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arXiv · 2109.05655

Generators and Relations for Real Stabilizer Operators

Justin Makary·Neil J. Ross·Peter Selinger
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Abstract

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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Justin Makary, Neil J. Ross, Peter Selinger. 2021-09-13. Generators and Relations for Real Stabilizer Operators. https://doi.org/10.4204/eptcs.343.2

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