zx-calculus

ZX-calculus is a sub-field of its own. A comprehensive bibliography is available at https://zxcalculus.com. This site only includes ZX-related papers that may be relevant to programming languages and/or program verification.

Geometry of Interaction for ZX-Diagrams

ZX-Calculus is a versatile graphical language for quantum computation equipped with an equational theory. Getting inspiration from Geometry of Interaction, in this paper we propose a token-machine-based asynchronous model of both pure ZX-Calculus and …

ZX-calculus for the working quantum computer scientist

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, surface codes and lattice surgery, measurement-based quantum …

The ZX-calculus is complete for stabilizer quantum mechanics

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), meaning any pure state, unitary operation and post-selected pure projective …

Interacting Quantum Observables: Categorical Algebra and Diagrammatics

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 derivations in the area of quantum computation and information. (ii) To …