Titouan Carette

I am currently assistant professor Monge in quantum computing at École Polytechnique. Before that I was a post-doctoral researcher at University of Latvia, in the Centre for Quantum Computer Science, and even before that in the QuaCS Inria team. I also did other things that can be found in this CV .

I am particularly interested in the design of graphical languages for quantum computing. This implies using abstract categorical frameworks, allowing the extension of classical concepts to the quantum setting. Precisely, I work on props and string diagrams, mostly ZX-calculus. I am also interested in the theory of programming languages, category theory in general, and the foundations of quantum physics.


I am currently investigating with more or less intensity the following subjects:

  • Links between tensor networks and symbolic dynamic
  • Promonads and programming
  • Combinatorial interpretation of ZW-calculus, matchgates, perfect matchings
  • Graphical languages for infinite-dimensional quantum mechanics
  • Foundations of graphical languages in the prop formalism
  • Categorical approach to relational quantum mechanics

If you are interested in discussing any of those topics, don't hesitate to reach me by mail:

carette(at)lix(dot)polytechnique(dot)fr

Publications

Preprints

Aperiodicity in Quantum Wang Tilings
Titouan Carette, Étienne Moutot, 2023,
arXiv:2302.04503
Operational Quantum Reference Frame Transformations
Titouan Carette, Jan Głowacki, Leon Loveridge, 2023,
arXiv:2303.14002

Conferences

Compositionality of planar perfect matchings
Titouan Carette, Etienne Moutot, Thomas Perez, Renaud Vilmart, ICALP 2023,
DOI :arXiv:2302.08767
Complete Graphical Language for Hermiticity-Preserving Superoperators
Titouan Carette, Thimothée Hoffreumon, Émile Larroque, LICS 2023,
DOI :arXiv:2302.04212
Central Submonads and Notions of Computation
TItouan Carette, Louis Lemonnier, Vladimir Zamdzhiev, LICS 2023,
DOI :arXiv:2207.09190
Complete ZX-Calculi for the Stabiliser Fragment in Odd Prime Dimensions
Robert Booth, Titouan Carette, MFCS 2022,
DOI :10.4230/LIPIcs.MFCS.2022.24
Quantum Algorithms and Oracles with the Scalable ZX-calculus
Titouan Carette, Yohann D'Anello, Simon Perdrix, QPL 2021,
DOI:10.4204/EPTCS.343.10
Graphical Language with Delayed Trace: Picturing Quantum Computing with Finite Memory
Titouan Carette, Marc De Visme, Simon Perdrix, LICS 2021,
DOI: 10.1109/LICS52264.2021.9470553
A recipe for quantum graphical languages
Titouan Carette, Emmanuel Jeandel, ICALP 2020,
DOI: 10.4230/LIPIcs.ICALP.2020.118
SZX-calculus: Scalable Graphical Quantum Reasoning
Titouan Carette, Dominic Horsman, Simon Perdrix, MFCS 2019,
DOI: 10.4230/LIPIcs.MFCS.2019.55
Completeness of Graphical Languages for Mixed State Quantum Mechanics
Titouan Carette, Emmanuel Jeandel, Simon Perdrix, Renaud Vilmart, ICALP 2019,
DOI: 10.4230/LIPIcs.ICALP.2019.108
Extended Learning Graphs for Triangle Finding
Titouan Carette, Mathieu Laurière, Frédéric Magniez, STACS 2017,
DOI: 10.4230/LIPIcs.STACS.2017.20

Journals

Fact-nets: towards a mathematical framework for relational quantum mechanics
Pierre Martin-Dussaud, Titouan Carette, Jan Głowacki, Vaclav Zatloukal, Federico Zalamea, Foundations of Physics,
DOI:10.1007/s10701-022-00653-y
Completeness of Graphical Languages for Mixed State Quantum Mechanics
Titouan Carette, Emmanuel Jeandel, Simon Perdrix, Renaud Vilmart, ACM Transactions in Quantum Computing,
DOI: 10.1145/3464693
Extended Learning Graphs for Triangle Finding
Titouan Carette, Mathieu Laurière, Frédéric Magniez, Algorithmica,
DOI: 10.1007/s00453-019-00627-z

Thesis

Wielding the ZX-calculus, Flaxsymmetry, Mixed states and Scalable notations
Titouan Carette, University of Lorraine,
Manuscript accessible here.

Notes and work in progress

Propification and the Scalable Comonad
Titouan Carette,
DOI:arXiv:2205.07760
Large-scale quantum diagrammatic reasoning tools, !-boxes vs. scalable notations
Titouan Carette, Louis Lemonnier,
DOI:arXiv:2204.11702