Improved Hamiltonian learning and sparsity testing through Bell sampling
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909779377520640 |
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| author | Sinha, Savar D. Tong, Yu |
| author_facet | Sinha, Savar D. Tong, Yu |
| contents | We consider the problem of learning an $M$-sparse Hamiltonian and the related problem of Hamiltonian sparsity testing. Through a detailed analysis of Bell sampling, we reduce the total evolution time required by the state-of-the-art algorithm for $M$-sparse Hamiltonian learning to $\widetilde{\mathcal{O}}(M/ε)$, where $ε$ denotes the $\ell^{\infty}$ error, achieving an improvement by a factor of $M$ (ignoring the logarithmic factor) while only requiring access to forward time-evolution. We then establish a connection between Hamiltonian learning and Hamiltonian sparsity testing through Bell sampling, which enables us to propose a Hamiltonian sparsity testing with state-of-the-art total evolution time scaling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07937 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Improved Hamiltonian learning and sparsity testing through Bell sampling Sinha, Savar D. Tong, Yu Quantum Physics We consider the problem of learning an $M$-sparse Hamiltonian and the related problem of Hamiltonian sparsity testing. Through a detailed analysis of Bell sampling, we reduce the total evolution time required by the state-of-the-art algorithm for $M$-sparse Hamiltonian learning to $\widetilde{\mathcal{O}}(M/ε)$, where $ε$ denotes the $\ell^{\infty}$ error, achieving an improvement by a factor of $M$ (ignoring the logarithmic factor) while only requiring access to forward time-evolution. We then establish a connection between Hamiltonian learning and Hamiltonian sparsity testing through Bell sampling, which enables us to propose a Hamiltonian sparsity testing with state-of-the-art total evolution time scaling. |
| title | Improved Hamiltonian learning and sparsity testing through Bell sampling |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2509.07937 |