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arXiv:2302.12454 · IEEE Access

Stochastic Simulated Quantum Annealing for Fast Solution of Combinatorial Optimization Problems

Naoya Onizawa, Ryoma Sasaki, Duckgyu Shin, Warren J. Gross, Takahiro Hanyu

Published Jan 1, 2024• 8 citations
arXivHTMLPDF

Abstract

Combinatorial optimization problems are frequently classified as NP-hard, which means that the time needed to find the optimal solution generally increases exponentially with the problem size. However, the existing research gap highlights the necessity to develop combinatorial optimization methods capable of scaling to large problems while maintaining low solution latency. In this paper, we introduce stochastic simulated quantum annealing (SSQA) for fast solution of combinatorial optimization problems. SSQA is designed based on stochastic computing, which can simulate quantum annealing (QA) by using multiple replicas of spins (probabilistic bits) in classical computing. The use of stochastic computing leads to an efficient parallel spin-state update algorithm, enabling quick search for a solution around the global minimum energy. Therefore, SSQA realizes quantum-like annealing for large-scale problems and can handle fully connected models in combinatorial optimization, unlike QA. The proposed method is evaluated in MATLAB on graph isomorphism problems, which are typical combinatorial optimization problems. It can handle a 100-times larger problem size compared to QA and a 25-times larger problem size compared to a traditional SA method, respectively, for similar convergence probabilities. The time to solution of SSQA is 11.5 times and 423 times smaller than that of the conventional stochastic simulated annealing method and traditional SA, respectively, when solving a 2,025-node combinatorial optimization problem.

DOI
10.1109/access.2024.3431540

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Combinatorial optimization problems are frequently classified as NP-hard, which means that the time needed to find the optimal solution generally increases exponentially with the problem size. However, the existing research gap highlights the necessity to develop combinatorial optimization methods capable of scaling to large problems while maintaining low solution latency. In this paper, we introduce stochastic simulated quantum annealing (SSQA) for fast solution of combinatorial optimization problems. SSQA is designed based on stochastic computing, which can simulate quantum annealing (QA) by using multiple replicas of spins (probabilistic bits) in classical computing. The use of stochastic computing leads to an efficient parallel spin-state update algorithm, enabling quick search for a solution around the global minimum energy. Therefore, SSQA realizes quantum-like annealing for large-scale problems and can handle fully connected models in combinatorial optimization, unlike QA. The proposed method is evaluated in MATLAB on graph isomorphism problems, which are typical combinatorial optimization problems. It can handle a 100-times larger problem size compared to QA and a 25-times larger problem size compared to a traditional SA method, respectively, for similar convergence probabilities. The time to solution of SSQA is 11.5 times and 423 times smaller than that of the conventional stochastic simulated annealing method and traditional SA, respectively, when solving a 2,025-node combinatorial optimization problem.
This paper introduces the Rerandomization technique of simulated stochastic quantum annealing (SSQA), which enables the solution of large-scale combinatorial optimization problems. Rerandomization is a technique that explores a wider solution space by resetting the spin states, and it shows excellent performance for large-scale problems when executed at the optimal timing. The optimal timing can be predicted using mathematical equations. The adoption of the predicted rerandomization timing is demonstrated to significantly improve the accuracy from 42% (without rerandomization) to 100% in the graph isomorphism problem, a common large-scale combinatorial optimization problem with a size of 2,500 bits. Furthermore, the proposed method shows to solve problems of four times the size at the same speed as traditional SA.
It is well-known that quantum annealing (QA) is an excellent algorithm for solving combinatorial optimization problems (COPs). However, its hardware implementation poses challenges, requiring quantum devices. Therefore, a quantum Monte Carlo (QMC) method-based annealing approach called Simulated Quantum Annealing (SQA), which aims to emulate quantum annealing using classical computers, has been proposed. In the demo-night session, we will demonstrate a SQA based on stochastic computing (SC) on a standard FPGA board, called “PYNQ”. The use of SC-based data representation, along with the realization of SC-based spin-gate circuits, makes it possible to drastically reduce hardware costs compared to QA. This enhances the suitability for extending large-scale COPs.
Quantum annealing approximately solves combinatorial optimization problems by leveraging the principles of adiabatic quantum systems. In this approach, the system's Hamiltonian evolves from an initial general state to a problem-specific state. This study introduces multi-tasking quantum annealing (MTQA), a method that enables the parallel processing of multiple optimization problems by embedding them into spatially distinct regions on quantum hardware. MTQA is evaluated using two NP-hard problems: the minimum vertex cover problem (MVCP) and the graph partitioning problem (GPP). This parallel approach optimizes quantum resource utilization by concurrently utilizing idle qubits. The findings demonstrate that MTQA achieves a solution quality comparable to single-problem quantum annealing and classical simulated annealing (SA), while notably reducing the time-to-solution (TTS) metrics. Eigenspectrum analysis further theoretically supports the hypothesis that parallel embedding preserves quantum coherence and does not increase computational complexity by efficiently utilizing available quantum hardware (e.g., qubits and couplers). MTQA enables efficient multitasking in quantum annealing, optimizing hardware utilization and improving throughput for concurrent tasks and demonstrating performance for problems up to 100 nodes in real-world applications.
A combinatorial optimization problem (COP) is the problem of finding the optimal solution in a finite set. When the size of the feasible solution set is large, the complexity of the problem increases, and it is not easy to solve in a reasonable time with the current classical computer technology. Quantum annealing (QA) is a method that replaces classical simulated annealing (SA) methods that do not solve these cases. Therefore, several attempts have been made to solve this problem using a special-purpose quantum annealer to which the QA method is applied. In this survey, we analyze recent studies that solve real-scale COPs using quantum annealers. Through this, we discuss how to reduce the size of the COP to be input to overcome the hardware limitations of the existing quantum annealer. Additionally, we demonstrated the applicability of quantum annealer to COP on a practical scale by comparing and analyzing the results of the classical simulated annealing (SA) and QA method from each study.
This paper investigates the application of quantum annealing for solving complex combinatorial optimization problems. The core claim is that quantum annealing leverages its global search capabilities to efficiently address such problems. The proposed mechanism involves formulating the combinatorial optimization problem as a quantum annealing problem and utilizing the simulated annealing process within quantum annealing to conduct a search for the optimal solution. This research explores the potential of quantum annealing in practical applications, acknowledging that its application in combinatorial optimization is still in its exploratory phase. The algorithm is designed to minimize the energy of a system described by a Hamiltonian, which evolves over time according to the time-dependent Schrödinger equation. The core of the algorithm lies in mapping the problem's constraints and objective function into this Hamiltonian. The search process is governed by quantum fluctuations, represented by the operator H^\hat{H}H^, which encourages transitions to lower energy states, effectively navigating the solution space. The effectiveness of the algorithm is evaluated based on the quality of the solution found and the computational resources required. This work provides a foundational exploration of quantum annealing's potential within the field of combinatorial optimization.
One of the vital roles of computing is to solve large-scale combinatorial optimization problems in a short time. In recent years, methods have been proposed that map optimization problems to ones of searching for the ground state of an Ising model by using a stochastic process. Simulated annealing (SA) is a representative algorithm. However, it is inherently difficult to perform a parallel search. Here we propose an algorithm called momentum annealing (MA), which, unlike SA, updates all spins of fully connected Ising models simultaneously and can be implemented on GPUs that are widely used for scientific computing. MA running in parallel on GPUs is 250 times faster than SA running on a modern CPU at solving problems involving 100 000 spin Ising models.