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