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Gauge-invariant quantum minimally entangled typical thermal states algorithm with mutually unbiased physical bases for Z2 lattice gauge theories at finite temperature and density

Reita Maeno*

  • *Contact author: maeno-reita916@g.ecc.u-tokyo.ac.jp
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Phys. Rev. Research 8, 033306 – Published 14 September, 2026

DOI: https://doi.org/10.1103/qyj2-97tw

Abstract

In quantum computations of gauge theories at finite temperature and finite density, enforcing Gauss's law for all states contributing to the thermal ensemble is a nontrivial challenge. In this work, we adapt the quantum minimally entangled typical thermal states (QMETTS) algorithm to Z2 gauge-constrained systems and propose a method for computing finite-temperature and finite-density expectation values without eliminating redundant gauge-field degrees of freedom. In QMETTS, the thermal ensemble is sampled via a Markov chain of pure states generated by imaginary-time evolution and projective measurements. To preserve gauge invariance while maintaining efficient sampling, we introduce measurement bases that are gauge invariant and mutually unbiased within the physical subspace. We show that such measurement bases can be constructed efficiently for Z2 lattice gauge theories in arbitrary spatial dimensions and arbitrary boundary conditions by exploiting the correspondence between Z2 lattice gauge theories and the stabilizer formalism. Furthermore, since expectation-value estimation on quantum hardware is inherently affected by shot noise, we explicitly incorporate shot noise into the analysis. By formulating a finite-shot version of QMETTS, we show that the resulting estimator remains unbiased and that using one observable-measurement shot per sampled state is nearly optimal in terms of variance when the total number of circuit executions used to generate the Markov chain and measure observables is fixed. This result indicates that it is often more efficient to generate more QMETTS samples than to accurately estimate the expectation value for each individual pure state. We validate the proposed method numerically in a (1+1)-dimensional Z2 lattice gauge theory coupled to staggered fermions. Our results provide a gauge-invariant sampling framework for finite-temperature and finite-density quantum algorithms for lattice gauge theories.

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Phys. Rev. Research 8, 033306– Published 14 September, 2026
  • Received 25 May 2026
  • Accepted 13 August 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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