8 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…
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…
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…
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…
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…