Noé Delorme

I am currently a Ph.D. student working on quantum computation under the supervison of Simon Perdrix in the MOCQUA research team at INRIA. My academic areas of interest are quantum computation, computational complexity theory and theoretical computer science in general.

Papers

Minimal Equational Theories for Quantum Circuits (arXiv:2311.07476), with Alexandre Clément and Simon Perdrix at LICS’24 (39th Annual ACM/IEEE Symposium on Logic in Computer Science).
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.
Quantum Circuit Completeness: Extensions and Simplifications (arXiv:2303.03117), with Alexandre Clément, Simon Perdrix, and Renaud Vilmart at CSL’24 (32nd Annual EACSL Conference on Computer Science Logic).
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.

Talks

16th July 2024 at QPL’24 (21st International Conference on Quantum Physics and Logic) in Buenos Aires, Argentina. "Minimal Equational Theories for Quantum Circuits". (slide of the talk)
9th July 2024 at LICS’24 (39th Annual ACM/IEEE Symposium on Logic in Computer Science) in Tallinn, Estonia. "Minimal Equational Theories for Quantum Circuits". (slide of the talk)
20th Feb. 2024 at CSL’24 (32nd Annual EACSL Conference on Computer Science Logic) in Naples, Italy. "Quantum Circuit Completeness: Extensions and Simplifications". (slide of the talk)
14th Nov. 2023 at the Workshop Defi EQIP 2023 in Lyon, France. "Minimal Equational Theories for Quantum Circuits" at the Workshop Defi EQIP 2023 in Lyon, France. (slide of the talk)

Last update on 13th March 2025.