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JSAP-OSA Joint Symposia

Simulated quantum annealing using a photon-counting random number generator for stochastic majority voting and cooperative spin manipulation of replicas

Akio Yoshizawa

Published Jan 1, 2018• 0 citations
Publisher

Abstract

An Ising calculation based on the path integral quantum Monte Carlo method is presented to classically simulate quantum annealing. For cooling stochastic majority voting is applied to each replica. For cooperative spin manipulation same indexed spins of neighboring replicas are stochastically aligned to be parallel. We use a photon-counting random number generator to add stochastic behaviors to majority voting and cooperative spin manipulation.

DOI
10.1364/opj.2018.30pbj8

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An Ising calculation based on the path integral quantum Monte Carlo method is presented to classically simulate quantum annealing. For cooling stochastic majority voting is applied to each replica. For cooperative spin manipulation same indexed spins of neighboring replicas are stochastically aligned to be parallel. We use a photon-counting random number generator to add stochastic behaviors to majority voting and cooperative spin manipulation.
The path integral Monte Carlo simulated quantum annealing algorithm is applied to the optimization of a large hard instance of the random satisfiability problem (N = 10,000). The dynamical behavior of the quantum and the classical annealing are compared, showing important qualitative differences in the way of exploring the complex energy landscape of the combinatorial optimization problem. At variance with the results obtained for the Ising spin glass and for the traveling salesman problem, in the present case the linear-schedule quantum annealing performance is definitely worse than classical annealing. Nevertheless, a quantum cooling protocol based on field-cycling and able to outperform standard classical simulated annealing over short time scales is introduced.
Quantum annealing was recently found experimentally in a disordered spin-12\frac{1}{2}21​ magnet to be more effective than its classical, thermal counterpart. We use the random two-dimensional Ising model as a test example and perform on it both classical and quantum (path-integral) Monte Carlo annealing. A systematic study of the dependence of the final residual energy on the annealing Monte Carlo time quantitatively demonstrates the superiority of quantum relative to classical annealing in this system. In order to determine the parameter regime for optimal efficiency of the quantum annealing procedure we explore a range of values of Trotter slice number P and temperature T. This identifies two different regimes of freezing with respect to efficiency of the algorithm, and leads to useful guidelines for the optimal choice of quantum annealing parameters.
In the near future, one of the main processes is solving large combinatorial optimization problems. However, the performance growth of von Neumann architecture will slow due to the end of semiconductor scaling. To resolve this problem, we propose an Ising computer that maps the optimization problems to the ground state search of Ising models. We previously proposed a computer that finds the ground state of Ising models by simulated annealing (SA) approximately. Though the solution quality of the previous prototype is comparable to that of SA, enhancing the solution quality will be required to solve real-world applications. In this paper, we present our FPGA-based Ising computer that executes simulated quantum annealing by using a path integral quantum Monte Carlo method for Ising models on a 48-by-48 king graph with 8-bit couplings. We also propose a shared random number supply, which contributes to decrease the number of random number generators to two. Experimental results indicate that the proposed Ising computer is more than 15 times faster to obtain 99.9%-solution with a probability of 99% than SA running on a state-of-the-art CPU.
The path-integral quantum Monte Carlo (PIQMC) method is widely used as a classical simulation algorithm for quantum annealing. Replicas represent different points in imaginary time. We propose and demonstrate a swarm-like ground-state searching algorithm based on the PIQMC method for automatically fluctuation-controlled simulated annealing. Replicas help one another to search for the ground state of an Ising system as if forming a swarm and working cooperatively. Their interactions are local, simple and fluctuate to a certain degree. Such fluctuations are necessary to escape local minima, but the fluctuations do not need to be explicitly controlled. The size of fluctuations is automatically adjusted as annealing proceeds. We solve max-cut problems for algorithm evaluation, each of which corresponds to a graph of 100 vertices. We also solve the same problems using a conventional method based on the Metropolis algorithm for comparison.
This article considers quantum annealing in the Ising framework for solving combinatorial optimization problems. The path-integral Monte Carlo simulation approach is often used to approximate quantum annealing and implement the approximation by classical computers, which refers to simulated quantum annealing (SQA). In this article, we introduce a data augmentation scheme into SQA and develop a new algorithm for its implementation. The proposed algorithm reveals new insights on the sampling behaviors in SQA. Theoretical analyses are established to justify the algorithm, and numerical studies are conducted to check its performance and to confirm the theoretical findings. Supplementary materials for this article are available online.
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.