The ZX calculus is incomplete for quantum mechanics
نویسندگان
چکیده
Backens recently proved that the ZX-calculus is complete for an important subset of quantum mechanics, namely stabilizer quantum mechanics, i.e. that for stabilizer quantum mechanics, any equation that can be shown to hold in the Dirac formalism can also be shown to hold within the ZX-calculus[2]. For her proof, she relied on operations on a special class of quantum states, namely graph states. This paper adresses the question of whether the ZX-calculus is complete for the whole of quantum mechanics, and the answer is found to be negative.
منابع مشابه
The ZX Calculus is incomplete for Clifford+T quantum mechanics
The ZX calculus is a diagrammatic language for quantum mechanics and quantum information processing. We prove that the ZX-calculus is not complete for the Clifford+T quantum mechanics. The completeness for this fragment has been stated as one of the main current open problems in categorical quantum mechanics [8]. The ZX calculus was known to be incomplete for quantum mechanics [7], on the other...
متن کاملSupplementarity is Necessary for Quantum Diagram Reasoning
The ZX-calculus is a powerful diagrammatic language for quantum mechanics and quantum information processing. We prove that its π4 -fragment is not complete, in other words the ZXcalculus 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 Coe...
متن کاملA Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics
We introduce the first complete and approximatively universal diagrammatic language for quantum mechanics. We make the ZX-Calculus, a diagrammatic language introduced by Coecke and Duncan, complete for the so-called Clifford+T quantum mechanics by adding four new axioms to the language. The completeness of the ZX-Calculus for Clifford+T quantum mechanics was one of the main open questions in ca...
متن کاملThe ZX-calculus is complete for stabilizer quantum mechanics
The ZX-calculus is a graphical calculus for reasoning about quantum systems and processes. It is known to be universal for pure state qubit quantum mechanics (QM), meaning any pure state, unitary operation and post-selected pure projective measurement can be expressed in the ZX-calculus. The calculus is also sound, i.e. any equality that can be derived graphically can also be derived using matr...
متن کامل