{"paper":{"title":"Improved Hamiltonian learning and sparsity testing through Bell sampling","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Savar D. Sinha, Yu Tong","submitted_at":"2025-09-09T17:18:46Z","abstract_excerpt":"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 $\\widetilde{\\mathcal{O}}(M/\\epsilon)$, where $\\epsilon$ 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 t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07937","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.07937/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}