Titouan Carette - Theoretical Quantum Computer Scientist
Office 1113
LIX - UMR 7161
1 rue Honoré d'Estienne d'Orves
Bâtiment Alan Turing
Campus de l'École Polytechnique
91120 Palaiseau
France
titouan(dot)carette(at)polytechnique(dot)edu

I am Assistant professor Monge at École polytechnique and member of PhiQus, a joint Inria project team between LIX and CPHT. I am also member of the BRCP.
Research
My research focuses on applying category theory and string diagrams to theoretical computer science and quantum physics. In practice, I am designing diagrammatical equational theories to reason on various kinds of processes with rewriting techniques. In particular, I am involved in the development and outreach of the ZX-calculus, a diagrammatical syntax for quantum processes. My current interests include:
- Picturing symplectic structures.
- Linking ZW-calculus, fermions and perfect matchings.
- Unifying symbolic dynamic and condensed matter.
- Formalizing the relational interpretation of quantum mechanics.
Publications
Preprints
-
Complete equational theories for classical and quantum Gaussian relations
with Robert Booth and Cole Comfort, 2024,
arXiv.2403.10479 -
Graphical Symplectic Algebra
with Robert Booth and Cole Comfort, 2024,
arXiv.2401.07914 -
Aperiodicity in Quantum Wang Tilings
with Étienne Moutot, 2023,
arXiv:2302.04503 -
Operational Quantum Reference Frame Transformations
with Jan Głowacki and Leon Loveridge, 2023,
arXiv:2303.14002
Conferences
-
The Qupit Stabiliser ZX-travaganza: Simplified Axioms, Normal Forms and Graph-Theoretic Simplification
with Boldizsár Poór, Robert I. Booth, John van de Wetering and Lia Yeh, QPL 2023,
10.4204/EPTCS.384.13 -
Compositionality of planar perfect matchings
with Etienne Moutot, Thomas Perez and Renaud Vilmart, ICALP 2023,
arXiv:2302.08767 -
Complete Graphical Language for Hermiticity-Preserving Superoperators
with Thimothée Hoffreumon and Émile Larroque, LICS 2023,
arXiv:2302.04212 -
Central Submonads and Notions of Computation
with Louis Lemonnier and Vladimir Zamdzhiev, LICS 2023,
arXiv:2207.09190 -
Complete ZX-Calculi for the Stabiliser Fragment in Odd Prime Dimensions
with Robert Booth, MFCS 2022,
10.4230/LIPIcs.MFCS.2022.24 -
Quantum Algorithms and Oracles with the Scalable ZX-calculus
with Yohann D'Anello and Simon Perdrix, QPL 2021,
10.4204/EPTCS.343.10 -
Graphical Language with Delayed Trace: Picturing Quantum Computing with Finite Memory
with Marc De Visme and Simon Perdrix, LICS 2021,
10.1109/LICS52264.2021.9470553 -
A recipe for quantum graphical languages
with Emmanuel Jeandel, ICALP 2020,
10.4230/LIPIcs.ICALP.2020.118 -
SZX-calculus: Scalable Graphical Quantum Reasoning
with Dominic Horsman and Simon Perdrix, MFCS 2019,
10.4230/LIPIcs.MFCS.2019.55 -
Completeness of Graphical Languages for Mixed State Quantum Mechanics
with Emmanuel Jeandel, Simon Perdrix and Renaud Vilmart, ICALP 2019,
10.4230/LIPIcs.ICALP.2019.108 -
Extended Learning Graphs for Triangle Finding
with Mathieu Laurière and Frédéric Magniez, STACS 2017,
10.4230/LIPIcs.STACS.2017.2
Journals
-
Fact-nets: towards a mathematical framework for relational quantum mechanics
with Pierre Martin-Dussaud, Jan Głowacki, Vaclav Zatloukal and Federico Zalamea, Foundations of Physics ,
10.1007/s10701-022-00653-y -
Completeness of Graphical Languages for Mixed State Quantum Mechanics
with Emmanuel Jeandel, Simon Perdrix and Renaud Vilmart, ACM Transactions in Quantum Computing,
10.1145/3464693 -
Extended Learning Graphs for Triangle Finding
with Mathieu Laurière and Frédéric Magniez, Algorithmica,
10.1007/s00453-019-00627-z
Thesis
-
Wielding the ZX-calculus, Flexsymmetry, Mixed states and Scalable notations
University of Lorraine, manuscript accessible here.
Notes and work in progress
-
Propification and the Scalable Comonad
arXiv:2205.07760 -
Large-scale quantum diagrammatic reasoning tools, !-boxes vs. scalable notations
with Louis Lemonnier,
arXiv:2204.11702