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Mapping graph coloring to quantum annealing

QUANTUM MACHINE INTELLIGENCE 2020年第2期2卷 1-19页

作者： Silva, Carla Aguiar, Ana Lima, Priscila M., V Dutra, Ines Univ Porto Fac Sci Dept Comp Sci Porto Portugal Fac Engn Inst Telecomunicacoes Porto Portugal Dept Elect & Comp Engn Porto Portugal PESC COPPE CT & Tercio Pacitti Inst CCMN Rio De Janeiro Brazil Univ Fed Rio de Janeiro Rio De Janeiro Brazil Univ Porto Fac Sci CINTESIS Porto Portugal

Quantum annealing provides a method to solve combinatorial optimization problems in complex energy landscapes by exploiting thermal fluctuations that exist in a physical system. This work introduces the mapping of a graph coloring problem based on pseudo-Boolean constraints to a working graph of the D-Wave Systems Inc. We start from the problem formulated as a set of constraints represented in propositional logic. We use the SATyrus approach to transform this set of constraints to an energy minimization problem. We convert the formulation to a quadratic unconstrained binary optimization problem (QUBO), applying polynomial reduction when needed, and solve the problem using different approaches: (a) classical QUBO using simulated annealing in a von Neumann machine;(b) QUBO in a simulated quantum environment;(c) actual quantum 1, QUBO using the D-Wave quantum machine and reducing polynomial degree using a D-Wave library;and (d) actual quantum 2, QUBO using the D-Wave quantum machine and reducing polynomial degree using our own implementation. We study how the implementations using these approaches vary in terms of the impact on the number of solutions found (a) when varying the penalties associated with the constraints and (b) when varying the annealing approach, simulated (SA) versus quantum (QA). Results show that both SA and QA produce good heuristics for this specific problem, although we found more solutions through the QA approach.

关键词： Adiabatic quantum computation quadratic unconstrained binary optimization Constraint and logic programming Symbolic calculus algorithms Pseudo-Boolean optimization

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Quantum computing for several AGV scheduling models

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SCIENTIFIC REPORTS 2024年第1期14卷 1-16页

作者： Tang, Liang Yang, Chao Wen, Kai Wu, Wei Guo, Yiyun Dalian Maritime Univ Coll Transportat Engn Dalian Peoples R China Beijing QBoson Quantum Technol Co Ltd Beijing Peoples R China Shizuoka Univ Fac Engn Hamamatsu Japan Ocean Univ China Dept Informat Sci & Engn Qingdao Peoples R China

Due to the high degree of automation, automated guided vehicles (AGVs) have been widely used in many scenarios for transportation, and traditional computing power is stretched in large-scale AGV scheduling. In recent years, quantum computing has shown incomparable performance advantages in solving specific problems, especially Combinatorial optimization problem. In this paper, quantum computing technology is introduced into the study of the AGV scheduling problem. Additionally two types of quadratic unconstrained binary optimisation (QUBO) models suitable for different scheduling objectives are constructed, and the scheduling scheme is coded into the ground state of Hamiltonian operator, and the problem is solved by using optical coherent Ising machine (CIM). The experimental results show that compared with the traditional calculation method, the optical quantum computer can save 92% computation time on average. It has great application potential.

关键词： Automated guided vehicles Scheduling Quantum computing quadratic unconstrained binary optimization Coherent Ising machine

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On the benefits of a new continuous reformulation for QUBO problems

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ANNALS OF OPERATIONS RESEARCH 2024年 1-13页

作者： Bartmeyer, Petra Maria Lyra, Christiano Univ Campinas UNICAMP Sch Elect & Comp Engn Dept Syst & Energy Ave Albert Einstein 400 BR-13083852 Campinas SP Brazil

The quadratic unconstrained binary optimization (QUBO) emerges as an alternative to modeling and solving a wide range of challenging practical applications. This paper proposes reformulating QUBO as a continuous quadratic optimization problem considering theoretical results concerning constraint penalization and diagonal regularization on the objective function. Our findings show that it is possible to address convexity by addressing the problem with the proposed continuous reformulation. The problem is explored with a series of computational experiments using reference instances for the QUBO problem, where up-to-date solutions are provided for benchmark instances. Complementary studies on custom instances show the benefits of using the proposed reformulations for cases with defined negative matrices.

