18 citations · 65 across the 19 of their papers we have counts for
28 papers
Minimality of the Pure Qubit ZX Calculus
Harry K. Stoltz, Renaud Vilmart
The ZX calculus is a graphical language for reasoning about quantum processes. In this paper, we develop a minimal pure-qubit ZX calculus based on the work of Vilmart [arXiv:1812.0…
Intuitionistic Unitary Linear Logic: A Proof-Theoretical Approach to Purely Quantum Higher-Order
Julien Lamiroy, Benoît Valiron, Renaud Vilmart
Although the circuit model for quantum computation is well established, it is incapable of representing non-causal higher-order quantum processes such as the quantum switch. If sev…
A Unique Normal Form for Tensor Trains over Arbitrary Fields
Renaud Vilmart
Tensor trains (or Matrix-Product States) are a data structure used in many fields of computer science and physics. They were recently shown to generalise binary decision diagrams w…
The Tensor-Plus Calculus
Kostia Chardonnet, Marc de Visme, Benoît Valiron +1
We propose a graphical language that accommodates two monoidal structures: a multiplicative one for pairing and an additional one for branching. In this colored PROP, whether wires…
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…
Resource-Efficient Synthesis of Sparse Quantum States
Renaud Vilmart, Sunheang Ty, Chetra Mang
Preparing a quantum circuit that implements a given sparse state is an important building block that is necessary for many different quantum algorithms. In the context of fault-tol…
Double-Logarithmic Depth Block-Encodings of Simple Finite Difference Method's Matrices
Sunheang Ty, Renaud Vilmart, Axel TahmasebiMoradi +1
Solving differential equations is one of the most computationally expensive problems in classical computing, occupying the vast majority of high-performance computing resources dev…
Minimality in Finite-Dimensional ZW-Calculi
Marc de Visme, Renaud Vilmart
The ZW-calculus is a graphical language capable of representing 2-dimensional quantum systems (qubit) through its diagrams, and manipulating them through its equational theory. We…
Rewriting and Completeness of Sum-Over-Paths in Dyadic Fragments of Quantum Computing
Renaud Vilmart
The "Sum-Over-Paths" formalism is a way to symbolically manipulate linear maps that describe quantum systems, and is a tool that is used in formal verification of such systems. We…
Quantum Circuit Completeness: Extensions and Simplifications
Alexandre Clément, Noé Delorme, Simon Perdrix +1
Although quantum circuits have been ubiquitous for decades in quantum computing, the first complete equational theory for quantum circuits has only recently been introduced. Comple…
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…
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…
Geometry of Interaction for ZX-Diagrams
Kostia Chardonnet, Benoît Valiron, Renaud Vilmart
ZX-Calculus is a versatile graphical language for quantum computation equipped with an equational theory. Getting inspiration from Geometry of Interaction, in this paper we propose…
The Many-Worlds Calculus
Kostia Chardonnet, Marc de Visme, Benoît Valiron +1
In this paper, we explore the interaction between two monoidal structures: a multiplicative one, for the encoding of pairing, and an additive one, for the encoding of choice. We pr…
Completeness of Sum-Over-Paths for Toffoli-Hadamard and the Dyadic Fragments of Quantum Computation
Renaud Vilmart
The "Sum-Over-Paths" formalism is a way to symbolically manipulate linear maps that describe quantum systems, and is a tool that is used in formal verification of such systems. We…
Classical simulation of quantum circuits with partial and graphical stabiliser decompositions
Aleks Kissinger, John van de Wetering, Renaud Vilmart
Recent developments in classical simulation of quantum circuits make use of clever decompositions of chunks of magic states into sums of efficiently simulable stabiliser states. We…
Formal Methods for Quantum Programs: A Survey
Christophe Chareton, Sébastien Bardin, Dongho Lee +3
While recent progress in quantum hardware open the door for significant speedup in certain key areas (cryptography, biology, chemistry, optimization, machine learning, etc), quantu…
Quantum Multiple-Valued Decision Diagrams in Graphical Calculi
Renaud Vilmart
Graphical calculi such as the ZH-calculus are powerful tools in the study and analysis of quantum processes, with links to other models of quantum computation such as quantum circu…
The Structure of Sum-Over-Paths, its Consequences, and Completeness for Clifford
Renaud Vilmart
We show that the formalism of "Sum-Over-Path" (SOP), used for symbolically representing linear maps or quantum operators, together with a proper rewrite system, has a structure of…
Completeness of the ZX-Calculus
Emmanuel Jeandel, Simon Perdrix, Renaud Vilmart
The ZX-Calculus is a graphical language for diagrammatic reasoning in quantum mechanics and quantum information theory. It comes equipped with an equational presentation. We focus…
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…
A Near-Optimal Axiomatisation of ZX-Calculus for Pure Qubit Quantum Mechanics
Renaud Vilmart
Recent developments in the ZX-Calculus have resulted in complete axiomatisations first for an approximately universal restriction of the language, and then for the whole language.…
A Generic Normal Form for ZX-Diagrams and Application to the Rational Angle Completeness
Emmanuel Jeandel, Simon Perdrix, Renaud Vilmart
Recent completeness results on the ZX-Calculus used a third-party language, namely the ZW-Calculus. As a consequence, these proofs are elegant, but sadly non-constructive. We addre…
A ZX-Calculus with Triangles for Toffoli-Hadamard, Clifford+T, and Beyond
Renaud Vilmart
We consider a ZX-calculus augmented with triangle nodes which is well-suited to reason on the so-called Toffoli-Hadamard fragment of quantum mechanics. We precisely show the form o…