Gibbs Sampling gives Quantum Advantage at Constant Temperatures with O(1)-Local Hamiltonians

TL;DR

This paper demonstrates that quantum computers can efficiently sample from Gibbs states of O(1)-local Hamiltonians at constant temperature, maintaining quantum advantage over classical methods even with imperfect measurements.

Contribution

It extends previous results to show quantum advantage for Gibbs states of O(1)-local Hamiltonians at constant temperature, including robustness to measurement imperfections.

Findings

Quantum advantage persists for 5-local Hamiltonians on 3D lattices.

Classical hardness-of-sampling is maintained at constant temperature.

Sampling remains robust despite imperfect measurements.

Abstract

Sampling from Gibbs states -- states corresponding to system in thermal equilibrium -- has recently been shown to be a task for which quantum computers are expected to achieve super-polynomial speed-up compared to classical computers, provided the locality of the Hamiltonian increases with the system size (Bergamaschi et al., arXiv: 2404.14639). We extend these results to show that this quantum advantage still occurs for Gibbs states of Hamiltonians with O(1)-local interactions at constant temperature by showing classical hardness-of-sampling and demonstrating such Gibbs states can be prepared efficiently using a quantum computer. In particular, we show hardness-of-sampling is maintained even for 5-local Hamiltonians on a 3D lattice. We additionally show that the hardness-of-sampling is robust when we are only able to make imperfect measurements.