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

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

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

    arXiv

  3. Simpler Presentations for Many Fragments of Quantum Circuits

    Colin Blake

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

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 Abstract

    Controlled Gates in Qudits

    NANQI 2026 - Workshop calcul et communications quantiques, Nancy

  • Upcoming

    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)