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

Area of Science:

• Quantum mechanics
• Machine learning
• Computational physics

Background:

• Artificial neural networks (ANNs) are effective for representing complex quantum states.
• Current methods use Markov-chain Monte Carlo (MCMC) sampling, which has computational and accuracy limitations.
• MCMC's local sampling restricts ANN depth/width and can yield imprecise results.

Purpose of the Study:

• To develop a new neural network architecture for quantum states.
• To enable efficient and exact sampling, bypassing MCMC.
• To improve the accuracy and scalability of quantum state representations.

Main Methods:

• Proposed a specialized neural network architecture inspired by generative models.
• Implemented efficient and exact sampling techniques, avoiding Markov-chain Monte Carlo.
• Applied the method to two-dimensional interacting spin models.

Main Results:

• Demonstrated accurate results for quantum simulations.
• Achieved accurate results on larger system sizes than previously possible with ANNs.
• Successfully circumvented the need for MCMC sampling.

Conclusions:

• The proposed neural network architecture offers a more efficient and accurate approach to representing quantum states.
• This method overcomes key limitations of MCMC sampling in quantum many-body problems.
• Enables the study of larger and more complex quantum systems.