The Qupit Stabiliser ZX-travaganza: Simplified Axioms, Normal Forms and Graph-Theoretic Simplification
| Autor: | Poór, Boldizsár, Booth, Robert I., Carette, Titouan, van de Wetering, John, Yeh, Lia |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | EPTCS 384, 2023, pp. 220-264 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4204/EPTCS.384.13 |
| Popis: | We present a smorgasbord of results on the stabiliser ZX-calculus for odd prime-dimensional qudits (i.e. qupits). We derive a simplified rule set that closely resembles the original rules of qubit ZX-calculus. Using these rules, we demonstrate analogues of the spider-removing local complementation and pivoting rules. This allows for efficient reduction of diagrams to the affine with phases normal form. We also demonstrate a reduction to a unique form, providing an alternative and simpler proof of completeness. Furthermore, we introduce a different reduction to the graph state with local Cliffords normal form, which leads to a novel layered decomposition for qupit Clifford unitaries. Additionally, we propose a new approach to handle scalars formally, closely reflecting their practical usage. Finally, we have implemented many of these findings in DiZX, a new open-source Python library for qudit ZX-diagrammatic reasoning. Comment: In Proceedings QPL 2023, arXiv:2308.15489. 45 pages, lots of figures |
| Databáze: | arXiv |
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