A universal completion of the ZX-calculus

2017/06/29 by Kang Feng Ng, Quanlong Wang, Ng, Kang Feng +1 · 4 citations
Computer Science · Physics and Astronomy · #Category Theory (math.CT) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Logic in Computer Science (cs.LO) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.1706.09877

openalex publication_date 2017/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Completeness for Fault Equivalence of Clifford ZX Diagrams
• A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics
• A Complete and Natural Rule Set for Multi-Qutrit Clifford Circuits
• Kindergarden quantum mechanics graduates (...or how I learned to stop gluing LEGO together and love the ZX-calculus)
• When Only Topology Matters

Related

• A Near-Optimal Axiomatisation of ZX-Calculus for Pure Qubit Quantum\n Mechanics
• Completeness of the ZX-calculus
• ZX-calculus is Complete for Finite-Dimensional Hilbert Spaces
• Completeness and the ZX-calculus
• Completeness of the ZX-calculus for Pure Qubit Clifford+T Quantum Mechanics