algebra is all you need for Transformer architectures

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arXiv 2024年

作者： Guo, Naixu Yu, Zhan Choi, Matthew Agrawal, Aman Nakaji, Kouhei Aspuru-Guzik, Alán Rebentrost, Patrick Centre for Quantum Technologies National University of Singapore 117543 Singapore Department of Computer Science University of Toronto TorontoONM5S 2E4 Canada Vector Institute for Artificial Intelligence TorontoONM5S 1M1 Canada Department of Mathematics National University of Singapore 119076 Singapore Department of Chemistry University of Toronto TorontoONM5G 1Z8 Canada 1-1-1 Umezono Ibaraki Tsukuba305-8568 Japan Quantum Computing Center Keio University 3-14-1 Hiyoshi Kohoku-ku Kanagawa Yokohama223-8522 Japan Department of Materials Science & Engineering University of Toronto TorontoONM5S 3E4 Canada Department of Chemical Engineering & Applied Chemistry University of Toronto TorontoONM5S 3E5 Canada Canadian Institute for Advanced Research TorontoONM5G 1Z8 Canada School of Computing National University of Singapore 117417 Singapore

Generative machine learning methods such as large-language models are revolutionizing the creation of text and images. While these models are powerful they also harness a large amount of computational resources. The transformer is a key component in large language models that aims to generate a suitable completion of a given partial sequence. In this work, we investigate transformer architectures under the lens of fault-tolerant quantum computing. The input model is one where trained weight matrices are given as block encodings and we construct the query, key, and value matrices for the transformer. We show how to prepare a block encoding of the self-attention matrix, with a new subroutine for the row-wise application of the softmax function. In addition, we combine quantum subroutines to construct important building blocks in the transformer, the residual connection and layer normalization, and the feed-forward neural network. Our subroutines prepare an amplitude encoding of the transformer output, which can be measured to obtain a prediction. Based on common open-source large-language models, we provide insights into the behavior of important parameters determining the run time of the quantum algorithm. We discuss the potential and challenges for obtaining a quantum advantage. © 2024, CC BY.

关键词： Network architecture

Study on Deep Reinforcement Learning for Multi-Task Scheduling in Cloud Manufacturing

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SSRN

SSRN 2022年

作者： Xiao, Jiuhong Cai, Yishuai Wang, Wanru Chen, Yong College of Economic and Social Development Nankai University Tianjin300072 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 School of Information Management and Artificial Intelligence Zhejiang University of Finance and Economics Hangzhou310018 China College of Civil Engineering and Architecture Zhejiang University Hangzhou310058 China

Cloud manufacturing is an emerging manufacturing paradigm, which enables the simultaneous processing of multiple manufacturing tasks submitted by customers through centralized management and planning of manufacturing services offered by distributed enterprises. To date, various meta-heuristics algorithms such as ant colony optimization algorithm, and genetic algorithm have been widely employed to solve the cloud manufacturing multi-task scheduling (CMMS) problem to improve the efficiency of multi-task scheduling. However, these algorithms need sophisticated design procedures and laborious parameter tuning, making their adaptation to dynamic, large-scale manufacturing environments difficult. Deep reinforcement learning (DRL), because of its efficiency and flexibility, has recently attracted increasing attention from researchers and has shown promising performance in solving combinatorial optimization problems. Nevertheless, little is known about the performance of DRL technologies in solving the CMMS problem. Therefore, in this study, three state-of-the-art DRL technologies, including proximal policy optimization (PPO), deep deterministic policy gradient, and normalized advantage function, are selected to systematically investigate the potential of DRL in solving the CMMS problem. A comprehensive comparison of these DRL technologies is conducted in terms of effectiveness and efficiency, robustness and adaptability, and scalability. Experimental results indicate that PPO is superior to other technologies in solving the CMMS problem. © 2022, The Authors. All rights reserved.

