Publications HAL

2024

Journal articles

ref_biblio
Renaud Vilmart. Rewriting and Completeness of Sum-Over-Paths in Dyadic Fragments of Quantum Computing. Logical Methods in Computer Science, 2024, 20 (1), ⟨10.46298/LMCS-20(1:20)2024⟩. ⟨hal-04496100⟩
Accès au texte intégral et bibtex
https://hal.science/hal-04496100/file/2307.14223.pdf BibTex

Conference papers

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Alexandre Clément, Noé Delorme, Simon Perdrix, Renaud Vilmart. Quantum Circuit Completeness: Extensions and Simplifications. International Conference on Computer Science Logic CSL 2024, Feb 2024, Naples, Italy. ⟨10.4230/LIPIcs.CSL.2024.20⟩. ⟨hal-04016498v3⟩
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https://hal.science/hal-04016498/file/main.pdf BibTex

Preprints, Working Papers, ...

ref_biblio
Renaud Vilmart, Marc de Visme. Minimality in Finite-Dimensional ZW-Calculi. 2024. ⟨hal-04496193⟩
Accès au texte intégral et bibtex
https://hal.science/hal-04496193/file/qudit-ZW.pdf BibTex

2023

Conference papers

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Titouan Carette, Etienne Moutot, Thomas Perez, Renaud Vilmart. Compositionality of planar perfect matchings: A universal and complete fragment of ZW-calculus. 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023), Jul 2023, Paderborn, Germany. pp.120:1--120:17, ⟨10.4230/LIPIcs.ICALP.2023.120⟩. ⟨hal-04002282⟩
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https://hal.science/hal-04002282/file/Compositionality%20of%20planar%20perfect%20matchings.pdf BibTex
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Titouan Carette, Timothée Hoffreumon, Émile Larroque, Renaud Vilmart. Complete Graphical Language for Hermiticity-Preserving Superoperators. 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) 2023, Jun 2023, Boston, United States. pp.1-22, ⟨10.1109/LICS56636.2023.10175712⟩. ⟨hal-04001823⟩
Accès au texte intégral et bibtex
https://hal.science/hal-04001823/file/Complete%20Graphical%20Language%20for%20Hermiticity-Preserving.pdf BibTex
ref_biblio
Renaud Vilmart. Completeness of Sum-Over-Paths for Toffoli-Hadamard and the Dyadic Fragments of Quantum Computation. CSL 2023 - 31st EACSL Annual Conference on Computer Science Logic, Feb 2023, Warsaw, Poland. pp.36:1--36:17, ⟨10.4230/LIPIcs.CSL.2023.36⟩. ⟨hal-03654438v2⟩
Accès au texte intégral et bibtex
https://hal.science/hal-03654438/file/SOP-TH.pdf BibTex

Book sections

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Christophe Chareton, Sébastien Bardin, Dongho Lee, Benoît Valiron, Renaud Vilmart, et al.. Formal Methods for Quantum Algorithms. Handbook of Formal Analysis and Verification in Cryptography, 1, CRC Press, pp.319-422, 2023, ⟨10.1201/9781003090052-7⟩. ⟨hal-04311441⟩
Accès au bibtex
https://arxiv.org/pdf/2109.06493 BibTex
ref_biblio
Christophe Chareton, Sébastien Bardin, Dong Ho Lee, Benoît Valiron, Renaud Vilmart, et al.. Formal Methods for Quantum Algorithms. Handbook of Formal Analysis and Verification in Cryptography, CRC Press; Taylor and Francis, pp.319-422, 2023, Prospect in Pure and Applied Mathematics, 9780367546656. ⟨cea-04479879⟩
Accès au texte intégral et bibtex
https://cea.hal.science/cea-04479879/file/main.pdf BibTex

