Optimising Clifford Circuits with Quantomatic

@inproceedings{Fagan2019OptimisingCC,
  title={Optimising Clifford Circuits with Quantomatic},
  author={Andrew Fagan and Ross Duncan},
  booktitle={QPL},
  year={2019}
}
We present a system of equations between Clifford circuits, all derivable in the ZX-calculus, and formalised as rewrite rules in the Quantomatic proof assistant. By combining these rules with some non-trivial simplification procedures defined in the Quantomatic tactic language, we demonstrate the use of Quantomatic as a circuit optimisation tool. We prove that the system always reduces Clifford circuits of one or two qubits to their minimal form, and give numerical results demonstrating its… 
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