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}
}
  • Matthew Amy, Jianxin Chen, Neil J. Ross
  • Published in QPL 2016
  • Computer Science, Physics, Mathematics
  • CoRR
  • 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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