# How does a superconducting qubit exists in the superposition of $|0\rangle$ and $|1\rangle$ states?

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.

• "I thought the system would only exist in specific energy eigenstates." Why?
– d_b
Nov 14, 2021 at 3:53
• 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? Nov 14, 2021 at 4:01
• 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. Nov 14, 2021 at 8:38