Decoherence rates in complex Josephson qubit circuits

A complete analysis of the decoherence properties of a Josephson junction qubit is presented. The qubit is of the flux type and consists of two large loops forming a gradiometer, one small loop, and three Josephson junctions. We develop a complete, quantitative description of the inductances and capacitances of the circuit. Including two stray capacitances makes the quantum mechanical modeling of the system five dimensional. To make the required calculation tractable, we devise a general Born-Oppenheimer approximation which reduces the effective dimensionality in the calculation to one. Contributions to relaxation (T₁) and dephasing (T_ϕ) arising from two different control circuits, one coupled to the small loop and one coupled to a large loop, is computed. We explore T₁ and T_ϕ along an optimal line in the space of applied fluxes; along this “S line” we see significant and rapidly varying contributions to the decoherence parameters, primarily from the circuit coupling to the large loop.