Understanding dynamics of coherent Ising machines through simulation of large-scale 2D Ising models

Fabian Böhm,Koji Enbutsu,Takahiro Inagaki,Takeshi Umeki,Ryoichi Kasahara,Hiroki Takesue,Kensuke Inaba,Toshimori Honjo

doi:10.1038/s41467-018-07328-1

Abstract

Many problems in mathematics, statistical mechanics, and computer science are computationally hard but can often be mapped onto a ground-state-search problem of the Ising model and approximately solved by artificial spin-networks of coupled degenerate optical parametric oscillators (DOPOs) in coherent Ising machines. To better understand their working principle and optimize their performance, we analyze the dynamics during the ground state search of 2D Ising models with up to 1936 mutually coupled DOPOs. For regular as well as frustrated and disordered 2D lattices, the machine finds the correct solution within just a few milliseconds. We determine that calculation performance is limited by freeze-out effects and can be improved by controlling the DOPO dynamics, which allows to optimize performance of coherent Ising machines in various tasks. Comparisons with Monte Carlo simulations reveal that coherent Ising machines behave like low temperature spin systems, thus making them suitable for optimization tasks.

Highlights

Many problems in mathematics, statistical mechanics, and computer science are computationally hard but can often be mapped onto a ground-state-search problem of the Ising model and approximately solved by artificial spin-networks of coupled degenerate optical parametric oscillators (DOPOs) in coherent Ising machines
By comparing our results against Monte Carlo simulations, we extract a temperature estimate and demonstrate that a DOPO network behaves like a low-temperature spin system, even though it operates at room temperature, showing the inherent suitability of coherent Ising machines (CIMs) for optimization tasks
To implement the coupling term Jij, the individual DOPOs are optically coupled through an opto-electronic feedback scheme in which a fieldprogrammable gate array (FPGA) generates the feedback signal and a push–pull modulator modulates the optical phase and amplitude of a train of external injection pulses

Summary

Introduction

Statistical mechanics, and computer science are computationally hard but can often be mapped onto a ground-state-search problem of the Ising model and approximately solved by artificial spin-networks of coupled degenerate optical parametric oscillators (DOPOs) in coherent Ising machines. Even with advances in algorithms and the processing power of modern supercomputers, such computationally hard problems can often not be solved exactly in a reasonable time, which presents a major challenge for many real-world applications such as finance, drug discovery, cryptography, machine learning and optimization and analysis of large networks[1,2,3] Many of these problems can be mapped onto the Ising model and solved by finding the ground state of the Ising Hamiltonian[4]. By comparing our results against Monte Carlo simulations, we extract a temperature estimate and demonstrate that a DOPO network behaves like a low-temperature spin system, even though it operates at room temperature, showing the inherent suitability of CIMs for optimization tasks

Methods

Results

Conclusion