Variational Neural-Network Ansatz for Continuum Quantum Field Theory

Abstract

Physicists dating back to Feynman have lamented the difficulties of applying the variational principle to quantum field theories. In non-relativistic quantum field theories, the challenge is to parameterize and optimize over the infinitely many $n$-particle wave functions comprising the state's Fock space representation. Here we approach this problem by introducing neural-network quantum field states, a deep learning ansatz that enables application of the variational principle to non-relativistic quantum field theories in the continuum. Our ansatz uses the Deep Sets neural network architecture to simultaneously parameterize all of the $n$-particle wave functions comprising a quantum field state. We employ our ansatz to approximate ground states of various field theories, including an inhomogeneous system and a system with long-range interactions, thus demonstrating a powerful new tool for probing quantum field theories.

For a pedagogical talk on this paper, see: youtu.be/rrvZDZMii-0

References in corpus (10)

• Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
• Continuous Matrix Product States for Quantum Fields
• Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems
• Variational neural network ansatz for steady states in open quantum systems
• Constructing neural stationary states for open quantum many-body systems
• NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems
• Machine learning technique to find quantum many-body ground states of bosons on a lattice
• Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas
• Continuous matrix-product states in inhomogeneous systems with long-range interactions
• Neural-Network Quantum States for Periodic Systems in Continuous Space

Cited by in corpus (6)

• Physics-informed neural networks for quantum control
• Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems
• Beyond MP2 initialization for unitary coupled cluster quantum circuits
• Highly efficient nuclear population transfer through physics-informed neural networks
• Holographic Tensor Networks as Tessellations of Geometry
• Variational Neural Network Approach to QFT in the Field Basis