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A complete analysis of the decoherence properties of a Josephson junctionqubit is presented. The qubit is of the flux type and consists of two largeloops forming a gradiometer and one small loop, and three Josephson junctions.The contributions to relaxation (T_1) and dephasing (T_\phi) arising from twodifferent control circuits, one coupled to the small loop and one coupled to alarge loop, is computed. We use a complete, quantitative description of theinductances and capacitances of the circuit. Including two stray capacitancesmakes the quantum mechanical modeling of the system five dimensional. Wedevelop a general Born-Oppenheimer approximation to reduce the effectivedimensionality in the calculation to one. We explore T_1 and T_\phi along anoptimal line in the space of applied fluxes; along this "S line" we seesignificant and rapidly varying contributions to the decoherence parameters,primarily from the circuit coupling to the large loop.Comment: 16 pages, 20 figures; v2: minor revisio

Decoherence rates in complex Josephson qubit circuits