Simulating Thermal Properties of Bose-Hubbard Models on a Quantum Computer

TL;DR

This paper develops a rigorous framework for Gibbs sampling of bosonic many-body systems on quantum computers, demonstrating efficient thermal state preparation for Bose-Hubbard models with potential quantum advantages.

Contribution

It introduces the first general rigorous Gibbs sampling method for bosonic systems, showing efficient thermal state preparation via gapped dissipative generators.

Findings

Bosonic models admit gapped dissipative generators enabling efficient thermal state preparation.

The spectral gap remains positive for Bose-Hubbard Hamiltonians, ensuring exponential convergence.

The approach applies to infinite-dimensional systems, advancing quantum simulation capabilities.

Abstract

While recent advances have established efficient quantum algorithms for preparing Gibbs states of finite-dimensional systems, comparable complexity results for bosonic and other infinite-dimensional models remain unexplored. We introduce the first general rigorous Gibbs sampling framework for bosonic many-body systems, showing that physically relevant bosonic models admit gapped dissipative generators, enabling efficient preparation of thermal states. Although our results hold for broad classes of models, we illustrate them using Bose-Hubbard Hamiltonians, both within and beyond the mean-field regime. In both cases, we show that the associated dissipative generators maintain a positive spectral gap, thereby implying exponential convergence to the thermal state. Our argument in the multi-mode case is based on a finite-rank reduction of the dissipative dynamics, which allows us to control the generator via compact perturbations and deduce the discreteness of the spectrum and the stability of the gap. We apply our results to provide efficient preparation of the corresponding Gibbs state on qubit hardware, and by that a quantum algorithm to compute thermal properties of the associated model. This provides the first mathematically controlled route to Gibbs sampling in infinite-dimensional systems, with implications for quantum simulation, thermalization, and many-body complexity, where quantum advantages may arise.