21 citations · 65 across the 19 of their papers we have counts for
5 papers · 1 filter
Central Submonads and Notions of Computation: Soundness, Completeness and Internal Languages
TItouan Carette, Louis Lemonnier, Vladimir Zamdzhiev
Monads in category theory are algebraic structures that can be used to model computational effects in programming languages. We show how the notion of "centre", and more generally…
Propification and the Scalable Comonad
Titouan Carette
String diagrams can nicely express numerous computations in symmetric strict monoidal categories (SSMC). To be entirely exact, this is only true for props: the SSMCs whose monoid o…
Large-scale quantum diagrammatic reasoning tools, !-boxes vs. scalable notations
Titouan Carette, Louis Lemonnier
The application of diagrammatic reasoning techniques to large-scale quantum processes needs specific tools to describe families of diagrams of arbitrary size. For now, large-scale…
Complete ZX-calculi for the stabiliser fragment in odd prime dimensions
Robert I. Booth, Titouan Carette
We introduce a family of ZX-calculi which axiomatise the stabiliser fragment of quantum theory in odd prime dimensions. These calculi recover many of the nice features of the qubit…
Fact-nets: towards a mathematical framework for relational quantum mechanics
Pierre Martin-Dussaud, Titouan Carette, Jan Głowacki +2
The relational interpretation of quantum mechanics (RQM) has received a growing interest since its first formulation in 1996. Usually presented as an interpretational layer over th…