Non-additivity of decoherence rates in superconducting qubits

TL;DR

This paper demonstrates that relaxation and decoherence rates in superconducting qubits are generally not additive when multiple noise sources are present, revealing complex interactions that affect qubit coherence times.

Contribution

The study provides a detailed calculation of non-additive decoherence rates in superconducting flux qubits due to multiple circuit impedances, introducing the concept of mixing terms.

Findings

Mixing terms in 1/T_1 and 1/T_2 can be positive or negative.

No mixing term exists in 1/T_.

The magnitude of mixing terms depends on circuit parameters.

Abstract

We show that the relaxation and decoherence rates 1/T_1 and 1/T_2 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 1/T_1 and 1/T_\phi 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 1/T_\phi and that the mixing terms in 1/T_1 and 1/T_2 can be positive or negative, leading to reduced or enhanced relaxation and decoherence times T_1 and T_2. The mixing term due to the circuit inductance L at the qubit transition frequency \omega_{01} is generally of second order in \omega_{01}L/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.