{"paper":{"title":"A note on polynomial-time tolerant testing stabilizer states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS"],"primary_cat":"quant-ph","authors_text":"Arkopal Dutt, Sergey Bravyi, Srinivasan Arunachalam","submitted_at":"2024-10-29T16:49:33Z","abstract_excerpt":"We show an improved inverse theorem for the Gowers-$3$ norm of $n$-qubit quantum states $|\\psi\\rangle$ which states that: for every $\\gamma\\geq 0$, if the $\\textsf{Gowers}(|\\psi \\rangle,3)^8 \\geq \\gamma$ then the stabilizer fidelity of $|\\psi\\rangle$ is at least $\\gamma^C$ for some constant $C>1$. This implies a constant-sample polynomial-time tolerant testing algorithm for stabilizer states which accepts if an unknown state is $\\varepsilon_1$-close to a stabilizer state in fidelity and rejects when $|\\psi\\rangle$ is $\\varepsilon_2 \\leq \\varepsilon_1^C$-far from all stabilizer states, promised"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.22220","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/2410.22220/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"}