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  • Open Access

Efficient Quantum Gibbs Sampling with Local Circuits

Dominik Hahn1,2,*, Ryan Sweke3,4,5,6, Abhinav Deshpande3, and Oles Shtanko2,†

  • *Contact author: dominik.hahn@ox.ac.uk
  • †Contact author: oles.shtanko@ibm.com
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PRX Quantum 7, 020314 – Published 23 April, 2026

DOI: https://doi.org/10.1103/m5zb-z4nn

Abstract

The problem of simulating the thermal behavior of quantum systems remains a central open challenge in quantum computing. Unlike well-established quantum algorithms for unitary dynamics, provably efficient algorithms for preparing thermal states—crucial for probing equilibrium behavior—became available only recently with breakthrough algorithms based on the simulation of well-designed dissipative processes, a quantum-analog to Markov chain Monte Carlo algorithms. We show a way to implement these algorithms avoiding expensive block encoding and relying only on dense local circuits, akin to Hamiltonian simulation. Specifically, our method leverages spatial truncation and Trotterization of exact quasilocal dissipative processes. We rigorously prove that the approximations we use have little effect on rapid mixing at high temperatures and allow convergence to the thermal state with small bounded error. Moreover, we accompany our analytical results with numerical simulations that show that this method, unlike previously thought, is within the reach of current generation of quantum hardware. These results provide the first provably efficient quantum thermalization protocol implementable on near-term quantum devices, offering a concrete path toward practical simulation of equilibrium quantum phenomena.

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Popular Summary

Simulating quantum Gibbs states is notoriously hard for classical computers—and not always easy for quantum ones either. Nevertheless, when it is feasible, the task likely can be performed with the emerging family of quantum Markov chain Monte Carlo (qMCMC) algorithms, which prepare Gibbs states through quasilocal dissipative dynamics. However, this quasilocality still remains a key barrier to implementation on near-term devices. We close this gap by introducing an efficient method to truncate and transpile qMCMC algorithms into fully local quantum circuits. Our results demonstrate compatibility with current quantum hardware, opening the door to long-sought applications in quantum statistical mechanics.

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PRX Quantum 7, 020314– Published 23 April, 2026
  • Received 30 June 2025
  • Revised 13 January 2026
  • Accepted 17 March 2026
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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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