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Variational Quantum Algorithms for Gibbs State Preparation

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Numerical Computations: Theory and Algorithms (NUMTA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14478))

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Abstract

Preparing the Gibbs state of an interacting quantum many-body system on noisy intermediate-scale quantum (NISQ) devices is a crucial task for exploring the thermodynamic properties in the quantum regime. It encompasses understanding protocols such as thermalization and out-of-equilibrium thermodynamics, as well as sampling from faithfully prepared Gibbs states could pave the way to providing useful resources for quantum algorithms. Variational quantum algorithms (VQAs) show the most promise in efficiently preparing Gibbs states, however, there are many different approaches that could be applied to effectively determine and prepare Gibbs states on a NISQ computer. In this paper, we provide a concise overview of the algorithms capable of preparing Gibbs states, including joint Hamiltonian evolution of a system–environment coupling, quantum imaginary time evolution, and modern VQAs utilizing the Helmholtz free energy as a cost function, among others. Furthermore, we perform a benchmark of one of the latest variational Gibbs state preparation algorithms, developed by Consiglio et al. [16], by applying it to the spin-1/2 one-dimensional XY model.

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Acknowledgments

MC would like to thank Jacopo Settino, Andrea Giordano, Carlo Mastroianni, Francesco Plastina, Salvatore Lorenzo, Sabrina Maniscalco, John Goold, and Tony J. G. Apollaro. MC acknowledges funding by TESS (Tertiary Education Scholarships Scheme), and project QVAQT (Quantum Variational Algorithms for Quantum Technologies) REP-2022-003 financed by the Malta Council for Science & Technology, for and on behalf of the Foundation for Science and Technology, through the FUSION: R&I Research Excellence Programme.

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  1. Department of Physics, University of Malta, Msida, MSD 2080, Malta

    Mirko Consiglio

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Correspondence to Mirko Consiglio .

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  1. University of Calabria, Rende, Italy

    Yaroslav D. Sergeyev

  2. University of Calabria, Rende, Italy

    Dmitri E. Kvasov

  3. University of Calabria, Rende, Italy

    Annabella Astorino

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Consiglio, M. (2025). Variational Quantum Algorithms for Gibbs State Preparation. In: Sergeyev, Y.D., Kvasov, D.E., Astorino, A. (eds) Numerical Computations: Theory and Algorithms. NUMTA 2023. Lecture Notes in Computer Science, vol 14478. Springer, Cham. https://doi.org/10.1007/978-3-031-81247-7_5

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