Neural network representation of quantum systems
arXiv:2403.11420 · doi:10.1088/2632-2153/ad81ac
Abstract
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.
arXiv comment24 pages, 6 figures
References in corpus (10)
- Solving the Quantum Many-Body Problem with Artificial Neural Networks
- Constructing exact representations of quantum many-body systems with deep neural networks
- Deep Learning and AdS/CFT
- Machine Learning Spatial Geometry from Entanglement Features
- Neural Networks and Quantum Field Theory
- Deep Learning and Holographic QCD
- AdS/CFT as a deep Boltzmann machine
- A Note on (Spin-) Coherent-State Path Integral
- Functional methods for disordered neural networks
- Unification of Symmetries Inside Neural Networks: Transformer, Feedforward and Neural ODE