Neural network representation of quantum systems
This work bridges machine learning and quantum physics by providing a general framework for representing quantum systems as neural networks, which is foundational for potential applications in quantum computing and simulation.
The authors tackled the problem of representing quantum systems using neural networks by developing a novel map that converts a wide class of quantum mechanical systems into neural network form with statistical summation over parameters, based on the universal approximation theorem to generate arbitrary paths in Feynman's path integral, applicable even to interacting systems away from the Gaussian limit.
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.