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

• URL: http://arxiv.org/abs/2606.03643v1
• Date: Tue, 02 Jun 2026 13:35:31 GMT
• Title: On the local equivalence of trapped-ion two-qudit gates
• Abstract summary: We derive a necessary condition of the local equivalence between two-qudit gates in terms of singular values of transformed gate matrices.<n>We use this condition to investigate the local equivalence of two widely used trapped-ion two-qubit gates in qudit space.
• Score: 0.09320657506524145
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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