Now I have understood that physical implementation of quantum computer need a universal quantum gate set like Clifford+T to realize any unitary quantum gate. However, I don't know if it is all the same gate sets for different physical implementation of quantum computer. For example, if the trapped ion and photonic implementation of quantum computer own the same universal quantum gate set. On the other hand, can the quantum computer of IBM and Google implement the same universal quantum gate?
I am interested in quantum simulator now, and I know that any unitary quantum gate will be decomposed into single qubit gate, and this process is done in simulator. After that, the simulation will send the after-decomposed single qubit gate into backend, which is a really physical implementation of quantum computer or emulator of classical computer and during this procedure the single qubit gates will be decomposed approximately into a sequence of gates within the universal quantum gates.
I don't know if my understanding of this issue is right.