# A finite presentation of CNOT-dihedral operators

@article{Amy2016AFP, title={A finite presentation of CNOT-dihedral operators}, author={Matthew Amy and Jianxin Chen and Neil J. Ross}, journal={CoRR}, year={2016}, volume={abs/1701.00140}, pages={84-97} }

We give a finite presentation by generators and relations of the 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… CONTINUE READING

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