{"paper":{"title":"Lower bounds for the CNOT-complexity of linear reversible operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"S{\\o}ren Fuglede J{\\o}rgensen","submitted_at":"2026-07-24T12:31:18Z","abstract_excerpt":"The CNOT-complexity of an invertible matrix over $\\mathbb{F}_2$ is the minimum number of CNOT gates needed to synthesize the corresponding linear reversible operator. While the maximum CNOT-complexity over all $n \\times n$ matrices is known to be $\\Theta(n^2 / \\log n)$, no explicit family of matrices requiring a superlinear number of CNOT gates is known, and until now the hardest explicitly known family has been the cyclic permutations, with CNOT-complexity $3(n-1)$. We show that lower bounds for the additive complexity of not-necessarily-reversible linear operators can be lifted to the revers"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.22248","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/2607.22248/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"}