Qufinite ZX-calculus: a unified framework of qudit ZX-calculi
- URL: http://arxiv.org/abs/2104.06429v5
- Date: Mon, 19 Sep 2022 17:20:29 GMT
- Title: Qufinite ZX-calculus: a unified framework of qudit ZX-calculi
- Authors: Quanlong Wang
- Abstract summary: We generalise qubit ZX-calculus to qudit ZX-calculus in any finite dimension.
We propose a graphical formalism called qufinite ZX-calculus as a unified framework for all qudit ZX-calculi.
- Score: 0.3655021726150367
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: ZX-calculus is graphical language for quantum computing which usually focuses
on qubits. In this paper, we generalise qubit ZX-calculus to qudit ZX-calculus
in any finite dimension by introducing suitable generators, especially a
carefully chosen triangle node. As a consequence we obtain a set of rewriting
rules which can be seen as a direct generalisation of qubit rules, and a normal
form for any qudit vectors. Based on the qudit ZX-calculi, we propose a
graphical formalism called qufinite ZX-calculus as a unified framework for all
qudit ZX-calculi, which is universal for finite quantum theory due to a normal
form for matrix of any finite size. As a result, it would be interesting to
give a fine-grained version of the diagrammatic reconstruction of finite
quantum theory [Selby2021reconstructing] within the framework of qufinite
ZX-calculus.
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