A universal completion of the ZX-calculus

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.

29 pages

References in corpus (1)

• The ZX-calculus is incomplete for quantum mechanics

Cited by in corpus (10)

• The algebra of entanglement and the geometry of composition
• Optimising Clifford Circuits with Quantomatic
• ZX-calculus for the working quantum computer scientist
• Relating Measurement Patterns to Circuits via Pauli Flow
• Completeness for arbitrary finite dimensions of ZXW-calculus, a unifying calculus
• Graphical Fourier Theory and the Cost of Quantum Addition
• Completeness of the Phase-free ZH-calculus
• Complete ZX-calculi for the stabiliser fragment in odd prime dimensions
• Kindergarden quantum mechanics graduates (...or how I learned to stop gluing LEGO together and love the ZX-calculus)
• Quantum Theory from Principles, Quantum Software from Diagrams