Markov chain Monte Carlo

Quantum mechanics

Quantum Monte Carlo

Bayesian probability

Statistics

Markov chain

Computer science

Mathematical optimization

Observable

Filter (signal processing)

Statistical physics

Physics

Mathematics

Sampling (signal processing)

Artificial intelligence

Quantum

Monte Carlo method

Artificial neural network

Quantum state

Machine learning

Computer vision

Physical Review Letters

Artificial neural networks were recently shown to be an efficient representation of highly entangled many-body quantum states. In practical applications, neural-network states inherit numerical schemes used in variational Monte Carlo method, most notably the use of Markov-chain Monte Carlo (MCMC) sampling to estimate quantum expectations. The local stochastic sampling in MCMC caps the potential advantages of neural networks in two ways: (i) Its intrinsic computational cost sets stringent practical limits on the width and depth of the networks, and therefore limits their expressive capacity; (ii) its difficulty in generating precise and uncorrelated samples can result in estimations of observables that are very far from their true value. Inspired by the state-of-the-art generative models used in machine learning, we propose a specialized neural-network architecture that supports efficient and exact sampling, completely circumventing the need for Markov-chain sampling. We demonstrate our approach for two-dimensional interacting spin models, showcasing the ability to obtain accurate results on larger system sizes than those currently accessible to neural-network quantum states.

Deep Autoregressive Models for the Efficient Variational Simulation of Many-Body Quantum Systems