9 citations · 9 across the 3 of their papers we have counts for
7 papers
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 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…