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DOI: 10.4230/LIPIcs.MFCS.2022.35
URN: urn:nbn:de:0030-drops-168334
URL: https://drops.dagstuhl.de/opus/volltexte/2022/16833/
Clément, Alexandre ; Heurtel, Nicolas ; Mansfield, Shane ; Perdrix, Simon ; Valiron, Benoît
LO_v-Calculus: A Graphical Language for Linear Optical Quantum Circuits
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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.
BibTeX - Entry
@InProceedings{clement_et_al:LIPIcs.MFCS.2022.35,
author = {Cl\'{e}ment, Alexandre and Heurtel, Nicolas and Mansfield, Shane and Perdrix, Simon and Valiron, Beno\^{i}t},
title = {{LO\underlinev-Calculus: A Graphical Language for Linear Optical Quantum Circuits}},
booktitle = {47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
pages = {35:1--35:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-256-3},
ISSN = {1868-8969},
year = {2022},
volume = {241},
editor = {Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16833},
URN = {urn:nbn:de:0030-drops-168334},
doi = {10.4230/LIPIcs.MFCS.2022.35},
annote = {Keywords: Quantum Computing, Graphical Language, Linear Optical Circuits, Linear Optical Quantum Computing, Completeness}
}
| Keywords: | Quantum Computing, Graphical Language, Linear Optical Circuits, Linear Optical Quantum Computing, Completeness | |
| Seminar: | 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022) | |
| Issue date: | 2022 | |
| Date of publication: | 22.08.2022 |
