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 …
B Coecke, R Duncan - New Journal of Physics, 2011 - iopscience.iop.org
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 …
A Hadzihasanovic - arXiv preprint arXiv:1709.08086, 2017 - arxiv.org
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 …