{"paper":{"title":"Bounds for Approximation in Total Variation Distance by Quantum Circuits","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"quant-ph","authors_text":"E. Knill","submitted_at":"1995-08-08T23:33:25Z","abstract_excerpt":"It was recently shown that for reasonable notions of approximation of states and functions by quantum circuits, almost all states and functions are exponentially hard to approximate [Knill 1995]. The bounds obtained are asymptotically tight except for the one based on total variation distance (TVD). TVD is the most relevant metric for the performance of a quantum circuit. In this paper we obtain asymptotically tight bounds for TVD. We show that in a natural sense, almost all states are hard to approximate to within a TVD of 2/e-\\epsilon even for exponentially small \\epsilon. The quantity 2/e i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9508007","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/quant-ph/9508007/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"}