  We analyze the influence of noise for qubits implemented using a triple
quantum dot spin system. We give a detailed description of the physical
realization and develop error models for the dominant external noise sources.
We use a Davies master equation approach to describe their influence on the
qubit. The triple dot system contains two meaningful realizations of a qubit:
We consider a subspace and a subsystem of the full Hilbert space to implement
the qubit. We test the robustness of these two implementations with respect to
the qubit stability. When performing the noise analysis, we extract the initial
time evolution of the qubit using a Nakajima-Zwanzig approach. We find that the
initial time evolution, which is essential for qubit applications, decouples
from the long time dynamics of the system. We extract probabilities for the
qubit errors of dephasing, relaxation and leakage. Using the Davies model to
describe the environment simplifies the noise analysis. It allows us to
construct simple toy models, which closely describe the error probabilities.
