Nuclear-spin qubit dephasing time in the integer quantum Hall effect regime

We report a theoretical estimate of the nuclear-spin dephasing time $T_2$ owing to the spin interaction with the two-dimensional electron gas, when the latter is in the integer quantum Hall state, in a two-dimensional heterojunction or quantum well at low temperature, and in large applied magnetic field. We argue that the leading mechanism of dephasing is due to the impurity potentials that influence the dynamics of the spin via virtual magnetic spin-exciton scattering. Implications of our results for implementation of nuclear spins as quantum bits (qubits) for quantum computing are discussed.