



@article {1925,
	title = {A finite presentation of CNOT-dihedral operators},
	year = {2016},
	month = {2016/12/31},
	abstract = {<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>},
	url = {https://arxiv.org/abs/1701.00140},
	author = {Matthew Amy and Jianxin Chen and Neil J. Ross}
}
