LOv-Calculus: A Graphical Language for Linear Optical Quantum Circuits
Quantum Physics
2022-11-15 v1 Logic in Computer Science
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.
Cite
@article{arxiv.2204.11787,
title = {LOv-Calculus: A Graphical Language for Linear Optical Quantum Circuits},
author = {Alexandre Clément and Nicolas Heurtel and Shane Mansfield and Simon Perdrix and Benoît Valiron},
journal= {arXiv preprint arXiv:2204.11787},
year = {2022}
}