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arXiv · 2408.01516

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

Joel Rajakumar·James D. Watson
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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.

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Joel Rajakumar, James D. Watson. 2024-08-02. Gibbs Sampling gives Quantum Advantage at Constant Temperatures with O(1)-Local Hamiltonians. https://doi.org/10.22331/q-2026-01-22-1981

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