2022

Conference papers

ref_biblio
Aleks Kissinger, Renaud Vilmart, John van de Wetering. Classical simulation of quantum circuits with partial and graphical stabiliser decompositions. 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022), Jul 2022, Urbana-Champaign, United States. pp.5:1 - 5:13, ⟨10.4230/LIPIcs.TQC.2022.5⟩. ⟨hal-03606226⟩
Accès au texte intégral et bibtex
https://hal.science/hal-03606226/file/partial_stab_decomp.pdf BibTex

Preprints, Working Papers, ...

ref_biblio
Kostia Chardonnet, Marc de Visme, Benoît Valiron, Renaud Vilmart. The Many-Worlds Calculus. 2022. ⟨hal-03654190v2⟩
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https://hal.science/hal-03654190/file/main.pdf BibTex

2021

Journal articles

ref_biblio
Titouan Carette, Emmanuel Jeandel, Simon Perdrix, Renaud Vilmart. Completeness of Graphical Languages for Mixed State Quantum Mechanics. ACM Transactions on Quantum Computing, 2021, ACM Transactions on Quantum Computing, 2 (4), pp.1-28. ⟨10.1145/3464693⟩. ⟨hal-04082921⟩
Accès au texte intégral et bibtex
https://inria.hal.science/hal-04082921/file/journalTQC.pdf BibTex

Conference papers

ref_biblio
Renaud Vilmart. Quantum Multiple-Valued Decision Diagrams in Graphical Calculi. MFCS 2021 - 46th International Symposium on Mathematical Foundations of Computer Science, Aug 2021, Tallinn, Estonia. pp.89:1--89:15, ⟨10.4230/LIPIcs.MFCS.2021.89⟩. ⟨hal-03277262⟩
Accès au texte intégral et bibtex
https://hal.science/hal-03277262/file/NF-decision-diagrams-hal.pdf BibTex
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Kostia Chardonnet, Benoît Valiron, Renaud Vilmart. Geometry of Interaction for ZX-Diagrams. MFCS 2021 - 46th International Symposium on Mathematical Foundations of Computer Science, Aug 2021, Tallinn, Estonia. pp.30:1--30:16, ⟨10.4230/LIPIcs.MFCS.2021.30⟩. ⟨hal-03154573⟩
Accès au texte intégral et bibtex
https://hal.science/hal-03154573/file/Geometry%20of%20Interaction%20for%20ZX-Diagrams.pdf BibTex
ref_biblio
Kostia Chardonnet, Benoît Valiron, Renaud Vilmart. Geometry of Interaction for ZX-Diagrams. TLLA 2021 - 5th International Workshop on Trends in Linear Logic and Applications, Jun 2021, Rome / Virtual, Italy. ⟨lirmm-03272411⟩
Accès au texte intégral et bibtex
https://hal-lirmm.ccsd.cnrs.fr/lirmm-03272411/file/TLLA_2021_paper_2.pdf BibTex
ref_biblio
Renaud Vilmart. The Structure of Sum-Over-Paths, its Consequences, and Completeness for Clifford. Foundations of Software Science and Computation Structures (FoSSaCS) 2021, Mar 2021, Luxembourg, Luxembourg. pp.531-550, ⟨10.1007/978-3-030-71995-1_27⟩. ⟨hal-02651473⟩
Accès au texte intégral et bibtex
https://hal.science/hal-02651473/file/path_sums.pdf BibTex

2020

Journal articles

ref_biblio
Emmanuel Jeandel, Simon Perdrix, Renaud Vilmart. Completeness of the ZX-Calculus. Logical Methods in Computer Science, 2020, 16 (2), pp.11:1 -- 11:72. ⟨10.23638/LMCS-16(2:11)2020⟩. ⟨hal-02400081⟩
Accès au bibtex
https://arxiv.org/pdf/1903.06035 BibTex

