Supplementarity is Necessary for Quantum Diagram Reasoning *
Abstract
The ZX-calculus is a powerful diagrammatic language for quantum mechanics and quantum information processing. We prove that its π 4-fragment is not complete, in other words the ZX-calculus is not complete for the so called "Clifford+T quantum mechanics". The completeness of this fragment was one of the main open problems in categorical quantum mechanics, a programme initiated by Abramsky and Coecke. The ZX-calculus was known to be incomplete for quantum mechanics. On the other hand, its π
Domains
Computer Science [cs]Origin | Publisher files allowed on an open archive |
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