



01044nas a2200133   4500008004100000245005300041210005000094260001500144520066000159100001700819700001800836700001900854856003700873       2016                        eng d00aA finite presentation of CNOT-dihedral operators0 afinite presentation of CNOTdihedral operators  c2016/12/313 a<p>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.</p>1 aAmy, Matthew1 aChen, Jianxin1 aRoss, Neil, J.  uhttps://arxiv.org/abs/1701.00140