Inductance effects in the persistent current qubit

A general method is illustrated to show that the Hamiltonian for circuits o f Josephson junctions can be expanded in terms of three Hamiltonians: a Ham iltonian representative of the inductance-free circuit, a Hamiltonian in th e form of an harmonic oscillator for the inductance effects of the circulat ing currents, and a small correction term. This method is used to show that the inductive effects are a small correction to the difference in energy l evels in the persistent current qubit.