Nonadditivity of decoherence rates in superconducting qubits

We show that the relaxation and decoherence rates T₁⁻¹ and T₂⁻¹ of a qubit coupled to several noise sources are in general not additive, i.e., that the total rates are not the sums of the rates due to each individual noise source. To demonstrate this, we calculate the relaxation and pure dephasing rates T₁⁻¹ and T_ϕ⁻¹ of a superconducting (SC) flux qubit in the Born-Markov approximation in the presence of several circuit impedances Z_i using network graph theory and determine their deviation from additivity (the mixing term). We find that there is no mixing term in T_ϕ⁻¹ and that the mixing terms in T₁⁻¹ and T₂⁻¹ can be positive or negative, leading to reduced or enhanced relaxation and decoherence times T₁ and T₂. The mixing term due to the circuit inductance L at the qubit transition frequency ω₀₁ is generally of second order in ω₀₁L∕Z_i, but of third order if all impedances Z_i are pure resistances. We calculate T_1,2 for an example of a SC flux qubit coupled to two impedances.