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. The main goal of this paper is to test if one of these implementations is favorable when the qubit interacts with realistic environments. 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.

• Received 22 November 2012

DOI:https://doi.org/10.1103/PhysRevB.87.195309