关键词： quadratic unconstrained binary optimization Combinatorial optimization Continuous reformulations

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Quantum Topology optimization via Quantum Annealing

IEEE TRANSACTIONS ON QUANTUM ENGINEERING

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IEEE TRANSACTIONS ON QUANTUM ENGINEERING 2023年第1期4卷 1页

作者： Ye, Zisheng Qian, Xiaoping Pan, Wenxiao Univ Wisconsin Dept Mech Engn Madison WI 53706 USA

We present a quantum annealing-based solution method for topology optimization (TO). In particular, we consider TO in a more general setting, i.e., applied to structures of continuum domains where designs are represented as distributed functions, referred to as continuum TO problems. According to the problem's properties and structure, we formulate appropriate subproblems that can be solved on an annealing-based quantum computer. The methodology established can effectively tackle continuum TO problems formulated as mixed-integer nonlinear programs. To maintain the resulting subproblems small enough to be solved on quantum computers currently accessible with small numbers of qubits and limited connectivity, we further develop a splitting approach that splits the problem into two parts: the first part can be efficiently solved on classical computers, and the second part with a reduced number of variables is solved on a quantum computer. By such, a practical continuum TO problem of varying scales can be handled on the D-Wave quantum annealer. More specifically, we concern the minimum compliance, a canonical TO problem that seeks an optimal distribution of materials to minimize the compliance with desired material usage. The superior performance of the developed methodology is assessed and compared with the state-of-the-art heuristic classical methods, in terms of both solution quality and computational efficiency. The present work hence provides a promising new avenue of applying quantum computing to practical designs of topology for various applications.

关键词： optimization Quantum annealing Annealing Linear programming Layout Logic gates Computational efficiency Mixed-integer nonlinear program quadratic unconstrained binary optimization quantum annealing topology optimization (TO)

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Tensor Decompositions and Adiabatic Quantum Computing for Discovering Practical Matrix Multiplication Algorithms 5

Tensor Decompositions and Adiabatic Quantum Computing for Di...

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2024 International Conference on Quantum Computing and Engineering

作者： Uotila, Valter Univ Helsinki Helsinki Finland

ISBN: (纸本)9798331541378

Quantum computing and modern tensor-based computing have a strong connection, which is especially demonstrated by simulating quantum computations with tensor networks. The other direction is less studied: quantum computing is not often applied to tensor-based problems. Considering tensor decompositions, we focus on discovering practical matrix multiplication algorithms and develop two algorithms to compute decompositions on quantum computers. The algorithms are expressed as higher-order unconstrained binary optimization (HUBO) problems, which are translated into quadratic unconstrained binary optimization (QUBO) problems. Our first algorithm is decompositional to keep the optimization problem feasible for the current quantum devices. Starting from a suitable initial point, the algorithm discovers tensor decomposition corresponding to the famous Strassen matrix multiplication algorithm, utilizing the current quantum annealers. Since the decompositional algorithm does not guarantee minimal length for found tensor decompositions, we develop a holistic algorithm that can find fixed-length decompositions. Theoretically, by fixing a shorter length than the length for the best-known decomposition, we can ensure that the solution to the holistic optimization problem would yield faster matrix multiplication algorithms.

关键词： higher-order unconstrained binary optimization quadratic unconstrained binary optimization tensor decompositions matrix multiplication algorithms

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01IP and QUBO: optimization Methods for Redundancy Allocation in Complex Systems 23

01IP and QUBO: Optimization Methods for Redundancy Allocatio...

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23rd International Conference on System Theory, Control and Computing (ICSTCC)

作者： Leon, Florin Cascaval, Petru Gheorghe Asachi Tech Univ Isai Dept Comp Sci & Engn Iasi Romania

ISBN: (纸本)9781728106991

This paper addresses the issue of optimal allocation of spare modules in complex series-parallel redundant systems in order to achieve a required reliability with minimal cost. To solve this problem, two optimization techniques are considered: Zero-One Integer Programming (01IP) and quadratic unconstrained binary optimization (QUBO). The results are compared with those given by an approximate analytical method based on Lagrange multipliers. For large systems, the numerical results presented show that the 01IP and QUBO methods give better solutions. A comparative time complexity analysis of 01IP and QUBO is also presented.

关键词： active redundancy cost minimization in reliability allocation zero-one integer programming quadratic unconstrained binary optimization

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Solving Scheduling Problems with Quantum Computing: a Study on Flexible Open Shop

Solving Scheduling Problems with Quantum Computing: a Study ...

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Genetic and Evolutionary Computation Conference (GECCO)

作者： Baioletti, Marco Oddi, Angelo Rasconi, Riccardo Univ Perugia Perugia Italy Natl Res Council Italy CNR Rome Italy

ISBN: (纸本)9798400701207

Despite quantum computing is revealing an increasingly promising technology that has the potential to introduce a significant speed-up in many areas of computation, the number of problems that it can represent and solve is currently rather limited. Therefore, one of the current challenges faced by the quantum computing community is to broaden the class of problems that can be tackled. Among these problems, scheduling problems are a class of particularly interesting and hard combinatorial problems;in this paper, we present a novel solution for representing and solving the Flexible Open Shop Scheduling Problem (FOSSP) to optimality by minimizing the makespan. We firstly present a compact formulation of this problem as a quadratic unconstrained binary optimization (QUBO), which can be used to solve this problem with a quantum annealer. Then, we proceed to the Quantum Approximate optimization Algorithm (QAOA) problem formulation, thus producing both the cost and mix Hamiltonians related to the problem. From the Hamiltonians, we provide the complete description of the quantum circuit that can be used to tackle the FOSSP within the QAOA framework. This second approach can be used to solve the optimization problem with a general-purpose quantum gate-based hardware.

