Gibbs Sampling gives Quantum Advantage at Constant Temperatures with O(1)-Local Hamiltonians
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908791777263616 |
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| author | Rajakumar, Joel Watson, James D. |
| author_facet | Rajakumar, Joel Watson, James D. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01516 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gibbs Sampling gives Quantum Advantage at Constant Temperatures with O(1)-Local Hamiltonians Rajakumar, Joel Watson, James D. Quantum Physics Other Condensed Matter Mathematical Physics 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. |
| title | Gibbs Sampling gives Quantum Advantage at Constant Temperatures with O(1)-Local Hamiltonians |
| topic | Quantum Physics Other Condensed Matter Mathematical Physics |
| url | https://arxiv.org/abs/2408.01516 |