  We report the first 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 establish 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.
