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Open Quantum Systems Decoherence
Quantum Simulation
Algebraic complete axiomatisation of ZX-calculus with a normal form via elementary matrix operations
arXiv
Authors: Quanlong Wang
Year
2020
Paper ID
21951
Status
Preprint
Abstract Read
~2 min
Abstract Words
82
Citations
N/A
Abstract
In this paper we give a complete axiomatisation of qubit ZX-calculus via elementary transformations which are basic operations in linear algebra. This formalism has two main advantages. First, all the operations of the phases are algebraic ones without trigonometry functions involved, thus paved the way for generalising complete axiomatisation of qubit ZX-calculus to qudit ZX-calculus and ZX-calculus over commutative semirings. Second, we characterise elementary transformations in terms of ZX diagrams, so a lot of linear algebra stuff can be done purely diagrammatically.
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- In this paper we give a complete axiomatisation of qubit ZX-calculus via elementary transformations which are basic operations in linear algebra.
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