Colin Blake

PhD student, Inria MOCQUA

Publications

  1. Completeness for Prime-Dimensional Phase-Affine Circuits

    Colin Blake

    Preprint | Preprint | 2026

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

    arXiv PDF

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

    Colin Blake

    Preprint | Preprint | 2026

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

    arXiv PDF

  3. Simpler Presentations for Many Fragments of Quantum Circuits

    Colin Blake

    FSCD 2026 proceedings | Proceedings of the 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.

    arXiv PDF

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

Talks

  • 17 June 2026 | LIQCS 2026 - Logic in Quantum Computer Science, Inria de Paris

    Slides Extended abstract

  • 26 March 2026 & 13 May 2026 | MOCQUA PhD Day - Nancy & Department of Formal Methods PhD Day - Nancy

    Slides

  • 26 November 2025 | Séminaires Jeunes chercheurs et chercheuses - Marne la Vallée

    Slides

  • 6 May 2025 | Département des méthodes formelles PhD Day - Nancy

    Slides

Completeness Is Not Enough: Simpler Presentations and Minimality for Near-Clifford Circuit Fragments

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

Slides Extended abstract

Completeness for a circuit fragment says that every valid identity is derivable, but it does not say which axioms are genuinely doing algebraic work. This talk revisits six near-Clifford fragments in a PROP setting, where wire permutations are treated as ambient structure, yielding smaller complete presentations for qubit Clifford, real Clifford, CNOT-dihedral, bounded-wire Clifford+T, bounded-wire Clifford+CS, and qutrit Clifford. The reduced presentations expose a smaller algebraic core and make minimality questions sharper: some fragments become fully minimal, while the remaining cases reduce to concrete low-arity independence problems.

Reasoning for Qudit Circuits

26 March 2026 & 13 May 2026 | MOCQUA PhD Day - Nancy & Department of Formal Methods PhD Day - Nancy

Slides

Quantum programs are most often represented as quantum circuits: sequences of gates acting on registers of quantum systems. But in practice, writing a circuit is only the beginning. To optimise code, adapt it to hardware constraints such as connectivity and mapping, and verify correctness, we need reliable ways to transform circuits while preserving their meaning. A convenient approach is equational reasoning: we specify a set of rewrite rules, or axioms, and use them to derive when two circuits are equivalent. My PhD focuses on extending this story beyond qubits, towards higher dimensions, and on making equational theories usable by reducing redundancy and organising rewrite systems around normal forms. In this talk I will first introduce the basic ideas of quantum circuits and explain why gate sets and circuit fragments play an important role in quantum software. I will then discuss how equational reasoning is used to reason about and optimise circuits, and how these ideas extend to higher-dimensional quantum systems. Finally, I will present some of my recent work on equational theories for different kinds of qudit circuits and explain how it fits into the broader goal of building practical tools for reasoning about quantum programs.

Quantum computing and ZX-calculus

26 November 2025 | Séminaires Jeunes chercheurs et chercheuses - Marne la Vallée

Slides

What if we could picture quantum computations not as daunting complex matrices, but as simple graphs of nodes and wires? The ZX-calculus offers exactly that: a rigorous graphical language where any quantum circuit can be represented as a network of connected nodes. In this interactive talk, I will introduce the basics of ZX-calculus in an accessible way. We'll start with a quick refresher on quantum computing, with no prior quantum background required, then see how these concepts translate into colorful ZX-diagrams. Using a handful of intuitive graph transformation rules, we will visually simplify and reason about quantum circuits, almost like solving a puzzle. For example, we'll demonstrate how the famous quantum teleportation protocol, when depicted in ZX form, collapses into a trivially simple diagram, revealing its essence at a glance. Along the way, a few fun quiz questions via Kahoot! will test and engage your intuition. Beyond the fun, we will discuss why this graphical approach is powerful for research. The ZX-calculus provides a sound framework for optimizing quantum programs and verifying algorithm correctness, and it even reveals surprising connections to combinatorics and algebra: its rewrite rules mirror an underlying Hopf algebra structure. I will also highlight current challenges and my ongoing work, in particular extending these diagrammatic techniques to qudits, quantum systems with more than two levels, an open problem at the frontier of quantum computing theory. By the end of the talk, you'll see quantum computing from a new angle and understand why one might say that "quantum computing is just graphs."

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

6 May 2025 | Département des méthodes formelles PhD Day - Nancy

Slides

Quantum circuits are commonly represented using matrices, but this approach becomes unwieldy for complex systems. In this talk, I will present a graphical methodology that utilizes equational rules to rewrite circuits, offering a more intuitive and structured framework. We will discuss the criteria for such a system to be sound, complete, and minimal, and explore the significance of these properties. Subsequently, I will introduce new minimal equational theories for various classes of quantum circuits, each with distinct expressive capabilities. These minimality results are significant because they simplify the equational theory by eliminating redundant rules, making it more practical for applications like circuit optimization and verification. No prior background in quantum computing is required; the emphasis will be on the foundational formal concepts.

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)