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Conference Papers Year : 2022

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

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.

Dates and versions

hal-03926660 , version 1 (06-01-2023)

Licence

Attribution - CC BY 4.0

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Cite

Alexandre Clément, Nicolas Heurtel, Shane Mansfield, Simon Perdrix, Benoît Valiron. LO_v-Calculus: A Graphical Language for Linear Optical Quantum Circuits. 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022), Aug 2022, Vienna, Austria. pp.35:1--35:16, ⟨10.4230/LIPIcs.MFCS.2022.35⟩. ⟨hal-03926660⟩
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