Generators and Relations for Real Stabilizers
Makary, Justin J.
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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 Clifford circuit to its normal form. This yields a presentation by generators and relations of the strict spatial monoidal category of real stabilizer operators.