The ZX-calculus is a graphical language for reasoning about quantum computation that has
recently seen an increased usage in a variety of areas such as quantum circuit optimisation …

The ZX-calculus is a graphical language for reasoning about ZX-diagrams, a type of tensor
networks that can represent arbitrary linear maps between qubits. Using the ZX-calculus, we …

This paper has two tightly intertwined aims:(i) to introduce an intuitive and universal
graphical calculus for multi-qubit systems, the ZX-calculus, which greatly simplifies …

We introduce the first complete and approximately universal diagrammatic language for
quantum mechanics. We make the ZX-Calculus, a diagrammatic language introduced by …

Categorical quantum mechanics places finite-dimensional quantum theory in the context of
compact closed categories, with an emphasis on diagrammatic reasoning. In this framework …

We introduce the theory IH R of interacting Hopf algebras, parametrised over a principal
ideal domain R. The axioms of IH R are derived using Lack's approach to composing …

String diagrams turn algebraic equations into topological moves that have recurring shapes,
involving the sliding of one diagram past another. We individuate, at the root of this fact, the …

Situated as a language between computer science, quantum physics and mathematics,
tensor network theory has steadily grown in popularity and can now be found in applications …

Diagrammatic techniques for reasoning about monoidal categories provide an intuitive
understanding of the symmetries and connections of interacting computational processes. In …

In this paper, we develop a graphical calculus to rewrite photonic circuits involving light-
matter interactions and non-linear optical effects. We introduce the infinite ZW calculus, a …