Variational Thermal State Preparation on Digital Quantum Processors Assisted by Matrix Product States

TL;DR

This paper presents a variational method using matrix product states to efficiently prepare thermal states on quantum processors, validated through extensive classical and quantum experiments.

Contribution

It introduces a scalable variational framework combining matrix product states with hardware-efficient ansatz for thermal state preparation in 1D and 2D systems.

Findings

Successfully prepared Gibbs states for 1D systems with up to 30 sites.

Prepared 2D Gibbs states on 6x6 lattices using up to 44 qubits.

Demonstrated practical implementation on a 156-qubit IBM quantum processor.

Abstract

The preparation of quantum Gibbs states at finite temperatures is a cornerstone of quantum computation, enabling applications in quantum simulation of many-body systems, machine learning via quantum Boltzmann machines, and optimization through thermal sampling techniques. In this work, we introduce a variational framework that leverages matrix product states for the efficient classical evaluation of the Helmholtz free energy, combining scalable entanglement entropy computation with a hardware efficient ansatz to accurately approximate thermal states in one- and two-dimensional systems. We conduct extensive benchmarking on key observables, including energy density, susceptibility, specific heat, and two-point correlations, comparing against exact analytical results for 1D systems and quantum Monte Carlo simulations for 2D lattices across various temperatures and ansatz configurations. Our large-scale numerical simulations demonstrate the capability to prepare high-quality Gibbs states for 1D lattice models with up to 30 sites and 2D systems with up to 6x6 sites, using up to 44 qubits. Finally, we demonstrate the framework's practical viability on a 156-qubit IBM Heron processor by preparing the approximate Gibbs state of a 30-site transverse-field Ising model. Leveraging a combination of error mitigation techniques, we reduce the relative errors in energy and susceptibility measurements by over 50% compared to unmitigated results.