Charge noise induced spin decoherence in a double quantum dot: Effects of a micromagnet

Charge noise is one of the largest error source preventing the high-fidelity quantum computing in semiconductor systems. We study the decoherence of an electron spin in a double quantum dot in the presence of an inhomogeneous magnetic field and induced by a non-Markovian charge noise. We derive a master equation based on the stochastic Schrodinger equation. By analyzing the physical process represented by each term in the master equation, we show how the properties of the charge noise affect spin decoherence and how an orbital charge noise affects the spin dynamics through the inhomogeneous magnetic field. We find that a longer correlation time can slow down spin decoherence, particularly during the early stage of an evolution. A relation between the spin relaxation rate and the gradient of the magnetic field is given. The stochastic approach used to derive master equation can be also extended to other semiconductor systems in the presence of charge noise. Our results present a systematic approach to study decoherence processes caused by charge noise, particularly for quantum dots in an inhomogeneous magnetic field.