{"paper":{"title":"Testing and learning structured quantum Hamiltonians","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","cs.DS"],"primary_cat":"quant-ph","authors_text":"Arkopal Dutt, Francisco Escudero Guti\\'errez, Srinivasan Arunachalam","submitted_at":"2024-10-31T17:54:13Z","abstract_excerpt":"We consider the problems of testing and learning an unknown $n$-qubit Hamiltonian $H$ from queries to its evolution operator $e^{-iHt}$ under the normalized Frobenius norm. We prove:\n  1. Local Hamiltonians: We give a tolerant testing protocol to decide if $H$ is $\\epsilon_1$-close to $k$-local or $\\epsilon_2$-far from $k$-local, with $O(1/(\\epsilon_2-\\epsilon_1)^{4})$ queries, solving open questions posed in a recent work by Bluhm et al. For learning a $k$-local $H$ up to error $\\epsilon$, we give a protocol with query complexity $\\exp(O(k^2+k\\log(1/\\epsilon)))$ independent of $n$, by leverag"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.00082","kind":"arxiv","version":2},"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/2411.00082/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"}