关键词： quantum computing scheduling flexible open-shop quadratic unconstrained binary optimization QAOA adiabatic quantum computing quantum circuits

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Benchmarking Metaheuristic-Integrated QAOA Against Quantum Annealing

Benchmarking Metaheuristic-Integrated QAOA Against Quantum A...

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Computing Conference

作者： Mazumder, Arul Rhik Sen, Anuvab Sen, Udayon Carnegie Mellon Univ Pittsburgh PA 15289 USA Indian Inst Engn Sci & Technol Sibpur 711103 India

ISBN: (纸本)9783031622717;9783031622694;9783031622687

The Quantum Approximate optimization Algorithm (QAOA) is one of the most promising Noisy Intermediate Quantum (NISQ) Algorithms in solving combinatorial optimizations and displays potential over classical heuristic techniques. Unfortunately, QAOA's performance depends on the choice of parameters and standard optimizers often fail to identify key parameters due to the complexity and mystery of these optimization functions. In this paper, we benchmark QAOA circuits modified with metaheuristic optimizers against classical and quantum heuristics to identify QAOA parameters. The experimental results reveal insights into the strengths and limitations of both Quantum Annealing and metaheuristic-integrated QAOA across different problem domains. The findings suggest that the hybrid approach can leverage classical optimization strategies to enhance the solution quality and convergence speed of QAOA, particularly for problems with rugged landscapes and limited quantum resources. Furthermore, the study provides guidelines for selecting the most appropriate approach based on the specific characteristics of the optimization problem at hand.

关键词： quadratic unconstrained binary optimization Quantum approximate optimization algorithm Quantum annealing Metaheuristics

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Graph-theoretic Formulation of QUBO for Scalable Local Search on GPUs 36

Graph-theoretic Formulation of QUBO for Scalable Local Searc...

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36th IEEE International Parallel and Distributed Processing Symposium (IEEE IPDPS)

作者： Yasudo, Ryota Nakano, Koji Ito, Yasuaki Kawamata, Yuya Katsuki, Ryota Ozaki, Shiro Yazane, Takashi Hamano, Kenichiro Hiroshima Univ Higashihiroshima Japan NTT Data Corp Tokyo Japan Kyoto Univ Kyoto Japan

ISBN: (纸本)9781665497473

Heuristic solvers of the quadratic unconstrained binary optimization (QUBO) problems have been rapidly studied because of their potentialities to solve a wide range of combinatorial optimization problems in a unified manner. QUBO solvers, however, face a limitation in the numbers of variables. To overcome this limitation, we reformulate QUBO as a maximum weight induced subgraph problem (MISG) and propose a graphtheoretic approach for solving MISG. It is a problem to find an induced subgraph with the maximum total weight for a given edge-weighted undirected graph. Naive local search that updates only one vertex at a time requires many iterations to obtain good solutions for large-scale problems. To accelerate it, we introduce a new technique to update multiple vertices that can improve the solution at the same time. We have implemented a MISG solver based on our algorithm on NVIDIA A100 GPUs, where flip operations are parallelized with GPU multithreaded computing. Our solver is scalable and supports up to 2(30) (1G) variables. Our results show that our algorithm outperforms the Gurobi optimizer in terms of solution qualities and the execution time.

关键词： quantum annealing quadratic unconstrained binary optimization GPGPU independent set induced subgraph

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Evaluating Ising Processing Units with Integer Programming 1

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16th International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR)

作者： Coffrin, Carleton Nagarajan, Harsha Bent, Russell Los Alamos Natl Lab Los Alamos NM USA

ISBN: (数字)9783030192129

ISBN: (纸本)9783030192129;9783030192112

The recent emergence of novel computational devices, such as adiabatic quantum computers, CMOS annealers, and optical parametric oscillators, present new opportunities for hybrid-optimization algorithms that are hardware accelerated by these devices. In this work, we propose the idea of an Ising processing unit as a computational abstraction for reasoning about these emerging devices. The challenges involved in using and benchmarking these devices are presented and commercial mixed integer programming solvers are proposed as a valuable tool for the validation of these disparate hardware platforms. The proposed validation methodology is demonstrated on a D-Wave 2X adiabatic quantum computer, one example of an Ising processing unit. The computational results demonstrate that the D-Wave hardware consistently produces high-quality solutions and suggests that as IPU technology matures it could become a valuable co-processor in hybrid-optimization algorithms.

关键词： Discrete optimization Ising model quadratic unconstrained binary optimization Integer programming Large Neighborhood Search Adiabatic quantum computation

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