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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.
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