It has been proposed that random wide neural networks near Gaussian process are quantum field theories around Gaussian fixed points. In this paper, we provide a novel map with which a wide class of quantum mechanical systems can be cast into the form of a neural network with a statistical summation over network parameters. Our simple idea is to use the universal approximation theorem of neural networks to generate arbitrary paths in the Feynman's path integral. The map can be applied to interacting quantum systems / field theories, even away from the Gaussian limit. Our findings bring machine learning closer to the quantum world.

翻译：已有研究提出，接近高斯过程的随机宽神经网络是围绕高斯不动点的量子场论。本文提供了一种新颖的映射方法，通过该方法可将一大类量子力学系统转化为神经网络形式，并伴有网络参数的统计求和。我们的核心思想是利用神经网络的通用逼近定理，在费曼路径积分中生成任意路径。该映射可应用于相互作用的量子系统/场论，甚至远离高斯极限的情况。本发现使机器学习更接近量子世界。