Characterizing noisy one-qubits gates

We develop an analytical description for the average dynamics of a noisy one-qubit gate. In particular we will describe a laser with phase noise or equivalently the effect of having an unshielded two-level system with fluctuating magnetic fields. We use this analytical approach to give better input in minimization schemes for quantum process tomography in the presence of additional projection noise. Also we use this approximation to predict the gate infidelity of real lasers from its experimental PSD.