Deterministic Ground-State Search in a Spatial Photonic Ising Machine by Phase Retrieval
Abstract
A spatial photonic Ising machine (SPIM) solves large-scale combinatorial optimization problems by computing the Ising Hamiltonian through an optical Fourier transform. However, the ground-state search relies on annealing, in which spins are optimized stochastically and sequentially. We propose a ground-state search based on phase retrieval (PR), in which all spins are updated simultaneously and deterministically. Imposing an amplitude constraint in the Fourier plane guides the modulated phase distribution, which encodes the spin configuration, toward the optimal solution. We numerically demonstrate that the proposed scheme reaches the ground state of rank-one Ising Hamiltonians with 104 spins in a single iteration for all trials. Moreover, a radial rearrangement of the amplitudes and an appropriately designed target pattern alleviate search stagnation and improve the optimization of spin configurations. The collective and deterministic spin update by phase retrieval enables a fast ground-state search for large-scale combinatorial optimization.
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BibTeX
@misc{shimomura2026deterministic,
title = {{Deterministic Ground-State Search in a Spatial Photonic Ising Machine by Phase Retrieval}},
author = {Suguru Shimomura and Jun Tanida and Yusuke Ogura},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.16474},
eprint = {2609.16474},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16474},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Deterministic Ground-State Search in a Spatial Photonic Ising Machine by Phase Retrieval
AU - Suguru Shimomura
AU - Jun Tanida
AU - Yusuke Ogura
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2609.16474
UR - https://arxiv.org/abs/2609.16474
AB - A spatial photonic Ising machine (SPIM) solves large-scale combinatorial optimization problems by computing the Ising Hamiltonian through an optical Fourier transform. However, the ground-state search relies on annealing, in which spins are optimized stochastically and sequentially. We propose a ground-state search based on phase retrieval (PR), in which all spins are updated simultaneously and deterministically. Imposing an amplitude constraint in the Fourier plane guides the modulated phase distribution, which encodes the spin configuration, toward the optimal solution. We numerically demonstrate that the proposed scheme reaches the ground state of rank-one Ising Hamiltonians with 10^4 spins in a single iteration for all trials. Moreover, a radial rearrangement of the amplitudes and an appropriately designed target pattern alleviate search stagnation and improve the optimization of spin configurations. The collective and deterministic spin update by phase retrieval enables a fast ground-state search for large-scale combinatorial optimization.
ER -