Why did it take us 50 years since the birth of the quantum mechanical formalism to discover
that unknown quantum states cannot be cloned? Yet, the proof of the 'no-cloning theorem'is …

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 …

Monoidal category theory serves as a powerful framework for describing logical aspects of
quantum theory, giving an abstract language for parallel and sequential composition, and a …

Reaction networks, or equivalently Petri nets, are a general framework for describing
processes in which entities of various kinds interact and turn into other entities. In chemistry …

This article is intended as a reference guide to various notions of monoidal categories and
their associated string diagrams. It is hoped that this will be useful not just to …

We propose a mathematical framework for a unification of the distributional theory of
meaning in terms of vector space models, and a compositional theory for grammatical types …

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 …

In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it
became clear that underlying these diagrams is a powerful analogy between quantum …

Our aim is to revisit the mathematical foundations of quantum mechanics from a novel point
of view. The standard axiomatic presentation of quantum mechanics in terms of Hilbert …

The ZX-calculus is a graphical calculus for reasoning about quantum systems and
processes. It is known to be universal for pure state qubit quantum mechanics (QM) …