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

• URL: http://arxiv.org/abs/2204.11787v1
• Date: Mon, 25 Apr 2022 16:59:26 GMT
• Title: LOv-Calculus: A Graphical Language for Linear Optical Quantum Circuits
• Authors: Alexandre Cl\'ement, Nicolas Heurtel, Shane Mansfield, Simon Perdrix, Beno\^it Valiron
• Abstract summary: We introduce the LOv-calculus, a graphical language for reasoning about linear optical quantum circuits. 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.
• Score: 58.720142291102135
• License: http://creativecommons.org/licenses/by/4.0/
• 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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