Deep autoregressive models for the efficient variational simulation of many-body quantum systems

By Or Sharir, Yoav Levine, Noam Wies, Giuseppe Carleo, Amnon Shashua. 2019

252 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry, Statistical and Nonlinear Physics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Andrea Pagnani
2. Martin Weigt
3. Francesco Zamponi

In Materials Chemistry

1. Andrea Pagnani
2. Martin Weigt
3. Francesco Zamponi
4. Pierfrancesco Urbani
5. Giorgio Parisi
6. Silvio Franz

In Statistical and Nonlinear Physics

1. Yoav Levine
2. Andrea Pagnani
3. Martin Weigt
4. Francesco Zamponi
5. Amnon Shashua
6. Noam Wies

Citations in the corpus

• Efficient generative modeling of protein sequences using simple autoregressive models (2021, methodology): “In this work, we choose the following parameterization, previously used in the context of statistical mechanics of classical [60] and quantum [47] systems:”
• Which transformer architecture fits my data? A vocabulary bottleneck in self-attention (2021, background): “, 2018a), and tied to quantum entanglement measures for proving that these deep learning architectures can model elaborate many-body quantum particle correlations (Levine et al., 2018b; 2019; Sharir et al., 2020).”