Abstract There are two elementary superconducting qubit types that derive directly from the quantum harmonic oscillator. In one, the inductor is replaced by a nonlinear Josephson junction to realize the widely used charge qubits with a compact phase variable and a discrete charge wave function. In the other, the junction is added in parallel, which gives rise to an extended phase variable, continuous wave functions, and a rich energy-level structure due to the loop topology.