关键词： Reinforcement learning

Why interference phenomena do not capture the essence of quantum theory

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arXiv 2021年

作者： Catani, Lorenzo Leifer, Matthew Schmid, David Spekkens, Robert W. Electrical Engineering and Computer Science Department Technische Universität Berlin Berlin10587 Germany Institute for Quantum Studies Schmid College of Science and Technology Chapman University One University Drive OrangeCA92866 United States International Centre for Theory of Quantum Technologies University of Gdansk Gdansk80-308 Poland Perimeter Institute for Theoretical Physics 31 Caroline Street North WaterlooONN2L 2Y5 Canada

quantum interference phenomena are widely viewed as posing a challenge to the classical worldview. Feynman even went so far as to proclaim that they are the only mystery and the basic peculiarity of quantum mechanics. Many have also argued that basic interference phenomena force us to accept a number of radical interpretational conclusions, including: that a photon is neither a particle nor a wave but rather a Jekyll-and-Hyde sort of entity that toggles between the two possibilities, that reality is observer-dependent, and that systems either do not have properties prior to measurements or else have properties that are subject to nonlocal or backwards-in-time causal influences. In this work, we show that such conclusions are not, in fact, forced on us by basic interference phenomena. We do so by describing an alternative to quantum theory, a statistical theory of a classical discrete field (the ‘toy field theory’) that reproduces the relevant phenomenology of quantum interference while rejecting these radical interpretational claims. It also reproduces a number of related interference experiments that are thought to support these interpretational claims, such as the Elitzur-Vaidman bomb tester, Wheeler’s delayed-choice experiment, and the quantum eraser experiment. The systems in the toy field theory are field modes, each of which possesses, at all times, both a particle-like property (a discrete occupation number) and a wave-like property (a discrete phase). Although these two properties are jointly possessed, the theory stipulates that they cannot be jointly known. The phenomenology that is generally cited in favour of nonlocal or backwards-in-time causal influences ends up being explained in terms of inferences about distant or past systems, and all that is observer-dependent is the observer’s knowledge of reality, not reality itself. © 2021, CC BY.

关键词： quantum interference devices

Cost of quantum Entanglement Simplified

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Physical Review Letters 2020年第4期125卷 040502-040502页

作者： Xin Wang Mark M. Wilde Institute for Quantum Computing Baidu Research Beijing 100193 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 and Center for Computation and Technology Louisiana State University Baton Rouge Louisiana 70803 USA

quantum entanglement is a key physical resource in quantum information processing that allows for performing basic quantum tasks such as teleportation and quantum key distribution, which are impossible in the classical world. Ever since the rise of quantum information theory, it has been an open problem to quantify entanglement in an information-theoretically meaningful way. In particular, every previously defined entanglement measure bearing a precise information-theoretic meaning is not known to be efficiently computable, or if it is efficiently computable, then it is not known to have a precise information-theoretic meaning. In this Letter, we meet this challenge by introducing an entanglement measure that has a precise information-theoretic meaning as the exact cost required to prepare an entangled state when two distant parties are allowed to perform quantum operations that completely preserve the positivity of the partial transpose. Additionally, this entanglement measure is efficiently computable by means of a semidefinite program, and it bears a number of useful properties such as additivity and faithfulness. Our results bring key insights into the fundamental entanglement structure of arbitrary quantum states, and they can be used directly to assess and quantify the entanglement produced in quantum-physical experiments.

关键词： Entanglement manipulation Entanglement measures quantum correlations in quantum information quantum entanglement Resource theories

SYNCHRONOUS VALUES OF GAMES

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arXiv 2021年

作者： William Helton, J. Mousavi, Hamoon Nezhadi, Seyed Sajjad Paulsen, Vern I. Russell, Travis B. Department of Mathematics University of California San Diego La Jolla CA92093-0112 United States Department of Computer Science Columbia University New YorkNY10027 United States Joint Center for Quantum Information and Computer Science Department of Computer Science University of Maryland College ParkMD20742 United States Institute for Quantum Computing Department of Pure Mathematics University of Waterloo WaterlooONN2L 3G1 Canada Department of Mathematics Texas Christian University Fort WorthTX76129 United States

We study synchronous values of games, especially synchronous games. It is known that a synchronous game has a perfect strategy if and only if it has a perfect synchronous strategy. However, we give examples of synchronous games, in particular graph colouring games, with synchronous value that is strictly smaller than their ordinary value. Thus, the optimal strategy for a synchronous game need not be synchronous. We derive a formula for the synchronous value of an XOR game as an optimization problem over a spectrahedron involving a matrix related to the cost matrix. We give an example of a game such that the synchronous value of repeated products of the game is strictly increasing. We show that the synchronous quantum bias of the XOR of two XOR games is not multiplicative. Finally, we derive geometric and algebraic conditions that a set of projections that yields the synchronous value of a game must satisfy. Copyright © 2021, The Authors. All rights reserved.

关键词： Matrix algebra