A universal completion of the ZX-calculus
Kang Feng Ng, Quanlong Wang
TL;DR
This paper presents a universal completion of the ZX-calculus applicable to all pure qubit quantum mechanics, establishing a connection with the ZW-calculus to ensure completeness.
Contribution
It introduces a universal completion of the ZX-calculus by leveraging the completeness of the ZW-calculus and providing direct translations between them.
Findings
ZX-calculus is now universally complete for pure qubit quantum mechanics
Established direct translations between ZX and ZW-calculi
Demonstrated the completeness of the combined graphical languages
Abstract
In this paper, we give a universal completion of the ZX-calculus for the whole of pure qubit quantum mechanics. This proof is based on the completeness of another graphical language: the ZW-calculus, with direct translations between these two graphical systems.
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Taxonomy
TopicsQuantum Mechanics and Applications · Quantum Computing Algorithms and Architecture · Quantum Information and Cryptography