5 papers
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…
The decohered ZX-calculus
Titouan Carette, Daniela Cojocaru, Renaud Vilmart
The discard ZX-calculus is known to be complete and universal for mixed-state quantum mechanics, allowing for both quantum and classical processes. However, if the quantum aspects…
Operational Quantum Reference Frame Transformations
Titouan Carette, Jan GÅowacki, Leon Loveridge
Quantum reference frames are needed in quantum theory for much the same reasons that reference frames are in classical theories: to manifest invariance in line with fundamental rel…
Complete Compositional Syntax for Finite Transducers on Finite and Bi-Infinite Words
Titouan Carette, Marc de Visme, Vivien Ducros +2
Minimizing finite automata, proving trace equivalence of labelled transition systems or representing sofic subshifts involve very similar arguments, which suggests the possibility…
Aperiodicity in Quantum Wang Tilings
Titouan Carette, Etienne Moutot
By reformulating Wang tiles with tensors, we propose a natural generalization to the probabilistic and quantum setting. In this new framework, we introduce notions of tilings and p…