Polynomial-time quantum Gibbs sampling for the weak and strong coupling regime of the Fermi-Hubbard model at any temperature

Nature Communications, vol. 16, pp. 10736

Abstract

Quantum computers hold the potential to revolutionise the simulation of quantum many-body systems, with profound implications for fundamental physics and applications like molecular and material design. However, demonstrating quantum advantage in simulating quantum systems of practical relevance remains a significant challenge. In this work, we introduce a quantum algorithm for preparing Gibbs states of interacting fermions on a lattice with provable polynomial resource requirements. Our approach builds on recent progress in theoretical computer science that extends classical Markov chain Monte Carlo methods to the quantum domain. We derive a bound on the mixing time for quantum Gibbs state preparation by showing that the generator of the quantum Markovian evolution is gapped at any temperature up to a maximal interaction strength. This enables the efficient preparation of low-temperature states of weakly interacting fermions and the calculation of their free energy. We present exact numerical simulations for small system sizes that support our results and identify well-suited algorithmic choices for simulating the Fermi-Hubbard model beyond our rigorous guarantees.

Authors 3

1. Štěpán Šmíd corresponding

   Imperial College London

   Affiliation as printed

   Department of Computing, Imperial College London, London, UK. s.smid23@imperial.ac.uk

   Department of Computing, Imperial College London, London, UK

2. Mario Berta Aachen Institute for Quantum Information

   RWTH Aachen University · Imperial College London

   Affiliation as printed

   Department of Computing, Imperial College London, London, UK

   Institute for Quantum Information, RWTH Aachen University, Aachen, Germany

3. Roberto Bondesan

   Imperial College London

   Affiliation as printed

   Department of Computing, Imperial College London, London, UK