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

Kenta Takata,Yoshitaka Haribara,Shoko Utsunomiya,Hiromasa Sakaguchi,Yoshihisa Yamamoto,Alireza Marandi,Ryan Hamerly,Shuhei Tamate,Daiki Maruo

doi:10.1038/srep34089

Abstract

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.

Highlights

Many combinatorial optimization problems[1] belong to the complexity classes, called nondeterministic polynomial-time (NP)-complete and NP-hard[2], and it is believed that they require a computation time scaling exponentially or faster with the number of input variables
A theoretical model and experimental data have been needed to investigate possible multi-mode effects on the machine performance. We show another experimental demonstration of a coherent Ising machine using sixteen telecom-band Degenerate optical parametric oscillators (DOPOs) pulses resonating in a single ring cavity and pulse-to-pulse phase-controlled interference via three optical delay lines
We have presented an experimental demonstration of a 16-pulse coherent Ising machine

Summary

Result

We use a single narrow blade for the chopper with a frequency of 20 Hz. The rise time (10–90% of the maximum) of the pump power is 206 μs corresponding to ~12,800 round trips for the 4.8 m ring cavity. The first model is based on the abruptly pumped single-mode DOPO network with discrete gain and coupling processes[38,39] It performs stepwise introduction of a constant pumping power of 2.7 times the oscillation threshold (Ith), which is comparable with the experiment, to the system in the vacuum state. Every peak of the output for t > 80 μs, with an interval between 100 and 200 round trips, includes the pattern for ground states This is not consistent with the slow convergence of the success probability by the simulation of the gradually pumped single-mode DOPO network, and suggests the accelerated computation by the multimode effect. When the pulses have enough amplitude, the switching between different configurations gets impossible and the system stably holds the ground state (Fig. 4(e))

Discussion

Findings

Conclusion

Methods