Generators and Relations for Real Stabilizer Operators

@article{Makary2021GeneratorsAR,
  title={Generators and Relations for Real Stabilizer Operators},
  author={Justin Makary and Neil J. Ross and Peter Selinger},
  journal={ArXiv},
  year={2021},
  volume={abs/2109.05655}
}
Real stabilizer operators, which are also known as real Clifford operators, are generated, through composition and tensor product, by the Hadamard gate, the Pauli Z gate, and the controlled-Z gate. We introduce a normal form for real stabilizer circuits and show that every real stabilizer operator admits a unique normal form. Moreover, we give a finite set of relations that suffice to rewrite any real stabilizer circuit to its normal form. 

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