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I asked earlier Which quantum gates can we use in terms of depth?. In the question, I asked

I want to measure the depth of a circuit, but I do not know which quantum gates should be used when the circuit is decomposed.

and the answers is

depending on hardware.

If we use the quantum computer made of ion trap, what is the gate set, especially two-qubit gate? I have heard that $XX$ rotation is one of them, is it right?

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In terms of single qubit gates, ion traps rather easily can do any arbitrary rotation on the Bloch sphere - those are all straightforward to do.

For two qubit gates, most trapped ion systems use a variant of the Molmer-Sorenson gate which physically couples spin and motion. Computationally, the Molmer-Sorenson gate corresponds to an $XX$ rotation gate as you described. Although, I should mention that you can easily have a laser setup which is different and get you a Molmer-Sorenson gate which is $YY$ instead. Nonetheless, since single qubit gates are cheap and rather easy with trapped ions, you can change basis to whatever you prefer.

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  • $\begingroup$ By "$XX$ gate", I assume you don't mean $X\otimes X$ (which would not be useful), but something like $(I+iX\otimes X)/\sqrt{2}$? $\endgroup$
    – DaftWullie
    Nov 7, 2022 at 7:17
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    $\begingroup$ @DaftWullie It's an $XX$ rotation, i.e. $\exp(i\theta/2 X\otimes X)$ $\endgroup$
    – Markus Heinrich
    Nov 7, 2022 at 8:23

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