Solving Quantum Statistical Mechanics with Variational Autoregressive Networks and Quantum Circuits

Abstract

We extend the ability of unitary quantum circuits by interfacing it with classical autoregressive neural networks. The combined model parametrizes a variational density matrix as a classical mixture of quantum pure states, where the autoregressive network generates bitstring samples as input states to the quantum circuit. We devise an efficient variational algorithm to jointly optimize the classical neural network and the quantum circuit for quantum statistical mechanics problems. One can obtain thermal observables such as the variational free energy, entropy, and specific heat. As a by product, the algorithm also gives access to low energy excitation states. We demonstrate applications to thermal properties and excitation spectra of the quantum Ising model with resources that are feasible on near-term quantum computers.

7 pages, 5 figures, code: https://github.com/wangleiphy/BetaVQE.jl

References in corpus (7)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• MADE: Masked Autoencoder for Distribution Estimation
• Quantum circuits for strongly correlated quantum systems
• Tree Tensor Networks for Generative Modeling
• Quantum Hamiltonian-Based Models and the Variational Quantum Thermalizer Algorithm
• Non-unitary operations for ground-state calculations in near term quantum computers
• Inferring the quantum density matrix with machine learning