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.

中文翻译：

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真实稳定器算子的生成器和关系

真实稳定算子，也称为真实 Clifford 算子，是由 Hadamard 门、泡利 Z 门和受控 Z 门通过组合和张量积生成的。我们介绍了真实稳定器电路的范式，并表明每个真正的稳定器算子都承认唯一的范式。此外，我们给出了一组有限的关系，足以将任何真实的稳定器电路改写为其正常形式。