The maximum independent set (MIS) problem is an optimization problem in graph theory and is related to various applications such as network design and resource allocation. Here we report that a coherent Ising machine based on a network of optical parametric oscillators can find large independent sets in graphs that consist of thousands of nodes faster than simulated annealing implemented many-core CPU.
The coherent Ising machine (CIM) is a network of optical parametric oscillators (OPOs) that solves for the ground state of Ising problems through OPO bifurcation dynamics. Here, we present experimental results comparing the performance of the CIM to quantum annealers (QAs) on two classes of NP-hard optimization problems: ground state calculation of the Sherrington-Kirkpatrick (SK) model and MAX-CUT. While the two machines perform comparably on sparsely-connected problems such as cubic MAX-CUT, on problems with dense connectivity, the QA shows an exponential performance penalty relative to CIMs. We attribute this to the embedding overhead required to map dense problems onto the sparse hardware architecture of the QA, a problem that can be overcome in photonic architectures such as the CIM.
We describe a large-scale degenerate optical parametric oscillator (DOPO) network for a coherent Ising machine that solves combinatorial optimization problems. By pumping a fiber-based phase-sensitive amplifier placed in a 1-km fiber cavity at a 2-GHz repetition frequency, we generated more than 10,000 DOPOs multiplexed in the time domain. We confirmed that the DOPO phases were discretized to {0, π} indicating that they could be used as stable artificial spins. We also implemented a one-dimensional Ising model by optically coupling adjacent DOPOs, and confirmed that the DOPOs well simulated the behavior of low-temperature spins.
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