{"paper":{"title":"Bounding Eigenstate Overlap from Hamiltonian Moments: Success Probability Guarantees for Quantum Phase Estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.chem-ph"],"primary_cat":"quant-ph","authors_text":"Artur F. Izmaylov, Junan Lin","submitted_at":"2025-03-15T18:24:12Z","abstract_excerpt":"Estimating the overlap between a prepared state and a target eigenstate is crucial for the efficiency of quantum phase estimation (QPE), since QPE succeeds with probability equal to this overlap. We present a systematically improvable method to compute certified upper and lower bounds on such overlaps using a finite set of Hamiltonian moments. Our approach constructs optimal polynomial upper/lower bounds on an energy-window indicator and evaluates them through linear and semidefinite programs, yielding the tightest bounds consistent with the available moment and spectral-interval information. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.12224","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/2503.12224/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"}