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

Authors Alexandre Clément , Nicolas Heurtel , Shane Mansfield, Simon Perdrix , Benoît Valiron

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LIPIcs.MFCS.2022.35.pdf
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ACM Subject Classification
  • Theory of computation → Quantum computation theory
  • Theory of computation → Axiomatic semantics
  • Hardware → Quantum computation
  • Hardware → Quantum communication and cryptography
Keywords
  • Quantum Computing
  • Graphical Language
  • Linear Optical Circuits
  • Linear Optical Quantum Computing
  • Completeness

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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.

Cite As Get BibTex

Alexandre Clément, Nicolas Heurtel, Shane Mansfield, Simon Perdrix, and Benoît Valiron. LO_v-Calculus: A Graphical Language for Linear Optical Quantum Circuits. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 35:1-35:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.MFCS.2022.35

Author Details

Alexandre Clément
  • Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France
Nicolas Heurtel
  • Quandela, 7 Rue Léonard de Vinci, 91300 Massy, France
  • Université Paris-Saclay, CentraleSupélec, Inria, CNRS, ENS Paris-Saclay, Laboratoire Méthodes Formelles, 91190 Gif-sur-Yvette, France
Shane Mansfield
  • Quandela, 7 Rue Léonard de Vinci, 91300 Massy, France
Simon Perdrix
  • Inria Mocqua, LORIA, CNRS, Université de Lorraine, F-54000 Nancy, France
Benoît Valiron
  • Université Paris-Saclay, CentraleSupélec, Inria, CNRS, ENS Paris-Saclay, Laboratoire Méthodes Formelles, 91190 Gif-sur-Yvette, France

Funding

This work is funded by ANR-17-CE25-0009 SoftQPro, ANR-17-CE24-0035 VanQuTe, PIA-GDN/Quantex, and LUE / UOQ, the PEPR integrated project EPiQ ANR-22-PETQ-0007 part of Plan France 2030, and by "Investissements d'avenir" (ANR-15-IDEX-02) program of the French National Research Agency; the European Project NExt ApplicationS of Quantum Computing (NEASQC), funded by Horizon 2020 Program inside the call H2020-FETFLAG-2020-01(Grant Agreement 951821), and the HPCQS European High-Performance Computing Joint Undertaking (JU) under grant agreement No 101018180.

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