A simplification strategy for ZX-diagrams is given based on the two graph transformations of local complementation and pivoting and it is shown that the resulting reduced diagram can be transformed back into a quantum circuit.Expand

This paper introduces PyZX, an open source library for automated reasoning with large ZX-diagrams, and shows how PyZX implements methods for circuit optimisation, equality validation, and visualisation and how it can be used in tandem with other software.Expand

This review discusses Clifford computation and graphically prove the Gottesman-Knill theorem, a recently introduced extension of the ZX-calculus that allows for convenient reasoning about Toffoli gates, and the recent completeness theorems that show that, in principle, all reasoning about quantum computation can be done using Zx-diagrams.Expand

A new method for reducing the number of T-gates in a quantum circuit based on the ZX-calculus is presented, which matches or beats previous approaches to T-count reduction on the majority of benchmark circuits in the ancilla-free case, in some cases yielding up to 50% improvement.Expand

This work gives the first circuit-extraction algorithm to work for one-way computations containing measurements in all three planes and having gflow, and brings together several known rewrite rules for measurement patterns and formalise them in a unified notation using the ZX-calculus.Expand

This paper establishes a correspondence between the ZH-calculus and the path-sum formalism, a technique recently introduced by Amy to verify quantum circuits, and finds a bijection between certain canonical forms of Zh-diagrams and path-Sum expressions.Expand

There is a long history of representing a quantum state using a quasi-probability distribution: a distribution allowing negative values. In this paper we extend such representations to deal withâ€¦ Expand

The ZX-calculus is a convenient formalism for expressing and reasoning about quantum circuits at a low level, whereas the recently-proposed ZH-calculus yields convenient expressions of mid-levelâ€¦ Expand

The fragment of the ZH-calculus that is phase-free is studied, and thus is closer aligned to physically implementable maps and the completeness result follows by reducing to Vilmart's rule-set for the phase- free $\Delta$ZX-Calculus.Expand

An often used model for quantum theory is to associate to every physical system a Câˆ—-algebra. From a physical point of view it is unclear why operator algebras would form a good description ofâ€¦ Expand