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  • Open Access

Fast Mixing of Weakly Interacting Fermionic Systems at Any Temperature

Yu Tong1,2,3,* and Yongtao Zhan4,5,†

  • *Contact author: yu.tong@duke.edu
  • †Contact author: yzhan@caltech.edu
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PRX Quantum 6, 030301 – Published 1 July, 2025

DOI: https://doi.org/10.1103/h1dx-ps5p

Abstract

We study the mixing time of a recently proposed efficiently implementable Lindbladian designed to prepare the Gibbs states in the setting of weakly interacting fermionic systems. We show that at any temperature, the Lindbladian spectral gap for even parity observables is lower bounded by a constant Δ, when the interaction strength (e.g., the on-site interaction strength for the Fermi-Hubbard model) is below a constant threshold Uβ. Both Δ and Uβ are independent of the system size. This leads to a mixing time estimate that is at most linear in the system size, thus showing that the corresponding Gibbs states can be prepared efficiently on quantum computers. Our result also implies exponential decay of correlation in these Gibbs states and efficient learnability of their properties.

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Simulating quantum systems is widely regarded as a leading application of quantum computing. In particular, computing the thermal properties of complex quantum systems is a central challenge in quantum chemistry and condensed-matter physics. Recently, progress in quantum algorithms has led to efficiently simulable dissipative processes that converge to target Gibbs states. This progress opens up new directions for studying quantum systems at thermal equilibrium, but the efficiency of the resulting quantum algorithms relies crucially on the mixing time—how long these processes must run in order to converge.

In this work, we provide asymptotic bounds for the mixing time in the context of weakly interacting fermionic systems. As an immediate consequence, we prove that a quantum algorithm of this type can efficiently prepare the Gibbs states of fermionic quantum systems when the nonquadratic interaction is sufficiently weak. Our main result also enables us to prove correlation decay and efficient learnability of these Gibbs states.

Our work leads to intriguing questions about the classical simulability of quantum systems and the boundary of quantum advantage. Specifically, one may ask whether rigorous results for simulating weakly interacting fermionic systems on classical computers can be obtained, given the good empirical performance of classical algorithms on these systems. On the other hand, by rigorously proving that a general-purpose quantum algorithm works well for this class of quantum systems, we pave the way for exploring their greater utility in more challenging applications.

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PRX Quantum 6, 030301– Published 1 July, 2025
  • Received 7 February 2025
  • Accepted 2 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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