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Please check this Rabi oscillations image1:
Now, let's say I want to create a superposition of E1 and E2, so I started an EM field tuned to a frequency related to E2-E1. But, let's say there is another energy difference E3-E1, as per the above image there is still some probability (though it will never be 1) that E1 to E3 transition might occur. Isn't it? Or is there something wrong in my understanding?
1 Source: https://commons.wikimedia.org/wiki/File:Mplwp_Rabi_oscillations.svg
Which of these transitions will occur will be governed by the operation regime of the apparatus and laser. It might happen, for example, that state 3 is unfavorable due to selection rules or it only acts as an auxiliary state. The very first step according to the D.Vincenzo's criteria is to identify and isolate the Hilbert space of the system to work with. This already implies that your operations are restricted and the energy domains too. You only perform certain operations that contribute to the q.computation and does not affect parts of the system to interfere and decohere the operating state. This is all a matter of experimental conditions.
