Solving complex optimization problems with a coherent Ising machine

Abstract

As the various systems in our society grow larger and more complex, their analysis and optimization grow increasingly important. Many such tasks are classified as combinatorial optimization problems, which can be mapped onto the ground-statesearch problems of the Ising model.1 Recently, several approaches to simulating the Ising model have been demonstrated using artificial spin networks, such as superconducting quantum bits (qubits)2 and CMOS devices.3 These physical Ising machines have suffered from a limited number of spin-spin couplings, however, because of the use of solid-state devices as artificial spins. We have realized a coherent Ising machine (i.e., an artificial spin network based on quantum electronics technologies, CIM) that is instead based on photonics.4 To achieve this, we used time-multiplexed degenerate optical parametric oscillators (DOPOs)5, 6 as artificial spins, and realized all-to-all coupling between 2048 DOPOs using a measurement-feedback scheme.7 We experimentally confirmed that our CIM can find solutions for NP-hard maximum cut problems of a 2000-node complete graph.4 The setup of our CIM is illustrated in Figure 1. A periodically poled lithium niobate (PPLN) waveguide module is placed in a fiber ring cavity, which includes a 1km fiber delay line, an optical bandpass filter, optical couplers, and a fiber stretcher for cavity-phase stabilization. When we inject pump pulses with a wavelength of p into the PPLN waveguide, pulsed spontaneous emission noise begins circulating in the cavity. If we limit the wavelength component to 2 p using the optical bandpass filter, parametric amplification occurs only at signal-idler degeneracy, i.e., where only lights with 0 or phase components Figure 1. The setup of our coherent Ising machine (CIM). The optical bandpass filter and fiber stretcher in the cavity are not shown for conciseness. FPGA: Field-programmable gate array. OPO: Optical parametric oscillator. PPLN: Periodically poled lithium niobate.