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arXiv · 2606.03643

On the local equivalence of trapped-ion two-qudit gates

Nikita V. Semenin·Pavel A. Kamenskikh·Ilia V. Zalivako·Anastasiia S. Nikolaeva·Evgeniy O. Kiktenko
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Abstract

We derive a necessary condition of the local equivalence between two-qudit gates in terms of singular values of transformed gate matrices. This condition is valid for arbitrary qudit dimensions $d$ and is thus a relatively simple general way of checking whether two gates can be reduced to one another with single-qudit (local) gates. We use this condition to investigate the local equivalence of two widely used trapped-ion two-qubit gates in qudit space: the Molmer-Sorensen (MS) gate and a special case of the Light-Shift (LS) gate, both of which we studied in one of our previous works.

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Nikita V. Semenin, Pavel A. Kamenskikh, Ilia V. Zalivako, Anastasiia S. Nikolaeva, Evgeniy O. Kiktenko. 2026-06-02. On the local equivalence of trapped-ion two-qudit gates. https://arxiv.org/abs/2606.03643

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