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Nonlinear Optics

Combinatorial optimization using networks of optical parametric oscillators

Peter L. McMahon, Alireza Marandi, Yoshitaka Haribara, Ryan Hamerly, Carsten Langrock, Shuhei Tamate, Takahiro Inagaki, Hiroki Takesue, Shoko Utsunomiya, Kazuyuki Aihara, Robert L. Byer, M. M. Fejer, Hideo Mabuchi, Y. Yamamoto

Published Jan 1, 2017• 1 citation
Publisher

Abstract

We use a network of 160 optical parametric oscillators, formed using fiber-coupled PPLN in a ~320-m fiber loop, to build an annealing machine that can find solutions to Ising problems with arbitrary spin connectivity.
DOI
10.1364/nlo.2017.nm2b.2

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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.
The analysis and optimization of complex systems can be reduced to mathematical problems collectively known as combinatorial optimization. Many such problems can be mapped onto ground-state search problems of the Ising model, and various artificial spin systems are now emerging as promising approaches. However, physical Ising machines have suffered from limited numbers of spin-spin couplings because of implementations based on localized spins, resulting in severe scalability problems. We report a 2000-spin network with all-to-all spin-spin couplings. Using a measurement and feedback scheme, we coupled time-multiplexed degenerate optical parametric oscillators to implement maximum cut problems on arbitrary graph topologies with up to 2000 nodes. Our coherent Ising machine outperformed simulated annealing in terms of accuracy and computation time for a 2000-node complete graph.
We introduce the recent progress of coherent Ising machine (CIM), which finds solutions to complex combinatorial optimization problems using a network of degenerate optical parametric oscillators (DOPO). We describe our effort to generate time-multiplexed DOPOs using long-distance fiber cavities including telecom-band phase sensitive amplifiers [1-4]. We then present our experiments where we found solutions to complex combinatorial optimization problems using a CIM with measurement-feedback scheme [5]. Finally, a future perspective of the CIM project will briefly described.
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.
Taking the pulse of optimization Finding the optimum solution of multiparameter or multifunctional problems is important across many disciplines, but it can be computationally intensive. Many such problems defined as computationally difficult can be mathematically mapped onto the so-called Ising problem, which looks at finding the minimum energy configuration for an array of coupled spins. Inagakiet al.and McMahonet al.show that an optical processing approach based on a network of coupled optical pulses in a ring fiber can be used to model and optimize large-scale Ising systems. Such a scalable architecture could help to optimize solutions to a wide range of complex problems. Science, this issue pp. 603 and 614