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arXiv · 2204.12531

Complete ZX-calculi for the stabiliser fragment in odd prime dimensions

Robert I. Booth·Titouan Carette
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Abstract

We introduce a family of ZX-calculi which axiomatise the stabiliser fragment of quantum theory in odd prime dimensions. These calculi recover many of the nice features of the qubit ZX-calculus which were lost in previous proposals for higher-dimensional systems. We then prove that these calculi are complete, i.e. provide a set of rewrite rules which can be used to prove any equality of stabiliser quantum operations. Adding a discard construction, we obtain a calculus complete for mixed state stabiliser quantum mechanics in odd prime dimensions, and this furthermore gives a complete axiomatisation for the related diagrammatic language for affine co-isotropic relations.

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Robert I. Booth, Titouan Carette. 2022-04-26. Complete ZX-calculi for the stabiliser fragment in odd prime dimensions. https://doi.org/10.4230/lipics.mfcs.2022.24

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