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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.07937 |
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Table of 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.