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 …

Phase gadget synthesis for shallow circuits

A Cowtan, S Dilkes, R Duncan, W Simmons… - arxiv preprint arxiv …, 2019 - arxiv.org
We give an overview of the circuit optimisation methods used by tket, a compiler system for
quantum software developed by Cambridge Quantum Computing Ltd. We focus on a novel …

Completeness for arbitrary finite dimensions of ZXW-calculus, a unifying calculus

B Poór, Q Wang, RA Shaikh, L Yeh… - 2023 38th Annual …, 2023 - ieeexplore.ieee.org
The ZX-calculus is a universal graphical language for qubit quantum computation, meaning
that every linear map between qubits can be expressed in the ZX-calculus. Furthermore, it is …

Graphical css code transformation using zx calculus

J Huang, SM Li, L Yeh, A Kissinger, M Mosca… - arxiv preprint arxiv …, 2023 - arxiv.org
In this work, we present a generic approach to transform CSS codes by building upon their
equivalence to phase-free ZX diagrams. Using the ZX calculus, we demonstrate …

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 …

Basic ZX-calculus for students and professionals

B Coecke - arxiv preprint arxiv:2303.03163, 2023 - arxiv.org
These are the lecture notes of guest lectures for Artur Ekert's course Introduction to Quantum
Information at the Mathematical Institute of Oxford University, Hilary Term 2023. Some basic …

Kindergarden quantum mechanics graduates... or how I learned to stop gluing LEGO together and love the ZX-calculus

B Coecke, D Horsman, A Kissinger, Q Wang - Theoretical Computer …, 2022 - Elsevier
This paper is a 'spiritual child'of the 2005 lecture notes Kindergarten Quantum Mechanics
Coecke (2005)[24], which showed how a simple, pictorial extension of Dirac notation …

A complete equational theory for quantum circuits

A Clément, N Heurtel, S Mansfield… - 2023 38th Annual …, 2023 - ieeexplore.ieee.org
We introduce the first complete equational theory for quantum circuits. More precisely, we
introduce a set of circuit equations that we prove to be sound and complete: two circuits …

Completeness of the ZX-Calculus

E Jeandel, S Perdrix, R Vilmart - Logical Methods in Computer …, 2020 - lmcs.episciences.org
The ZX-Calculus is a graphical language for diagrammatic reasoning in quantum mechanics
and quantum information theory. It comes equipped with an equational presentation. We …