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Max-flow min-cut theorem in quantum computing

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2024年 649卷

作者： Singh, Nongmeikapam Brajabidhu Roy, Arnab Saha, Anish Kumar Natl Inst Technol Silchar Dept Comp Sci & Engn Silchar 788010 India

The max-flow min-cut theorem in graph theory states that the maximum flow of a network is equal to the minimum cut of edges of the flow network. Max-flow and min-cut are related as two primal-dual linear programs. The theorem is applicable in applications like network connectivity, graph matching problems, transportation and logistics, and scheduling problems. The aim of the paper is to model the classical max-flow and min-cut theorem in quantum computing. Two well-known methods for quantum optimization are quantum annealing and quantum approximate optimization algorithm. The max-flow min-cut is converted to its equivalent model of the above two methods for execution in polynomial time. This paper shows detailed classical to quantum conversion, analysis, implementation, and result of the theorem.

关键词： Quadratic unconstrained binary optimization Ising model quantum annealing quantum approximate optimization algorithm

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Robust Control optimization for quantum approximate optimization algorithms

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IFAC-PapersOnLine 2020年第2期53卷 242-249页

作者： Yulong Dong Xiang Meng Lin Lin Robert Kosut K. Birgitta Whaley Berkeley Center for Quantum Information and Computation Berkeley California 94720 USA Department of Chemistry University of California Berkeley California 94720 USA Department of Mathematics University of California Berkeley California 94720 USA Computational Research Division Lawrence Berkeley National Laboratory Berkeley CA 94720 USA SC Solutions Sunnyvale California 94085 USA

quantum variational algorithms have garnered significant interest recently, due to their feasibility of being implemented and tested on noisy intermediate scale quantum (NISQ) devices. We examine the robustness of the quantum approximate optimization algorithm (QAOA), which can be used to solve certain quantum control problems, state preparation problems, and combinatorial optimization problems. We demonstrate that the error of QAOA simulation can be significantly reduced by robust control optimization techniques, specifically, by sequential convex programming (SCP), to ensure error suppression in situations where the source of the error is known but not necessarily its magnitude. We show that robust optimization improves both the objective landscape of QAOA as well as overall circuit fidelity in the presence of coherent errors and errors in initial state preparation.

关键词： quantum approximate optimization algorithm robust control sequential convex programming error mitigation

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quantum Testing of Recommender algorithms on GPU-Based quantum Simulators

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COMPUTERS 2025年第4期14卷

作者： Liu, Chenxi Lee, W. Bernard Constantinides, Anthony G. Hong Kong Polytech Univ Dept Comp Hong Kong Peoples R China HedgeSPA Pvt Ltd 12 Woodlands Sq05-70 Woods Sq Tower 1 Singapore 737715 Singapore Imperial Coll London AI & Data Analyt Lab London SW7 2AZ England

This study explores the application of quantum computing in asset management, focusing on the use of the quantum approximate optimization algorithm (QAOA) to solve specific classes of financial asset recommendation problems. While quantum computing holds promise for combinatorial optimization tasks, its application to portfolio management faces significant challenges in scalability for practical implementations. In this work, we model the problem using a graph representation where nodes represent investors, and edges reflect significant similarities in asset choices. We test the proposed method using quantum simulators, including cuquantum, Cirq-GPU, and Cirq with IonQ, and compare the performance of quantum optimization against classical brute-force methods. Our results suggest that quantum algorithms may offer computational advantages for certain use cases, though classical heuristics also provide competitive performance for smaller datasets. This study contributes to the ongoing investigation into the potential of quantum computing for real-time financial decision-making, providing insights into both its applicability and limitations in asset management for larger and more complex investor datasets.

