2026-07-21T15:08:02Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:26356 2026-07-15T06:01:56Z ddc:004 open_access

Simpler Presentations for Many Fragments of Quantum Circuits Blake, Colin Quantum circuits Clifford group equational theories minimality qutrit 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 completeness theorems, we transfer completeness into this setting and remove redundant non-structural rules, then check minimality by separating interpretations tailored to individual axioms; 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Colin Blake 2026 Is Part Of LIPIcs, Volume 378, 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSCD.2026.6 urn:nbn:de:0030-drops-263562 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2026.6 eng https://creativecommons.org/licenses/by/4.0/legalcode