Noé Delorme

noe.delorme (at) inria.fr
I am currently a Ph.D. student working on quantum computing under the supervison of Simon Perdrix in the MOCQUA research team at INRIA. My thesis is about graphical languages for quantum circuits. Beyong my thesis, my academic areas of interest are quantum physics, complexity theory, and theoretical computer science in general.
Diagrammatic Reasoning with Control as a Constructor, Applications to Quantum Circuits. Work in progress paper (arxiv preprint).
Control is a predominant concept in quantum and reversible computational models. It allows to apply or not a transformation on a system, depending on the state of another system. We introduce a general framework for diagrammatic reasoning featuring control as a constructor. To do so, we provide an elementary axiomatisation of control functors, extending the standard formalism of props (symmetric monoidal categories with the natural numbers as objects) to controlled props. As an application, we show that controlled props ease diagrammatic reasoning for quantum circuits by allowing a simple complete set of relations that only involves relations acting on at most three qubits, whereas it is known that in the standard prop setting any complete axiomatisation requires relations acting on arbitrarily many qubits.
PDF CITE August 2025
Minimal Equational Theories for Quantum Circuits. Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2024).
We introduce the first minimal and complete equational theory for quantum circuits. Hence, we show that any true equation on quantum circuits can be derived from simple rules, all of them being standard except a novel but intuitive one which states that a multi-control 2π rotation is nothing but the identity. Our work improves on the recent complete equational theories for quantum circuits, by getting rid of several rules including a fairly impractical one. One of our main contributions is to prove the minimality of the equational theory, i.e. none of the rules can be derived from the other ones. More generally, we demonstrate that any complete equational theory on quantum circuits (when all gates are unitary) requires rules acting on an unbounded number of qubits. Finally, we also simplify the complete equational theories for quantum circuits with ancillary qubits and/or qubit discarding.
PDF DOI CITE July 2024
Quantum Circuit Completeness: Extensions and Simplifications. Proceedings of the 32nd EACSL Annual Conference on Computer Science Logic 2024 (CSL 2024).
Although quantum circuits have been ubiquitous for decades in quantum computing, the first complete equational theory for quantum circuits has only recently been introduced. Completeness guarantees that any true equation on quantum circuits can be derived from the equational theory. We improve this completeness result in two ways: (i) We simplify the equational theory by proving that several rules can be derived from the remaining ones. In particular, two out of the three most intricate rules are removed, the third one being slightly simplified. (ii) The complete equational theory can be extended to quantum circuits with ancillae or qubit discarding, to represent respectively quantum computations using an additional workspace, and hybrid quantum computations. We show that the remaining intricate rule can be greatly simplified in these more expressive settings, leading to equational theories where all equations act on a bounded number of qubits. The development of simple and complete equational theories for expressive quantum circuit models opens new avenues for reasoning about quantum circuits. It provides strong formal foundations for various compiling tasks such as circuit optimisation, hardware constraint satisfaction and verification.
PDF DOI CITE February 2024
Last update on 1st September 2025.