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In the presentation of superconducting qubits, it is often said that a non-linear inductor is what allows the present of an anharmonic oscillator. This means that because the difference between the $|0\rangle$ and $|1\rangle$ states is driven by a different frequency than what would be necessary for the jump between the $|1\rangle$ and $|2\rangle$ states, we can effectively think of it as a 2-state system.

What I don't understand is then how you produce a superposition of $|0\rangle$ and $|1\rangle$ states? I thought the system would only exist in specific energy eigenstates.

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  • $\begingroup$ "I thought the system would only exist in specific energy eigenstates." Why? $\endgroup$
    – d_b
    Nov 14, 2021 at 3:53
  • $\begingroup$ let's say it starts out in ground state -- you can apply a pulse of $w_10$ to move it up to the 1st energy eigenstate. how can you construct a specific super position of the two? $\endgroup$ Nov 14, 2021 at 4:01
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    $\begingroup$ Have the pulse be in a superposition of present and absent states, and then your qubit will be in a superposition of transitioned and not-transitioned states. If your pulse is photonic, use a beam splitter to get the superposition. $\endgroup$
    – Ruslan
    Nov 14, 2021 at 8:38

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