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arXiv · 2204.11787

LOv-Calculus: A Graphical Language for Linear Optical Quantum Circuits

Alexandre Clément·Nicolas Heurtel·Shane Mansfield·Simon Perdrix·Benoît Valiron
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Abstract

We introduce the LOv-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 LOv-circuits represent the same quantum process if and only if one can be transformed into the other with the rules of the LOv-calculus. We give a confluent and terminating rewrite system to rewrite any polarisation-preserving LOv-circuit into a unique triangular normal form, inspired by the universal decomposition of Reck et al. (1994) for linear optical quantum circuits.

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Alexandre Clément, Nicolas Heurtel, Shane Mansfield, Simon Perdrix, Benoît Valiron. 2022-04-25. LOv-Calculus: A Graphical Language for Linear Optical Quantum Circuits. https://doi.org/10.4230/lipics.mfcs.2022.35

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