关键词： quantum computing quantum approximate optimization algorithm max-cut problem financial asset recommendation IonQ graph neural networks

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optimization Applications as quantum Performance Benchmarks

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ACM TRANSACTIONS ON quantum COMPUTING 2024年第3期5卷 1-44页

作者： Lubinski, Thomas Coffrin, Carleton McGeoch, Catherine Sathe, Pratik Apanavici, Joshua Neira, David Bernal Quantum Circuits Inc New Haven CT 06520 USA Los Alamos Natl Lab Adv Network Sci Initiat Los Alamos CA USA D Wave Syst Inc Burnaby BC Canada Univ Calif Los Angeles Dept Phys & Astron Los Angeles CA USA Los Alamos Natl Lab Theoret Div T 4 Los Alamos CA USA Univ Space Res Assoc Res Inst Adv Comp Sci Mountain View CA USA Johns Hopkins Univ Appl Phys Lab Baltimore MD 21218 USA NASA Quantum Artificial Intelligence Lab Ames Res Ctr Mountain View CA USA Purdue Univ Syst W Lafayette IN USA

Combinatorial optimization is anticipated to be one of the primary use cases for quantum computation in the coming years. The quantum approximate optimization algorithm and quantum Annealing can potentially demonstrate significant run-time performance benefits over current state-of-the-art solutions. Inspired by existing methods to characterize classical optimization algorithms, we analyze the solution quality obtained by solving Max-cut problems using gate-model quantum devices and a quantum annealing device. This is used to guide the development of an advanced benchmarking framework for quantum computers designed to evaluate the trade-off between run-time execution performance and the solution quality for iterative hybrid quantum-classical applications. The framework generates performance profiles through compelling visualizations that show performance progression as a function of time for various problem sizes and illustrates algorithm limitations uncovered by the benchmarking approach. As an illustration, we explore the factors that influence quantum computing system throughput, using results obtained through execution on various quantum simulators and quantum hardware systems.

关键词： quantum Computing Benchmarks Benchmarking algorithms Applica- tion Benchmarks QAOA quantum approximate optimization algorithm Max-cut

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Hybrid quantum approximate optimization Using Enhanced Ant Colony optimization to Solve Large-Scale Combinatorial optimization Problems 8

Hybrid Quantum Approximate Optimization Using Enhanced Ant C...

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8th International Conference on Soft Computing & Machine Intelligence (ISCMI)

作者： Ghimire, Bishad Mahmood, Ausif Elleithy, Khaled Univ Bridgeport Comp Sci & Engn Bridgeport CT 06604 USA

ISBN: (纸本)9781728186832

quantum computing is a promising technology that may provide breakthrough solutions to today's difficult problems such as breaking encryption and solving large-scale combinatorial optimization problems. A class of algorithms referred to as quantum approximate optimization algorithm (QAOA) have been recently proposed. QAOA attempts to approximately solve hard problems using a protocol know as bang-bang. The technique is based on the unitary evolution using a Hamiltonian encoding of the objective function of the combinatorial optimization problem. QAOA has been explored in the context of several optimization problems such as Max-Cut problem, variational Eigenvalue problem etc. Recently, attempts have been made to create QAOA for the Traveling Salesman Problem (TSP). Due to small node size and limited solution capability of the currently available quantum computers and/or simulators, we develop a hybrid approach where subgraphs of a TSP tour are executed on a quantum computer and the results from the quantum optimization are combined in further optimization of the whole tour. Since the local optimization of a subgraph is prone to getting stuck in a local minima, we overcome this problem by using a parallel Ant Colony optimization algorithm with periodic pheromone exchange between colonies. Our results are encouraging and yield optimum results for benchmarks with less than 50 nodes, and usually within 1% of the optimal solution for benchmarks with around 200 nodes.

关键词： quantum algorithm quantum approximate optimization algorithm combinatorial optimization problem ant colony optimization algorithm

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Dynamic resource allocation scheme for mobile edge computing

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JOURNAL OF SUPERCOMPUTING 2023年第15期79卷 17187-17207页

作者： Gong, Changqing He, Wanying Wang, Ting Gani, Abdullah Qi, Han Shenyang Aerosp Univ Sch Comp Sci Shenyang 110000 Peoples R China Univ Malaysia Sabah Fac Comp & Informat Labuan Int Campus Labuan 87000 Malaysia

Mobile edge computing is a promising paradigm that provides edge users with dependable computing services. However, due to the dynamic nature of mobile users and the limited resources of edge servers, it is essential to emphasize the load balancing of edge servers and the cooperation of heterogeneous computing resources. This paper proposes a Dynamic Resource Allocation (DRA) scheme based on a quantum approximate optimization algorithm (QAOA). The DRA is composed of the two components listed below. Firstly, we apply generative adversarial network to predict the future user density in various regions, which is an effective resource allocation aid. Secondly, QAOA is utilized to pre-allocate edge servers resources based on an advanced model of user density. The simulation results demonstrate that the efficient application of DRA ensures the load balancing of edge servers and simultaneously alleviates communication latency.

