We had a fairly detailed study of a mechanical simple harmonic oscillator in the previous chapter. The most important thing we have learned was to promote a pair of conjugate variables to operators ( \(\hat {x}\) and \(\hat {p}\) in the mechanical SHO). They have a special commutation relationship resulting in quantization as we saw. The same idea is not limited to the mechanical SHO. In other problems, they have their own conjugate variables. For example, in an electrical circuit, charge and flux are one of the conjugate variable pairs. In this chapter, we will apply the procedure in the previous chapter to a simple circuit, the LC tank, and quantize it. This forms the foundation of a superconducting qubit. We will also appreciate why a dilution refrigerator is necessary to operate a superconducting qubit.