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arXiv:2208.07502 · Quantum

Combinatorial optimization solving by coherent Ising machines based on spiking neural networks

Bo Lü, Yong‐Pan Gao, Kai Wen, Chuan Xi Wang

Published Oct 24, 2023• 14 citations
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Abstract

Spiking neural network is a kind of neuromorphic computing that is believed to improve the level of intelligence and provide advantages for quantum computing. In this work, we address this issue by designing an optical spiking neural network and find that it can be used to accelerate the speed of computation, especially on combinatorial optimization problems. Here the spiking neural network is constructed by the antisymmetrically coupled degenerate optical parametric oscillator pulses and dissipative pulses. A nonlinear transfer function is chosen to mitigate amplitude inhomogeneities and destabilize the resulting local minima according to the dynamical behavior of spiking neurons. It is numerically shown that the spiking neural network-coherent Ising machines have excellent performance on combinatorial optimization problems, which is expected to offer new applications for neural computing and optical computing.

DOI
10.22331/q-2023-10-24-1151

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Spiking neural network is a kind of neuromorphic computing that is believed to improve the level of intelligence and provide advantages for quantum computing. In this work, we address this issue by designing an optical spiking neural network and find that it can be used to accelerate the speed of computation, especially on combinatorial optimization problems. Here the spiking neural network is constructed by the antisymmetrically coupled degenerate optical parametric oscillator pulses and dissipative pulses. A nonlinear transfer function is chosen to mitigate amplitude inhomogeneities and destabilize the resulting local minima according to the dynamical behavior of spiking neurons. It is numerically shown that the spiking neural network-coherent Ising machines have excellent performance on combinatorial optimization problems, which is expected to offer new applications for neural computing and optical computing.
Coherent Ising machines (CIMs) are a promising approach for quantum computation. It exhibits excellent per-formance in solving the combinatorial optimization problems, however, the existence of amplitude heterogeneity limits the applications of CIMs. Here in this work, we present a system of the spiking neural network composed of antisymmetrically coupled degenerate optical parametric oscillator pulses and dissipative pulses. It works based on the principles of CIM during solving the combinatorial optimization problems. Moreover, a nonlinear transfer function is chosen to mitigate the amplitude inhomogeneities and destabilize the resulting local minima ac-cording to the dynamical behavior of spiking neurons.
Coherent Ising machine (CIM) is a hardware solver that simulates the Ising model and finds optimal solutions to combinatorial optimization problems. However, for practical tasks, the computational process may be trapped in local minima, which is a key challenge for CIM. In this work, we design a CIM structure with a spiking neural network by adding dissipative pulses, which are anti-symmetrically coupled to the degenerate optical parametric oscillator pulses in CIM with a measurement feedback system. We find that the unstable oscillatory region of the spiking neural network could assist the CIM to escape from the trapped local minima. Moreover, we show that the machine has a different search mechanism than CIM, which can achieve a higher solution success probability and speed-up effect.
ABSTRACT The coherent Ising machine (CIM) is a quantum‐inspired computing platform that leverages optical parametric oscillation dynamics to solve combinatorial optimization problems by searching for the ground state of Ising Hamiltonian. Conventional CIM implementations face challenges in handling non‐uniform coupling strengths and maintaining amplitude stability during computation. In this paper, a new Global mean‐amplitude Feedback‐enhanced spiking neural network CIM (GF‐SNN‐CIM) is introduced with a physics‐driven amplitude stabilization mechanism to dynamically balance nonlinear gain saturation and coupling effects. This modification enhances synchronization in the optical pulse network, leading to more robust convergence under varying interaction strengths. Numerical simulation validation on Max‐Cut problems demonstrates that the GF‐SNN‐CIM achieves improvements in average cut rate compared to conventional spiking neural network CIM. Further application to the traffic assignment problem (TAP) confirms the method's generality. The GF‐SNN‐CIM achieves near‐continuous accuracy (deviations 0.035%) even at coarse discretization, while large‐scale tests on Beijing's road network (481 spins) validate its real‐world applicability. These advances establish a physics‐consistent optimization framework, where optical pulse dynamics directly encode combinatorial problems, paving the way for scalable, high‐performance CIM implementations in complex optimization tasks.
Coherent Ising machines (CIMs) are increasingly anticipated as a new computer that can solve combinatorial optimization problems. CIMs use degenerate optical parametric oscillator pulses as artificial spins. We constructed a 100,512-spin coherent Ising machine, the world's largest. Our CIM can find good solutions to maximum cut problems of 100,000-node graphs ~1000 times faster than simulated annealing. Furthermore, it provides both very good scores and a broad distribution when we operate it near the phase transition point.
Recently, new optimization machines based on non-silicon physical systems, such as quantum annealing machines, have been developed, and their commercialization has been started. These machines solve the problems by searching the state of the Ising spins, which minimizes the Ising Hamiltonian. Such a property of minimization of the Ising Hamiltonian can be applied to various combinatorial optimization problems. In this paper, we introduce the coherent Ising machine (CIM), which can solve the problems in a milli-second order, and has higher performance than the quantum annealing machines especially on the problems with dense mutual connections in the corresponding Ising model. We explain how a target problem can be implemented on the CIM, based on the optimization scheme using the mutually connected neural networks. We apply the CIM to traveling salesman problems as an example benchmark, and show experimental results of the real machine of the CIM. We also apply the CIM to several combinatorial optimization problems in wireless communication systems, such as channel assignment problems. The CIM's ultra-fast optimization may enable a real-time optimization of various communication systems even in a dynamic communication environment.