Colin Blake

PhD student, Inria MOCQUA

Publications

  1. Completeness for Prime-Dimensional Phase-Affine Circuits

    Colin Blake

    Preprint | 2026

    Presents complete PROP presentations and normal forms for affine circuits with bounded-degree phase-polynomial extensions over prime fields.

    arXiv

  2. A Complete Equational Presentation of Qudit Circuits via Polycontrolled PROPs

    Colin Blake

    51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026) proceedings; Best Student Paper award | 2026

    Gives a finite dimension-uniform equational presentation for exact qudit circuits using primitive value-control in a polycontrolled PROP.

    arXiv DOI

  3. Simpler Presentations for Many Fragments of Quantum Circuits

    Colin Blake

    11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026) proceedings | 2026

    Transfers six circuit-fragment completeness theorems to PROP presentations with structural permutations and proves minimality results for the resulting axiom systems.

    Update 1: For Clifford+T, rule (TX) can use #{H, ω8}2 instead of the #{H, T, ω8}2 used in the paper.

    Update 2: The Heuristics tool below implements more arguments than the paper uses, including the amalgam normal form, which seems especially useful for Euler-style equations, and a Spin-group interpretation that separates pattern (19) on n wires in the recent real Clifford+CH presentation, where this was left open.

    Update 3: Thanks to Alexandre Clément, who gave a meta-argument for the remaining qutrit Clifford equation (I), validating the conjecture that the presentation in the paper is minimal for every n.

    arXiv DOI Heuristics tool

Cite

A Complete Equational Presentation of Qudit Circuits via Polycontrolled PROPs 

@InProceedings{blake:LIPIcs.MFCS.2026.6,
  author =	{Blake, Colin},
  title =	{{A Complete Equational Presentation of Qudit Circuits via Polycontrolled PROPs}},
  booktitle =	{51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026)},
  pages =	{6:1--6:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-442-0},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{386},
  editor =	{Kouck\'{y}, Michal and Petrișan, Daniela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2026.6},
  URN =		{urn:nbn:de:0030-drops-273875},
  doi =		{10.4230/LIPIcs.MFCS.2026.6},
  annote =	{Keywords: Qudit circuits, Quantum circuits, Completeness, Control, Categorical quantum mechanics}
}

Cite

Simpler Presentations for Many Fragments of Quantum Circuits 

@InProceedings{blake:LIPIcs.FSCD.2026.6,
  author =	{Blake, Colin},
  title =	{{Simpler Presentations for Many Fragments of Quantum Circuits}},
  booktitle =	{11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)},
  pages =	{6:1--6:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-433-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{378},
  editor =	{Pfenning, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2026.6},
  URN =		{urn:nbn:de:0030-drops-263562},
  doi =		{10.4230/LIPIcs.FSCD.2026.6},
  annote =	{Keywords: Quantum circuits, Clifford group, equational theories, minimality, qutrit}
}

If you want slides or other supplementary material around these papers, feel free to email me.

Talks

  • Upcoming

    Equations for quantum circuits: from qubits to qudits

    Séminaire d'informatique théorique, Université de Rouen Normandie

  • Abstract

    Controlled Gates in Qudits

    NANQI 2026 - Workshop calcul et communications quantiques, Nancy

  • Slides

    A Complete Equational Presentation of Qudit Circuits via Polycontrolled PROPs

    MFCS 2026 - 51st International Symposium on Mathematical Foundations of Computer Science, Paris

  • Slides

    Completeness for Prime-Dimensional Phase-Affine Circuits

    QPL 2026 - 23rd International Conference on Quantum Physics and Logic, Amsterdam

  • Slides

    Simpler Presentations for Many Fragments of Quantum Circuits

    FSCD 2026 - 11th International Conference on Formal Structures for Computation and Deduction, Lisbon

  • Slides

    A Complete Equational Presentation of Qudit Circuits via Polycontrolled PROPs

    FMQC 2026 - Second Workshop on Formal Methods in Quantum Computing, Lisbon

  • Slides Extended abstract

    Simpler Presentations for Many Fragments of Quantum Circuits

    LIQCS 2026 - Logic in Quantum Computer Science, Inria de Paris

  • Slides

    Reasoning for Qudit Circuits

    Department of Formal Methods PhD Day - Nancy

  • Slides

    Reasoning for Qudit Circuits

    MOCQUA PhD Day - Nancy

  • Slides

    Quantum computing and ZX-calculus

    Séminaires Jeunes chercheurs et chercheuses - Marne la Vallée

  • Slides

    Escape the Matrix: Graphical Reasoning and Minimal Axioms for Quantum Circuits

    Département des méthodes formelles PhD Day - Nancy

STEM Outreach

  • Cap sur le numerique a Bercy - Semaine NSI 2025

    8 December 2025 | Ministere de l'Economie et des Finances, Paris

    Outreach appearance for the opening event of Semaine NSI 2025, where I presented quantum-computing research and research careers to middle-school, high-school, and BTS students as part of Inria's broader scientific-mediation programme.

    Inria article LinkedIn recap

  • Village des Sciences - Fete de la Science 2025

    10-11 October 2025 | Faculte des Sciences et Technologies, Vandoeuvre-les-Nancy

    Public-facing workshop built around Les Chevaliers du Quantique during the Village des Sciences, combining the playable game with a hands-on tile activity to help school groups and the general public explore qubits and quantum-circuit simplification.

    Event page Loria article NanSciNum article LinkedIn recap

  • Les Chevaliers du Quantique

    Scientific Game Jam Nancy 2025 | First prize

    Video-game adaptation of a printable circuit-simplification tutorial game built from my research, turning quantum-circuit rewriting into an accessible puzzle format for middle-school students and above.

    Play online Original printable game (PDF) NanSciNum article Pixees article Press clipping (PDF)

  • Quantum circuit simplification game

    Printable classroom game | Original tabletop version

    French-language tutorial game for learning quantum-circuit simplification as a rewrite puzzle. Players solve missions representing quantum circuits by removing all tiles column by column with rules for H, X, Z, basis changes, entanglement, controls, phases, stabilisers, and transfer-style identities.

    Printable rules and missions (PDF)