关键词： quantum approximate optimization algorithm Generative adversarial network Mobile edge computing Dynamic resource allocation

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Multiple Query optimization Using a Gate-Based quantum Computer

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IEEE ACCESS 2023年 11卷 114031-114043页

作者： Fankhauser, Tobias Soler, Marc E. Fuchslin, Rudolf Marcel Stockinger, Kurt Univ Zurich Dept Informat CH-8050 Zurich Switzerland Univ St Gallen Dept Informat CH-9000 St Gallen Switzerland ZHAW Zurich Univ Appl Sci Dept Informat CH-8050 Winterthur Switzerland European Ctr Living Technol I-30123 Venice Italy

quantum computing promises to solve difficult optimization problems in chemistry, physics and mathematics more efficiently than classical computers. However, it requires fault-tolerant quantum computers with millions of qubits;a technological challenge still not mastered by engineers. To lower the barrier, hybrid algorithms combining classical and quantum computers are used, where quantum computing is only used for those parts of computation that cannot be solved efficiently otherwise. In this paper, we tackle the multiple query optimization problem (MQO), an important NP-hard problem in database research. We present an implementation based on a scheme called quantum approximate optimization algorithm to solve the MQO on a gate-based quantum computer. We perform a detailed experimental evaluation of our implementation and compare its performance against a competing approach that employs a quantum annealer - another type of quantum computer. Our implementation shows a qubit efficiency of close to 99%, which is almost a factor of 2 higher than the state-of-the-art implementation. We emphasize that the problems we can solve with current gate-based quantum technology are fairly small and might not seem practical yet compared to state-of-the-art classical query optimizers. However, our experiments on using a hybrid approach of classical and quantum computing show that our implementation scales favourably with larger problem sizes. Hence, we conclude that our approach shows promising results for near-term quantum computers and thus sets the stage for a challenging avenue of novel database research.

关键词： optimization Databases databases multiple query optimization quantum approximate optimization algorithm experimental evaluation

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Opportunities and Challenges of quantum Computing for Engineering optimization

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JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING 2023年第6期23卷 060817页

作者： Wang, Yan Kim, Jungin E. Suresh, Krishnan Georgia Inst Technol Sch Mech Engn Atlanta GA 30332 USA Univ Wisconsin Dept Mech Engn Madison WI 53706 USA

quantum computing as the emerging paradigm for scientific computing has attracted significant research attention in the past decade. quantum algorithms to solve the problems of linear systems, eigenvalue, optimization, machine learning, and others have been developed. The main advantage of utilizing quantum computer to solve optimization problems is that quantum superposition allows for massive parallel searching of solutions. This article provides an overview of fundamental quantum algorithms that can be utilized in solving optimization problems, including Grover search, quantum phase estimation, quantum annealing, quantum approximate optimization algorithm, variational quantum eigensolver, and quantum walk. A review of recent applications of quantum optimization methods for engineering design, including materials design and topology optimization, is also given. The challenges to develop scalable and reliable quantum algorithms for engineering optimization are discussed.

