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Quantum finite-temperature Lanczos method

Gian Gentinetta1,2,*, Friederike Metz1,2, William Kirby3, and Giuseppe Carleo1,2

  • *Contact author: gian.gentinetta@epfl.ch
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Phys. Rev. Research 8, 023285 – Published 11 June, 2026

DOI: https://doi.org/10.1103/f3q5-cm1n

Abstract

The computation of thermal properties of quantum many-body systems is a central challenge in our understanding of quantum mechanics. We introduce the quantum finite-temperature Lanczos method (QFTLM), which extends the finite-temperature Lanczos method to quantum computers by combining real-time quantum Krylov methods with efficient preparation of typical states for trace estimation. This approach enables the computation of thermal expectation values while avoiding the exponential scaling inherent to classical exact simulation techniques. Numerical experiments on the transverse-field Ising model show that QFTLM can reproduce thermal observables over a wide temperature range. We further analyze the influence of Krylov dimension, number of trace-estimator states, and Trotter error, and show that suitable regularization is essential for robustness in noisy settings. These results establish QFTLM as a promising framework for finite-temperature quantum simulation.

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Phys. Rev. Research 8, 023285– Published 11 June, 2026
  • Received 31 March 2026
  • Accepted 19 May 2026
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