Network of time-multiplexed optical parametric oscillators as a coherent Ising machine

Finding the ground states of the Ising Hamiltonian(1) maps to various combinatorial optimization problems in biology, medicine, wireless communications, artificial intelligence and social network. So far, no efficient classical and quantum algorithm is known for these problems and intensive research is focused on creating physical systems-Ising machines-capable of finding the absolute or approximate ground states of the Ising Hamiltonian(2-6). Here, we report an Ising machine using a network of degenerate optical parametric oscillators (OPOs). Spins are represented with above-threshold binary phases of the OPOs and the Ising couplings are realized by mutual injections(7). The network is implemented in a single OPO ring cavity with multiple trains of femtosecond pulses and configurable mutual couplings, and operates at room temperature. We programmed a small non-deterministic polynomial time-hard problem on a 4-OPO sing machine and in 1,000 runs no computational error was detected.