Exact representations of many body interactions with RBM neural networks

Abstract

Restricted Boltzmann Machines (RBM) are simple statistical models defined on a bipartite graph which have been successfully used in studying more complicated many-body systems, both classical and quantum. In this work, we exploit the representation power of RBMs to provide an exact decomposition of many-body contact interactions into one-body operators coupled to discrete auxiliary fields. This construction generalizes the well known Hirsch's transform used for the Hubbard model to more complicated theories such as Pionless EFT in nuclear physics, which we analyze in detail. We also discuss possible applications of our mapping for quantum annealing applications and conclude with some implications for RBM parameter optimization through machine learning.

References in corpus (9)

• Three-body forces: From cold atoms to nuclei
• Self-Learning Monte Carlo Method
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• Local chiral effective field theory interactions and quantum Monte Carlo applications
• Quantum Monte Carlo calculation of the equation of state of neutron matter
• On the construction of model Hamiltonians for adiabatic quantum computation and its application to finding low energy conformations of lattice protein models
• Neural Networks for Modeling and Control of Particle Accelerators
• Ground-state properties of unitary bosons: from clusters to matter
• Sampling General N-Body Interactions with Auxiliary Fields

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• Machine-learning approach to finite-size effects in systems with strongly interacting fermions
• Neural-network Quantum States for Spin-1 systems: spin-basis and parameterization effects on compactness of representations
• Exact block encoding of imaginary time evolution with universal quantum neural networks
• Investigation of bi-particle states in gate-array-controlled quantum-dot systems aided by machine learning techniques
• Neural Network Statistical Mechanics
• Seeding neural network quantum states with tensor network states
• Efficient bit encoding of neural networks for Fock states
• Neural quantum states for entanglement depth certification from randomized Pauli measurements
• Adaptive Latent Space Tuning for Non-Stationary Distributions