Polynomial-time quantum Gibbs sampling for the weak and strong coupling regime of the Fermi-Hubbard model at any temperature

Štěpán Šmíd (), Richard Meister, Mario Berta and Roberto Bondesan
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Štěpán Šmíd: Imperial College London, Department of Computing
Richard Meister: Imperial College London, Department of Computing
Mario Berta: Imperial College London, Department of Computing
Roberto Bondesan: Imperial College London, Department of Computing

Nature Communications, 2025, vol. 16, issue 1, 1-8

Abstract: 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.

Date: 2025
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DOI: 10.1038/s41467-025-65765-1

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