Recently, spatial photonic Ising machines (SPIM) have been demonstrated to compute the minima of Hamiltonians for large-scale spin systems. Here we propose to implement an antiferromagnetic model through optoelectronic correlation computing with SPIM. Also we exploit the gauge transformation which enables encoding the spins and the interaction strengths in a single phase-only spatial light modulator. With a simple setup, we experimentally show the ground state search of an antiferromagnetic model with $40000$ spins in number-partitioning problem. Thus such an optoelectronic computing exhibits great programmability and scalability for the practical applications of studying statistical systems and combinatorial optimization problems.

中文翻译：

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反铁磁空间光子伊辛机的光电相关计算

最近，空间光子伊辛机（SPIM）已被证明可以为大规模自旋系统计算哈密顿量的最小值。在这里，我们建议通过使用SPIM进行光电相关计算来实现反铁磁模型。我们还利用轨距变换，该变换可以在仅单个相位的空间光调制器中对自旋和相互作用强度进行编码。通过简单的设置，我们实验性地显示了在数字分配问题中自旋为$ 40000 $的反铁磁模型的基态搜索。因此，这种光电子计算对于研究统计系统和组合优化问题的实际应用表现出很大的可编程性和可扩展性。