A Finite Presentation of CNOTDihedral Operators
Abstract
We give a finite presentation by generators and relations of the unitary operators expressible over the {CNOT, T, X} gate set, also known as CNOTdihedral operators. To this end, we introduce a notion of normal form for CNOTdihedral circuits and prove that every CNOTdihedral 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 CNOTdihedral 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:

arXiv eprints
 Pub Date:
 December 2016
 DOI:
 10.48550/arXiv.1701.00140
 arXiv:
 arXiv:1701.00140
 Bibcode:
 2017arXiv170100140A
 Keywords:

 Quantum Physics;
 Computer Science  Emerging Technologies;
 Computer Science  Logic in Computer Science
 EPrint:
 In Proceedings QPL 2017, arXiv:1802.09737