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A finite presentation of CNOT-dihedral operators

Abstract

We give a finite presentation by generators and relations of unitary operators expressible over the CNOT, T, X gate set, also known as CNOT-dihedral operators. To this end, we introduce a notion of normal form for CNOT-dihedral circuits and prove that every CNOT-dihedral operator admits a unique normal form. Moreover, we show that in the presence of certain structural rules only finitely many circuit identities are required to reduce an arbitrary CNOT-dihedral circuit to its normal form. By appropriately restricting our relations, we obtain a finite presentation of unitary operators expressible over the CNOT, T gate set as a corollary.

Publication Details

Authors
Publication Type
Journal Article
Year of Publication
2016
Journal
arXiv
Date Published
12/2016