In situ differentiable complex-field calibration for high-fidelity Hamiltonian evaluation in spatial photonic Ising machines
Phys. Rev. Applied 26, 034077 – Published 30 September, 2026
DOI: https://doi.org/10.1103/dgf5-pcc1
Abstract
Spatial photonic Ising machines (SPIMs) exploit free-space Fourier propagation to perform parallel optical computation of spin-spin couplings, providing a promising platform for large-scale combinatorial optimization. However, their fidelity is limited by intrinsic optical aberrations and nonuniform incident-field amplitudes, which distort the mapping between the modulating plane and the corresponding Fourier plane, thereby degrading energy resolution and annealing reliability. In this work, we propose an in situ differentiable complex-field calibration framework. Based on paired random phase patterns and Fourier-plane captured intensity distributions, the implicit system error can be numerically backpropagated to an exact complex-amplitude distribution on a pixel sampling grid. In single-spin-flip tests, the typical relative deviation between the measured energy and the theoretical value is reduced to 1.31%. Under general SPIM annealing settings, the coefficient of determination between the experimental and theoretical Hamiltonian reaches 0.9998. This work provides a plug-and-play in situ calibration route toward ultrahigh Hamiltonian-evaluation fidelity in more complicated SPIMs.
