Abstract

The spatial photonic Ising machine has achieved remarkable advancements in solving combinatorial optimization problems. However, it still remains a huge challenge to flexibly map an arbitrary problem to the Ising model. In this paper, we propose a general spatial photonic Ising machine based on the interaction matrix eigendecomposition method. The arbitrary interaction matrix can be configured in the two-dimensional Fourier transformation based spatial photonic Ising model by using values generated by matrix eigendecomposition. The error in the structural representation of the Hamiltonian decreases substantially with the growing number of eigenvalues utilized to form the Ising machine. In combination with the optimization algorithm, as low as ${\sim}65\%$ of the eigenvalues are required by intensity modulation to guarantee the best probability of optimal solution for a 20-vertex graph Max-cut problem, and this percentage decreases to below ${\sim}20\%$ for near-zero probability. The 4-spin experiments and error analysis demonstrate the Hamiltonian linear mapping and ergodic optimization. Our work provides a viable approach for spatial photonic Ising machines to solve arbitrary combinatorial optimization problems with the help of the multi-dimensional optical property.

© 2024 Optica Publishing Group

Adiabatic evolution on a spatial-photonic Ising machine

Davide Pierangeli, Giulia Marcucci, and Claudio Conti
Optica 7(11) 1535-1543 (2020)

Spatial-photonic Ising machine by space-division multiplexing with physically tunable coefficients of a multi-component model

Takumi Sakabe, Suguru Shimomura, Yusuke Ogura, Ken-ichi Okubo, Hiroshi Yamashita, Hideyuki Suzuki, and Jun Tanida
Opt. Express 31(26) 44127-44138 (2023)

Accelerating recurrent Ising machines in photonic integrated circuits

Mihika Prabhu, Charles Roques-Carmes, Yichen Shen, Nicholas Harris, Li Jing, Jacques Carolan, Ryan Hamerly, Tom Baehr-Jones, Michael Hochberg, Vladimir Čeperić, John D. Joannopoulos, Dirk R. Englund, and Marin Soljačić
Optica 7(5) 551-558 (2020)

Quadrature photonic spatial Ising machine

Wenchen Sun, Wenjia Zhang, Yuanyuan Liu, Qingwen Liu, and Zuyuan He
Opt. Lett. 47(6) 1498-1501 (2022)

Accuracy-enhanced coherent Ising machine using the quantum adiabatic theorem

Lin Li, Hongjun Liu, Nan Huang, and Zhaolu Wang
Opt. Express 29(12) 18530-18539 (2021)