Generators and Relations for Real Stabilizer Operators
arXiv:2109.05655 · doi:10.4204/EPTCS.343.2
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.
arXiv commentIn Proceedings QPL 2021, arXiv:2109.04886
References in corpus (10)
- Improved Simulation of Stabilizer Circuits
- The ZX-calculus is complete for stabilizer quantum mechanics
- Hadamard-free circuits expose the structure of the Clifford group
- ZH: A Complete Graphical Calculus for Quantum Computations Involving Classical Non-linearity
- Pivoting makes the ZX-calculus complete for real stabilizers
- Real Randomized Benchmarking
- Generators and relations for n-qubit Clifford operators
- Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits
- A ZX-Calculus with Triangles for Toffoli-Hadamard, Clifford+T, and Beyond
- A Finite Presentation of CNOT-Dihedral Operators