Suppose we are tasked to design a quantum harmonic oscillator having well-defined flux states, which of the following energy scale relation regimes will you choose?

What is the average flux carried by the first excited state of the quantum LC oscillator with resonant frequency ω0=(2π)×2GHz{“version”:”1.1″,”math”:”\(\omega_0 = (2\pi) \times 2 \, \text{GHz}\)”} ? Note that Φ0{“version”:”1.1″,”math”:”\(\Phi_0\) “} denotes the flux quantum.

We have seen that to design a two-qubit gate, two transmon qubits are capacitively coupled giving rise to a transverse coupling between the two transmon qubits. When on-resonance, the Hamiltonian of this interaction in the rotating wave approximation is given by H=g{“version”:”1.1″,”math”:”\(H = g \)”}. What is the final state of the two qubits starting from the initial state is |10⟩{“version”:”1.1″,”math”:”\(\vert 1 0 \rangle\)”} when the time duration for which the transmons are in-resonance is t=π/(4g){“version”:”1.1″,”math”:”\(t=\pi/(4g)\)”}?

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