关键词： quantum algorithm Grover search quantum phase estimation quantum annealing quantum approximate optimization algorithm variational quantum eigensolver quantum walk computational foundations for engineering optimization topology and shape optimization

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Novel Resolution of Unit Commitment Problems Through quantum Surrogate Lagrangian Relaxation

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IEEE TRANSACTIONS ON POWER SYSTEMS 2023年第3期38卷 2460-2471页

作者： Feng, Fei Zhang, Peng Bragin, Mikhail A. Zhou, Yifan SUNY Stony Brook Dept Elect & Comp Engn Stony Brook NY 11794 USA

Unit commitment (UC) problems faced by Independent System Operators on a daily basis are becoming increasingly complex due to the recent push for renewables and the consideration of sub-hourly UC to accommodate the increasing variability in the net load. A disruptive solution methodology to address the growing complexity is therefore required. quantum computing offers a promise to overcome the combinatorial complexity through the use of the so-called "qubits." To make the best use of near-term quantum computers to solve UC problems with a much larger number of binary variables than the number of qubits available, this paper devises a novel solution methodology based on a synergistic combination of quantum computing and Surrogate Lagrangian Relaxation (SLR) to solve UC problems. Our new contributions include: 1) A quantum-SLR (QSLR) algorithm incorporating quantum approximate optimization algorithm (QAOA) into the SLR method, which overcomes the fundamental difficulties of previous LR-based quantum methods such as zigzagging of multipliers and the need to know or estimate the optimal dual value for convergence;2) A Distributed QSLR framework (D-QSLR) capable of coordinating local quantum/classical computing resources with those within neighborhoods and, in the meantime, protecting data privacy;3) A Quantized UC model to obtain accurate commitment unit subproblems decision by using a quantum machine;and 4) A time-unit-decomposed quantum UC approach to overcoming the quantum resources' limitations. Promising quantum test results validate the effectiveness of QSLR and the scalability of the UC-oriented D-QSLR algorithm, which demonstrate QSLR's enormous potential in UC optimization.

关键词： quantum computing optimization Qubit Complexity theory quantum entanglement Computers Approximation algorithms Distributed quantum optimization quantum approximate optimization algorithm quantum computing surrogate lagrangian relaxation unit commitment

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A Predictive Approach for Selecting the Best quantum Solver for an optimization Problem 5

A Predictive Approach for Selecting the Best Quantum Solver ...

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2024 International Conference on quantum Computing and Engineering

作者： Volpe, Deborah Quetschlich, Nils Graziano, Mariagrazia Turvani, Giovanna Wille, Robert Politecn Torino Dept Elect & Telecommun Turin Italy Tech Univ Munich Chair Design Automat Munich Germany Politecn Torino Dept Appl Sci & Technol Turin Italy Software Competence Ctr Hagenberg GmbH SCCH Hagenberg Austria

ISBN: (纸本)9798331541378

Leveraging quantum computers for optimization problems holds promise across various application domains. Nevertheless, utilizing respective quantum computing solvers requires describing the optimization problem according to the Quadratic Unconstrained Binary optimization (QUBO) formalism and selecting a proper solver for the application of interest with a reasonable setting. Both demand significant proficiency in quantum computing, QUBO formulation, and quantum solvers, a background that usually cannot be assumed by end users who are domain experts rather than quantum computing specialists. While tools aid in QUBO formulations, support for selecting the best-solving approach remains absent. This becomes even more challenging because selecting the best solver for a problem heavily depends on the problem itself. In this work, we are accepting this challenge and propose a predictive selection approach, which aids end users in this task. To this end, the solver selection task is first formulated as a classification task that is suitable to be solved by supervised machine learning. Based on that, we then propose strategies for adjusting solver parameters based on problem size and characteristics. Experimental evaluations, considering more than 500 different QUBO problems, confirm the benefits of the proposed solution. In fact, we show that in more than 70% of the cases, the best solver is selected, and in about 90% of the problems, a solver in the top two, i.e., the best or its closest suboptimum, is selected. This exploration proves the potential of machine learning in quantum solver selection and lays the foundations for its automation, broadening access to quantum optimization for a wider range of users. The pre-trained classifier is integrated into the MQT quantum Auto Optimizer (MQT QAO) framework, publicly available on GitHub (https://***/cda-tum/mqt-qao) as part of the Munich quantum Toolkit (MQT).

关键词： Machine Learning Predictive Models QUBO quantum optimization quantum Annealer quantum approximate optimization algorithm Variational quantum Eigensolver Grover Adaptive Search

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