Shuhei Tamate

A coherent Ising machine for 2000-node optimization problems

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. Inagaki et al. and McMahon et 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 An optical-based processor is developed to solve a broad class of complex optimization problems. 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.

A 16-bit Coherent Ising Machine for One-Dimensional Ring and Cubic Graph Problems

Many tasks in our modern life, such as planning an efficient travel, image processing and optimizing integrated circuit design, are modeled as complex combinatorial optimization problems with binary variables. Such problems can be mapped to finding a ground state of the Ising Hamiltonian, thus various physical systems have been studied to emulate and solve this Ising problem. Recently, networks of mutually injected optical oscillators, called coherent Ising machines, have been developed as promising solvers for the problem, benefiting from programmability, scalability and room temperature operation. Here, we report a 16-bit coherent Ising machine based on a network of time-division-multiplexed femtosecond degenerate optical parametric oscillators. The system experimentally gives more than 99.6% of success rates for one-dimensional Ising ring and nondeterministic polynomial-time (NP) hard instances. The experimental and numerical results indicate that gradual pumping of the network combined with multiple spectral and temporal modes of the femtosecond pulses can improve the computational performance of the Ising machine, offering a new path for tackling larger and more complex instances.

Combinatorial optimization using networks of optical parametric oscillators

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.

Boltzmann sampling for an XY model using a non-degenerate optical parametric oscillator network

We present an experimental scheme of implementing multiple spins in a classical XY model using a non-degenerate optical parametric oscillator (NOPO) network. We built an NOPO network to simulate a one-dimensional XY Hamiltonian with 5000 spins and externally controllable effective temperatures. The XY spin variables in our scheme are mapped onto the phases of multiple NOPO pulses in a single ring cavity and interactions between XY spins are implemented by mutual injections between NOPOs. We show the steady-state distribution of optical phases of such NOPO pulses is equivalent to the Boltzmann distribution of the corresponding XY model. Estimated effective temperatures converged to the setting values, and the estimated temperatures and the mean energy exhibited good agreement with the numerical simulations of the Langevin dynamics of NOPO phases.

Coherent Computing with Injection-Locked Laser Network

Combinatorial optimization problems are ubiquitous in our modern life. The classic examples include the protein folding in biology and medicine, the frequency assignment in wireless communications, traffic control and routing in air and on surface, microprocessor circuit design, computer vision and graph cut in machine learning, and social network control. They often belong to NP, NP-complete and NP-hard classes, for which modern digital computers and future quantum computers cannot find solutions efficiently, i.e. in polynomial time [1].