Optical Ising machines with two-body interactions have shown potential in solving combinatorial optimization problems which are extremely hard to solve with digital computers. Yet, some physical systems cannot be properly described by only two-body interactions. Here, we propose and demonstrate a nonlinear optics approach to emulate Ising machines containing many spins (up to a million in the absence of optical imperfections) and with tailored all-to-all two and four-body interactions. Our approach employs a spatial light modulator to encode and control the spins in the form of the binary-phase values, and emulates the high-order interaction with frequency conversion in a nonlinear crystal. By implementing adaptive feedback, the system can be evolved into effective spin configurations that well-approximate the ground-states of Ising Hamiltonians with all-to-all connected many-body interactions. Our technique could serve as a tool to probe complex, many-body physics and give rise to exciting applications in big-data optimization, computing, and analytics.

具有两主体相互作用的光学Ising机已显示出解决组合优化问题的潜力，而组合优化问题是用数字计算机很难解决的。但是，某些物理系统不能仅通过两体相互作用来正确描述。在这里，我们提出并演示了一种非线性光学方法，用于模拟包含许多自旋（在没有光学缺陷的情况下，最多可旋转一百万次）并且具有量身定制的所有两个和四个主体相互作用的Ising机器。我们的方法采用空间光调制器以二进制相位值的形式编码和控制自旋，并在非线性晶体中模拟具有频率转换的高阶相互作用。通过实施自适应反馈，该系统可以演化为有效的自旋配置，可以很好地近似伊辛·哈密顿人的基态，并具有所有对所有连接的多体相互作用。我们的技术可以用作探测复杂的多体物理的工具，并在大数据优化，计算和分析中引起令人兴奋的应用程序。