Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Sinha, Savar D., Tong, Yu
Institution: California Institute of Technology
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416068656