Wavelength-division multiplexing optical Ising simulator enabling fully programmable spin couplings and external magnetic fields

Recently various physical systems have been proposed for modeling Ising spin Hamiltonians appealing to solve combinatorial optimization problems with remarkable performance. However, how to implement arbitrary spin-spin interactions is a critical and challenging problem in various kinds of unconventional Ising machines. Here we propose a general gauge transformation scheme to enable arbitrary spin-spin interactions and external magnetic fields as well, by decomposing an Ising Hamiltonian into multiple Mattis-type interactions. Based on this scheme, a wavelength-division multiplexing spatial photonic Ising machine (SPIM) is developed to show the programmable capability of general spin coupling interactions. We exploit the wavelength-division multiplexing SPIM to simulate three spin systems: pm J models, Sherrington-Kirkpatrick models, and only locally connected J1/J2 models and observe the phase transitions among the spin-glass, the ferromagnetic, the paramagnetic and the stripe-antiferr..., , , **These datasets include code as well as experimental data for analyzing the solution of the Max-cut problem.**

## Datasets included:

A) **Experimentally collected data**

1. The three '.mat' files correspond to the experimental data for three graphs. For example, 'ExperimentdataA.mat' corresponds to the experimental data for graph A.
2. In each '.mat' file, for the first row: the first column represents the element values of the interaction **J**, as a 16\*16 matrix; the second column represents the values of the temperature during each annealing process as an array; and the third column is the number of iterations at each temperature; the fourth column represents the plotting index, i.e., the index of run taken from the total 100 experimental runs.
3. In each '.mat' file, the third row shows the experimental results obtained from a complete experiment run. For the third row: the first column is the detected intensity during annealing process as an array; the second column is the Ham...

近来，诸多物理系统被提出用于构建伊辛自旋哈密顿量（Ising spin Hamiltonians）模型，以出色性能求解组合优化问题。然而，在各类非常规伊辛计算机中，实现任意自旋-自旋相互作用仍是一项关键且极具挑战的课题。
本文提出一种通用规范变换方案：通过将伊辛哈密顿量分解为多个马蒂斯型（Mattis-type）相互作用，即可实现任意自旋-自旋相互作用与外磁场。基于该方案，我们研发了波分复用空间光子伊辛机（wavelength-division multiplexing spatial photonic Ising machine, SPIM），以展示通用自旋耦合相互作用的可编程能力。
我们利用该波分复用空间光子伊辛机模拟了三类自旋系统：pm J模型、舍灵顿-柯克帕特里克（Sherrington-Kirkpatrick）模型，以及仅局部连接的J1/J2模型，并观测到自旋玻璃态、铁磁态、顺磁态与条纹反铁磁态……之间的相变。**本数据集包含用于分析最大割（Max-cut）问题求解结果的代码与实验数据。**

## 包含数据集：
A) **实验采集数据**
1. 三个.mat格式文件分别对应三类图的实验数据。例如，"ExperimentdataA.mat"对应图A的实验数据。
2. 每个.mat文件中，第一行的内容如下：第一列为相互作用项**J**的元素值，为16×16矩阵；第二列为各次退火过程的温度值数组；第三列为各温度下的迭代次数；第四列为绘图索引，即从总计100次实验运行中选取的单次运行的索引。
3. 每个.mat文件的第三行展示了完整实验运行得到的实验结果。对于第三行：第一列为退火过程中检测到的强度值数组；第二列为Ham...