# Complete ZX-Calculi for the Stabiliser Fragment in Odd Prime Dimensions

@inproceedings{Booth2022CompleteZF, title={Complete ZX-Calculi for the Stabiliser Fragment in Odd Prime Dimensions}, author={Robert Ivan Booth and Titouan Carette}, booktitle={MFCS}, year={2022} }

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…

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### Simplification Strategies for the Qutrit ZX-Calculus

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- 2021

The main contribution of this work is the derivation of efﬁcient rewrite strategies for the stabiliser fragment of the qutrit ZX-calculus, which constitutes a first non-trivial step towards the simplification ofqutrit quantum circuits.

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