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Light Science & Applications

Large-scale coherent Ising machine based on optoelectronic parametric oscillator

Qizhuang Cen, Hao Ding, Tengfei Hao, Shanhong Guan, Zhiqiang Qin, Jiaming Lyu, Wei Li, Ninghua Zhu, Kun Xu, Yitang Dai, Ming Li

Published Nov 25, 2022• 75 citations
Publisher

Abstract

Ising machines based on analog systems have the potential to accelerate the solution of ubiquitous combinatorial optimization problems. Although some artificial spins to support large-scale Ising machines have been reported, e.g., superconducting qubits in quantum annealers and short optical pulses in coherent Ising machines, the spin stability is fragile due to the ultra-low equivalent temperature or optical phase sensitivity. In this paper, we propose to use short microwave pulses generated from an optoelectronic parametric oscillator as the spins to implement a large-scale Ising machine with high stability. The proposed machine supports 25,600 spins and can operate continuously and stably for hours. Moreover, the proposed Ising machine is highly compatible with high-speed electronic devices for programmability, paving a low-cost, accurate, and easy-to-implement way toward solving real-world optimization problems.

DOI
10.1038/s41377-022-01013-1

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Ising machines based on analog systems have the potential to accelerate the solution of ubiquitous combinatorial optimization problems. Although some artificial spins to support large-scale Ising machines have been reported, e.g., superconducting qubits in quantum annealers and short optical pulses in coherent Ising machines, the spin stability is fragile due to the ultra-low equivalent temperature or optical phase sensitivity. In this paper, we propose to use short microwave pulses generated from an optoelectronic parametric oscillator as the spins to implement a large-scale Ising machine with high stability. The proposed machine supports 25,600 spins and can operate continuously and stably for hours. Moreover, the proposed Ising machine is highly compatible with high-speed electronic devices for programmability, paving a low-cost, accurate, and easy-to-implement way toward solving real-world optimization problems.
Abstract Ising machines based on analog systems have the potential of acceleration in solving ubiquitous combinatorial optimization problems. Although some artificial spins to support large-scale Ising machine is reported, e.g. superconducting qubits in quantum annealers and short optical pulses in coherent Ising machines, the spin coherence is fragile due to the ultra-low equivalent temperature or optical phase sensitivity. In this paper, we propose to use short microwave pulses generated from an optoelectronic parametric oscillator as the spins to implement the Ising machine with large scale and also high coherence under room temperature. The proposed machine supports 10,000 spins, and the high coherence leads to accurate computation. Moreover, the Ising machine is highly compatible with high-speed electronic devices for programmability, paving a low-cost, accurate, and easy-to-implement way toward to solve real-world optimization problems.
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.
Combinatorial optimizers using physical systems, or "Ising machines," have been intensively studied as a way of computation that is more efficient than current digital computers. Here, we demonstrate that a coherent Ising machine (CIM) based on degenerate optical parametric oscillator (DOPO) pulses can find solutions to large-scale maximum independent set problems, which is an essential optimization problem that is closely related to real-world optimization tasks. We implemented a stable external field for each Ising spin as an interaction between a DOPO pulse and a group of ferromagnetically coupled auxiliary pulses. Consequently, the CIM delivered independent sets for dense graphs with up to 40,000 nodes. We compared the performance of the CIM with that of optimized simulated annealing algorithm implemented on a digital computer and found that the CIM outperformed the central processing unit (CPU) in terms of the time needed to obtain good approximate solutions when the graph size exceeded several thousand nodes.
Various artificial spin systems with networked physical devices are now emerging as a way to simulate the Ising model. Combinatorial optimization problems for many applications can be mapped onto ground state search problems of the Ising model and solved efficiently with the artificial spin system. Here, we report a coherent Ising machine based on 2,048 networked degenerate optical parametric oscillators. All-to-all couplings were achieved with a measurement and feedback scheme to implement arbitrary graph structures with up to 2,048 nodes. The coherent Ising machine can simulate large-scale Ising model and obtain good solutions for the optimization of a 2,000-node complete graph.
Coherent Ising machines (CIMs) constitute a promising approach to solve computationally hard optimization problems by mapping them to ground state searches of the Ising model and implementing them with optical artificial spin-networks. However, while CIMs promise speed-ups over conventional digital computers, they are still challenging to build and operate. Here, we propose and test a concept for a fully programmable CIM, which is based on opto-electronic oscillators subjected to self-feedback. Contrary to current CIM designs, the artificial spins are generated in a feedback induced bifurcation and encoded in the intensity of coherent states. This removes the necessity for nonlinear optical processes or large external cavities and offers significant advantages regarding stability, size and cost. We demonstrate a compact setup for solving MAXCUT optimization problems on regular and frustrated graphs with 100 spins and can report similar or better performance compared to CIMs based on degenerate optical parametric oscillators.
We report a coherent Ising machine (CIM), which is a network of degenerate optical parametric oscillators for simulating the Ising model. Using a long-distance fiber cavity that includes a telecom-band phase sensitive amplifier, we generated large number of degenerate optical parametric oscillator (DOPO) pulses multiplexed in time domain, which represent the Ising spins. By using a measurement and feedback scheme, we could implement all-to-all coupling among 2048 DOPOs. We experimentally confirmed that the CIM could find solutions to maximum cut problems for graphs with as many as 2000 nodes.