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…
Operational Quantum Reference Frame Transformations
Titouan Carette, Jan Głowacki, 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…
Compositionality of planar perfect matchings
Titouan Carette, Etienne Moutot, Thomas Perez +1
We exhibit a strong connection between the matchgate formalism introduced by Valiant and the ZW-calculus of Coecke and Kissinger. This connection provides a natural compositional f…
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…
Complete Graphical Language for Hermiticity-Preserving Superoperators
Titouan Carette, Timothée Hoffreumon, Émile Larroque +1
Universal and complete graphical languages have been successfully designed for pure state quantum mechanics, corresponding to linear maps between Hilbert spaces, and mixed states q…
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…
Quantum Algorithms and Oracles with the Scalable ZX-calculus
Titouan Carette, Yohann D'Anello, Simon Perdrix
The ZX-calculus was introduced as a graphical language able to represent specific quantum primitives in an intuitive way. The recent completeness results have shown the theoretical…
When Only Topology Matters
Titouan Carette
Graphical languages are symmetric monoidal categories presented by generators and equations. The string diagrams notation allows to transform numerous axioms into low dimension top…
Graphical Language with Delayed Trace: Picturing Quantum Computing with Finite Memory
Titouan Carette, Marc de Visme, Simon Perdrix
Graphical languages, like quantum circuits or ZX-calculus, have been successfully designed to represent (memoryless) quantum computations acting on a finite number of qubits. Meanw…
A note on diagonal gates in SZX-calculus
Titouan Carette
This note describes how the the scalable ZXH calculus can be used to represent in a compact way the quantum gates that are diagonal in the computational basis. This includes contro…
On a recipe for quantum graphical languages
Titouan Carette, Emmanuel Jeandel
Different graphical calculi have been proposed to represent quantum computation. First the ZX- calculus [4], followed by the ZW-calculus [12] and then the ZH-calculus [1]. We can w…
Colored props for large scale graphical reasoning
Titouan Carette, Simon Perdrix
The prop formalism allows representation of processes withstring diagrams and has been successfully applied in various areas such as quantum computing, electric circuits and contro…
SZX-calculus: Scalable Graphical Quantum Reasoning
Titouan Carette, Dominic Horsman, Simon Perdrix
We introduce the Scalable ZX-calculus (SZX-calculus for short), a formal and compact graphical language for the design and verification of quantum computations. The SZX-calculus is…
Completeness of Graphical Languages for Mixed States Quantum Mechanics
Titouan Carette, Emmanuel Jeandel, Simon Perdrix +1
There exist several graphical languages for quantum information processing, like quantum circuits, ZX-Calculus, ZW-Calculus, etc. Each of these languages forms a dagger-symmetric m…
Extended Learning Graphs for Triangle Finding
Titouan Carette, Mathieu Laurière, Frédéric Magniez
We present new quantum algorithms for Triangle Finding improving its best previously known quantum query complexities for both dense and spare instances.For dense graphs on ver…