Posted

Savar D. Sinha, Yu Tong (Sep 10 2025).
Abstract: We consider the problem of learning an MM-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 MM-sparse Hamiltonian learning to O~(M/ϵ)\widetilde{\mathcal{O}}(M/\epsilon), where ϵ\epsilon denotes the \ell^{\infty} error, achieving an improvement by a factor of MM (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.

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