Work

Variational neural and tensor network approximations of thermal states

Year: 2025

Type: article

Abstract: We introduce a variational Monte Carlo algorithm for approximating finite-temperature quantum many-body systems, based on the minimization of a modified free energy. This approach directly approximates the state at a fixed temperature, allowing for systematic improvement of the expressiveness without accumulating errors from iterative imaginary-time evolution. We employ a variety of trial states—both tensor networks as well as neural networks—as variational for our numerical optimization. We benchmark and compare different constructions in the above classes, both for one- and two-dimensional problems, with systems made of up to N = 100 spins. Our results demonstrate that while restricted Boltzmann machines show limitations, string bond tensor network states exhibit systematic improvements with increasing bond dimensions and the number of strings.

Source: Physical review. B./Physical review. B

DOI: 10.1103/physrevb.111.075102

Authors: Sirui Lu, Giacomo Giudice, J. Ignacio Cirac

Institutions: Max Planck Institute of Quantum Optics, Munich Center for Quantum Science and Technology

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Funder: Deutsche Forschungsgemeinschaft

Awards: G1768993395, EXC 2111: Munich Center for Quantum Science and Technology (MCQST)