Programmable optical differential Ising machines

Optical Ising machines provide a hardware approach for combinatorial optimization and physical-system emulation, but their scalability is limited by redundant matrix operations and analog modulation precision. Here we show a programmable optical differential Ising machine that directly evaluates Hamiltonian changes rather than the full Hamiltonian. Numerical simulations from 60 to 2000 spins show that 6-bit analog–digital conversion and 5-bit digital–analog conversion are sufficient to obtain solution quality close to high-precision digital references, with a phase-error tolerance of about 0.3–0.4 rad. Experiments on a dual-channel fiber-optic prototype reproduce phase-transition behavior in representative Ising models and solve MaxCut benchmarks through a multi-spin parallel tempering (PT) routine. The system reaches the best-known cut for the 800-spin G1 instance and 99.66% of the best-known cut for the 2000-spin G22 instance within fewer than 500 PT iterations. These results establish differential optical feedback as a route for scalable Ising-model computation. The authors develop a programmable optical differential Ising machine that directly computes Hamiltonian variations to eliminate redundant full-matrix calculations for Ising combinatorial optimization and physical system emulation. Simulations and fiber-optic prototype experiments verify that the hardware only requires 5-bit DACs and 6-bit ADCs with a phase-error tolerance of 0.3–0.4 rad, and it yields optimal MaxCut solutions for the 800-spin benchmark and 99.66% of the known optimum for the 2000-spin instance via multi-spin parallel tempering.