Generators and Relations for Real Stabilizer Operators

Justin Makary
(Dalhousie University)
Neil J. Ross
(Dalhousie University)
Peter Selinger
(Dalhousie University)

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.

In Chris Heunen and Miriam Backens: Proceedings 18th International Conference on Quantum Physics and Logic (QPL 2021), Gdansk, Poland, and online, 7-11 June 2021, Electronic Proceedings in Theoretical Computer Science 343, pp. 14–36.
Published: 18th September 2021.

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