If so, why? How to create the RYY-gate in the composer?
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The $R_{YY}$ gate is not available within the Qiskit composer. This is because you can build it from other available gates within the composer. For instance, there is a nice way to represent $R_{YY}$ using the set $\{ R_{XX}, R_X, R_Y, P \}$. That is, suppose you want to implement $R_{YY}(\theta)$ then you can do it as:
Now, there is an option to add custom gate within the composer. Thus, you can embed this circuit in in as your $R_{YY}$ gate. That is one way to do it.
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$\begingroup$ Thank you so much for your explanation. It seems involves too many other gates. Seem this will occupy many hardware resources, am I right? I just touched this composer few days ago. What is the P in blue shown above? $\endgroup$ May 11, 2021 at 3:30
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$\begingroup$ Well, first note that $R_{XX}$ gate is not a native gate to the IBM hardware even though it is presented in the composer! What that means is that even the $R_{XX}$ gate must be decomposed down when run on the hardware in term of other gates (the native gates to the IBM hardware). So yes, implementing either $R_{XX}$ or $R_{YY}$ is costly. The $P$ gate is the phase gate $ P(\theta) = \begin{pmatrix} 1 & 0 \\ 0 & e^{i\theta} \end{pmatrix}$ $\endgroup$– KAJ226May 11, 2021 at 3:50