{"paper":{"title":"Simpler Presentations for Many Fragments of Quantum Circuits","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Treating wire permutations as structural yields minimal rewrite rules for six near-Clifford quantum circuit fragments.","cross_cats":["cs.LO"],"primary_cat":"quant-ph","authors_text":"Colin Blake","submitted_at":"2026-02-10T15:17:24Z","abstract_excerpt":"Equational reasoning is central to quantum circuit optimisation and verification: one replaces subcircuits by provably equivalent ones using a fixed set of rewrite rules viewed as equations. A finite rule set is most informative when it separates the genuine algebra of a circuit fragment from the structural treatment of wires. This paper gives six near-Clifford fragments a common PROP treatment, where wire permutations are structural: qubit Clifford, real Clifford, Clifford+T (up to two qubits), Clifford+CS (up to three qubits), CNOT-dihedral, and qutrit Clifford. Starting from prior completen"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The resulting presentations are minimal in all arities for qubit Clifford, real Clifford, and CNOT-dihedral, minimal in bounded ranges for the remaining fragments, and comparable by one transfer-and-separation pattern.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the prior completeness theorems can be transferred into the PROP setting while preserving completeness and allowing removal of non-structural rules without losing any equivalences.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Simpler minimal rule sets are derived for qubit Clifford, real Clifford, Clifford+T (up to two qubits), Clifford+CS (up to three qubits), CNOT-dihedral, and qutrit Clifford by transferring completeness from prior theorems and removing redundant non-structural rules.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Treating wire permutations as structural yields minimal rewrite rules for six near-Clifford quantum circuit fragments.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d7e0ebc33c9502db0c8bc977500aac82a45b34f3e8637efa4331ffb0dbb86aa2"},"source":{"id":"2602.09874","kind":"arxiv","version":2},"verdict":{"id":"091d7c7c-6705-427a-aeec-64a46b56a23c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T05:15:01.723984Z","strongest_claim":"The resulting presentations are minimal in all arities for qubit Clifford, real Clifford, and CNOT-dihedral, minimal in bounded ranges for the remaining fragments, and comparable by one transfer-and-separation pattern.","one_line_summary":"Simpler minimal rule sets are derived for qubit Clifford, real Clifford, Clifford+T (up to two qubits), Clifford+CS (up to three qubits), CNOT-dihedral, and qutrit Clifford by transferring completeness from prior theorems and removing redundant non-structural rules.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the prior completeness theorems can be transferred into the PROP setting while preserving completeness and allowing removal of non-structural rules without losing any equivalences.","pith_extraction_headline":"Treating wire permutations as structural yields minimal rewrite rules for six near-Clifford quantum circuit fragments."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.09874/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"}