Optimising Clifford Circuits with Quantomatic. Fagan, A. and Duncan, R. Electronic Proceedings in Theoretical Computer Science, 287:85–105, January, 2019. ZSCC: 0000011 arXiv: 1901.10114
Optimising Clifford Circuits with Quantomatic [link]Paper  doi  abstract   bibtex   
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 performance on larger Clifford circuits.
@article{fagan_optimising_2019,
	title = {Optimising {Clifford} {Circuits} with {Quantomatic}},
	volume = {287},
	issn = {2075-2180},
	url = {http://arxiv.org/abs/1901.10114},
	doi = {10/gf8t32},
	abstract = {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 performance on larger Clifford circuits.},
	urldate = {2019-09-26},
	journal = {Electronic Proceedings in Theoretical Computer Science},
	author = {Fagan, Andrew and Duncan, Ross},
	month = jan,
	year = {2019},
	note = {ZSCC: 0000011 
arXiv: 1901.10114},
	pages = {85--105}
}
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