2019

Conference papers

ref_biblio
Renaud Vilmart. A Near-Minimal Axiomatisation of ZX-Calculus for Pure Qubit Quantum Mechanics. LICS 2019 - 34th Annual ACM/IEEE Symposium on Logic in Computer Science, Jun 2019, Vancouver, Canada. ⟨10.1109/LICS.2019.8785765⟩. ⟨hal-01963426⟩
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https://hal.science/hal-01963426/file/euler.pdf BibTex
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Emmanuel Jeandel, Simon Perdrix, Renaud Vilmart. A Generic Normal Form for ZX-Diagrams and Application to the Rational Angle Completeness. LICS 2019 - 34th Annual ACM/IEEE Symposium on Logic in Computer Science, Jun 2019, Vancouver, Canada. ⟨10.1109/LICS.2019.8785754⟩. ⟨hal-01791791⟩
Accès au texte intégral et bibtex
https://hal.science/hal-01791791/file/normal-forms-NF.pdf BibTex
ref_biblio
Titouan Carette, Simon Perdrix, Renaud Vilmart, Emmanuel Jeandel. Completeness of Graphical Languages for Mixed States Quantum Mechanics. ICALP, 2019, Patras, Greece. ⟨10.4230/LIPIcs.ICALP.2019.108⟩. ⟨hal-02025720⟩
Accès au texte intégral et bibtex
https://hal.science/hal-02025720/file/discard.pdf BibTex

Theses

ref_biblio
Renaud Vilmart. ZX-Calculi for Quantum Computing and their Completeness. Logic in Computer Science [cs.LO]. Université de Lorraine, 2019. English. ⟨NNT : 2019LORR0130⟩. ⟨tel-02395443⟩
Accès au texte intégral et bibtex
https://hal.science/tel-02395443/file/these-Vilmart.pdf BibTex

2018

Conference papers

ref_biblio
Emmanuel Jeandel, Simon Perdrix, Renaud Vilmart. A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics. The 33rd Annual {ACM/IEEE} Symposium on Logic in Computer Science, {LICS} 2018, Jul 2018, Oxford, United Kingdom. pp.559--568, ⟨10.1145/3209108.3209131⟩. ⟨hal-01529623v2⟩
Accès au texte intégral et bibtex
https://hal.science/hal-01529623/file/pi_4-completeness-arxiv-v2.pdf BibTex
ref_biblio
Emmanuel Jeandel, Simon Perdrix, Renaud Vilmart. Diagrammatic Reasoning beyond Clifford+T Quantum Mechanics. The 33rd Annual Symposium on Logic in Computer Science, Jul 2018, Oxford, United Kingdom. pp.569--578, ⟨10.1145/3209108.3209139⟩. ⟨hal-01716501⟩
Accès au texte intégral et bibtex
https://hal.science/hal-01716501/file/beyond_clifford%2BT-arxiv.pdf BibTex
ref_biblio
Renaud Vilmart. A ZX-Calculus with Triangles for Toffoli-Hadamard, Clifford+T, and Beyond. QPL 2018, Jun 2018, Halifax, Canada. pp.313-344, ⟨10.4204/EPTCS.287.18⟩. ⟨hal-01762264⟩
Accès au texte intégral et bibtex
https://hal.science/hal-01762264/file/Toffoli-arxiv.pdf BibTex

2017

Conference papers

ref_biblio
Emmanuel Jeandel, Simon Perdrix, Renaud Vilmart, Quanlong Wang. ZX-Calculus: Cyclotomic Supplementarity and Incompleteness for Clifford+T quantum mechanics. MFCS 2017 - 42nd International Symposium on Mathematical Foundations of Computer Science, Aug 2017, Aalborg, Denmark. pp.15. ⟨hal-01445707v2⟩
Accès au texte intégral et bibtex
https://hal.science/hal-01445707/file/Cyclotomic-Supplementarity-with-appendix.pdf BibTex
ref_biblio
Emmanuel Jeandel, Simon Perdrix, Renaud Vilmart. Y-Calculus: A language for real Matrices derived from the ZX-Calculus. International Conference on Quantum Physics and Logics (QPL), 2017, Nijmegen, Netherlands. ⟨hal-01445948⟩
Accès au texte intégral et bibtex
https://hal.science/hal-01445948/file/Y-Calculus.pdf BibTex