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LOv-Calculus: A Graphical Language for Linear Optical Quantum Circuits
A. Cl'ement, Nicolas Heurtel, Shane Mansfield, S. Perdrix, Benoît Valiron·April 25, 2022·DOI: 10.4230/LIPIcs.MFCS.2022.35
Computer SciencePhysics
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Abstract
We introduce the LO v -calculus, a graphical language for reasoning about linear optical quantum circuits with so-called vacuum state auxiliary inputs. We present the axiomatics of the language and prove its soundness and completeness: two LO v -circuits represent the same quantum process if and only if one can be transformed into the other with the rules of the LO v -calculus. We give a confluent and terminating rewrite system to rewrite any polarisation-preserving LO v -circuit into a unique triangular normal form, inspired by the universal decomposition of Reck et al. (1994) for linear optical quantum circuits. 2012