21 citations · 65 across the 19 of their papers we have counts for
24 papers
Premonoidal Semantics and Scalable Diagrammatics of Fermionic Quantum Computing
Thomas Perez, Titouan Carette
Local fermionic mode (LFM) based quantum computation has pure state spaces that are isomorphic, via the Jordan-Wigner representation, to qubit state spaces, but its compositional s…
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…
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…
Complete equational theories for classical and quantum Gaussian relations
Robert I. Booth, Titouan Carette, Cole Comfort
We give generators and relations for the hypergraph props of Gaussian relations and positive affine Lagrangian relations. The former extends Gaussian probabilistic processes by com…
Graphical Symplectic Algebra
Robert I. Booth, Titouan Carette, Cole Comfort
We give complete presentations for the dagger-compact props of affine Lagrangian and coisotropic relations over an arbitrary field. This provides a unified family of graphical lang…
The Qupit Stabiliser ZX-travaganza: Simplified Axioms, Normal Forms and Graph-Theoretic Simplification
Boldizsár Poór, Robert I. Booth, Titouan Carette +2
We present a smorgasbord of results on the stabiliser ZX-calculus for odd prime-dimensional qudits (i.e. qupits). We derive a simplified rule set that closely resembles the origina…