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I saw that qiskit was just incorporated in a trapped ion device.

I transpiled my circuit to 2 backends: ibm superconducting device and aqt trapped ion device. I noticed that for ibm, the $X$ gate is transpiled into $U_3(\pi,0,\pi)$, whereas for aqt it is $R_x(-\pi)$.

Since both objectives of them are to take $0$ to $1$, why do they use a different quantum gate to do that?

By the way, for the aqt device, $H$ gate $= R_y(\pi/2)R_x(\pi)$. I was wondering, why are the two representations equal?

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A particular gate's implementation is intrinsically tied to the underlying architecture. A U3 gate on IBM's superconducting backends is just a combination of 3 rotations alternatively around just two axes (for example rotate around X-axis, then Y-axis and then again X-axis; there are several other combinations to choose from). In fact this is the most general way in which you could take one point on a bloch sphere to any other point on it. In essence, that's what a U3 gate's signature means.

Now, to answer why this implementation of rotation varies on different backengs, here are my thoughts:

  1. We'd like to keep the noise minimal while making any of those rotations. You might want to read more about how a Z gate is implemented on IBM's superconducting systems (It's virtually free of any noise). I'm not so well-wersed with Trapped-Ion device's transpiled code so can't comment on it's optimality.
  2. I believe it could also have something to do with keeping gate abstractions intuitive enough for programmers which might give rise to different signatures for different backends.
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