ZX-calculus for the working quantum computer scientist

J van de Wetering - arxiv preprint arxiv:2012.13966, 2020 - arxiv.org
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 …

[BOOK][B] Categories for Quantum Theory: an introduction

C Heunen, J Vicary - 2019 - books.google.com
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 …

[HTML][HTML] Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus

R Duncan, A Kissinger, S Perdrix… - Quantum, 2020 - quantum-journal.org
We present a completely new approach to quantum circuit optimisation, based on the ZX-
calculus. We first interpret quantum circuits as ZX-diagrams, which provide a flexible, lower …

There and back again: A circuit extraction tale

M Backens, H Miller-Bakewell, G de Felice… - Quantum, 2021 - quantum-journal.org
Translations between the quantum circuit model and the measurement-based one-way
model are useful for verification and optimisation of quantum computations. They make …

A complete axiomatisation of the ZX-calculus for Clifford+ T quantum mechanics

E Jeandel, S Perdrix, R Vilmart - Proceedings of the 33rd Annual ACM …, 2018 - dl.acm.org
We introduce the first complete and approximately universal diagrammatic language for
quantum mechanics. We make the ZX-Calculus, a diagrammatic language introduced by …

A universal completion of the ZX-calculus

KF Ng, Q Wang - arxiv preprint arxiv:1706.09877, 2017 - arxiv.org
arxiv:1706.09877v1 [quant-ph] 29 Jun 2017 Page 1 arxiv:1706.09877v1 [quant-ph] 29 Jun
2017 A universal completion of the ZX-calculus Kang Feng Ng Quanlong Wang Department of …

Diagrammatic reasoning beyond Clifford+ T quantum mechanics

E Jeandel, S Perdrix, R Vilmart - Proceedings of the 33rd Annual ACM …, 2018 - dl.acm.org
The ZX-Calculus is a graphical language for diagrammatic reasoning in quantum mechanics
and quantum information theory. An axiomatisation has recently been proven to be complete …

SZX-calculus: Scalable graphical quantum reasoning

T Carette, D Horsman, S Perdrix - arxiv preprint arxiv:1905.00041, 2019 - arxiv.org
We introduce the Scalable ZX-calculus (SZX-calculus for short), a formal and compact
graphical language for the design and verification of quantum computations. The SZX …

A near-minimal axiomatisation of ZX-calculus for pure qubit quantum mechanics

R Vilmart - 2019 34th Annual ACM/IEEE Symposium on Logic …, 2019 - ieeexplore.ieee.org
Recent developments in the ZX-Calculus have resulted in complete axiomatisations first for
an approximately universal restriction of the language, and then for the whole language. The …

Completeness of graphical languages for mixed state quantum mechanics

T Carette, E Jeandel, S Perdrix, R Vilmart - ACM Transactions on …, 2021 - dl.acm.org
There exist several graphical languages for quantum information processing, like quantum
circuits, ZX-calculus, ZW-calculus, and so on. Each of these languages forms a†-symmetric …