Polynomial-time quantum Gibbs sampling for the weak and strong coupling regime of the Fermi-Hubbard model at any temperature
File(s)
Published version
Author(s)
Šmíd, Štěpán
Meister, Richard
Berta, Mario
Bondesan, Roberto
Type
Journal Article
Abstract
Quantum computers hold the potential to revolutionise the simulation of quantum many-body systems, with profound implications for fundamental physics and applications like molecular and material design. However, demonstrating quantum advantage in simulating quantum systems of practical relevance remains a significant challenge. In this work, we introduce a quantum algorithm for preparing Gibbs states of interacting fermions on a lattice with provable polynomial resource requirements. Our approach builds on recent progress in theoretical computer science that extends classical Markov chain Monte Carlo methods to the quantum domain. We derive a bound on the mixing time for quantum Gibbs state preparation by showing
that the generator of the quantum Markovian evolution is gapped at any temperature up to a maximal interaction strength. This enables the efficient preparation of low-temperature states of weakly interacting fermions and the
calculation of their free energy. We present exact numerical simulations for small system sizes that support our results and identify well-suited algorithmic
choices for simulating the Fermi-Hubbard model beyond our rigorous guarantees.
that the generator of the quantum Markovian evolution is gapped at any temperature up to a maximal interaction strength. This enables the efficient preparation of low-temperature states of weakly interacting fermions and the
calculation of their free energy. We present exact numerical simulations for small system sizes that support our results and identify well-suited algorithmic
choices for simulating the Fermi-Hubbard model beyond our rigorous guarantees.
Date Issued
2025-11-28
Date Acceptance
2025-10-23
Citation
Nature Communications, 2025, 16
ISSN
2041-1723
Publisher
Nature Portfolio
Journal / Book Title
Nature Communications
Volume
16
Copyright Statement
© The Author(s) 2025 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
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Publication Status
Published
Article Number
10736
Date Publish Online
2025-11-28