Wang Shaomeng, Zhang Wenjia, Ye Xin, He Zuyuan
Appl Opt. 2024 Apr 10;63(11):2973-2980. doi: 10.1364/AO.521061.
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 ∼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 ∼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.
空间光子伊辛机在解决组合优化问题方面取得了显著进展。然而，将任意问题灵活映射到伊辛模型仍然是一个巨大的挑战。在本文中，我们提出了一种基于相互作用矩阵特征分解方法的通用空间光子伊辛机。通过使用矩阵特征分解生成的值，可以在基于二维傅里叶变换的空间光子伊辛模型中配置任意相互作用矩阵。随着用于构成伊辛机的特征值数量的增加，哈密顿量结构表示中的误差大幅降低。结合优化算法，对于一个20顶点图的最大割问题，通过强度调制，低至约65%的特征值就足以保证最优解的最佳概率，而对于接近零的概率，这个百分比降至约20%以下。四自旋实验和误差分析证明了哈密顿量的线性映射和遍历优化。我们的工作为空间光子伊辛机借助多维光学特性解决任意组合优化问题提供了一种可行的方法。
