The basic concept, principle and implementation of coherent Ising machines are presented. A fully programmable 100 spin machine with all-to-all connections solves ground states and randomly samples low-energy excited states of NP-hard Ising problems.
A versatile coherent Ising machine platform based on degenerate optical parametric oscillators has emerged as a powerful approach for solving NP-hard combinatorial optimization problems across diverse applications. Recent work demonstrated breakthroughs using femtosecond laser pumping, achieving a 55% success rate for 100-vertex Max-Cut problems with stable performance maintained for over 8 h. This versatile platform supports fully connected problem mapping and has been successfully validated across multiple domains including molecular docking and credit scoring, substantiating the practical potential of optical approaches for large-scale optimization and paving the way for broad integration into industrial applications.
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) 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.
A degenerate optical parametric oscillator network is proposed to solve the NP-hard problem of finding a ground state of the Ising model. The underlying operating mechanism originates from the bistable output phase of each oscillator and the inherent preference of the network in selecting oscillation modes with the minimum photon decay rate. Computational experiments are performed on all instances reducible to the NP-hard MAX-CUT problems on cubic graphs of order up to 20. The numerical results reasonably suggest the effectiveness of the proposed network.
Computers based on physical systems are increasingly anticipated to overcome the impending limitations on digital computer performance. One such computer is a coherent Ising machine (CIM) for solving combinatorial optimization problems. Here, we report a CIM with 100,512 degenerate optical parametric oscillator pulses working as the Ising spins. We show that the CIM delivers fine solutions to maximum cut problems of 100,000-node graphs drastically faster than standard simulated annealing. Moreover, the CIM, when operated near the phase transition point, provides some extremely good solutions and a very broad distribution. This characteristic will be useful for applications that require fast random sampling such as machine learning.