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

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 bergamaschi2024sample. 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.