We describe a quantum information processor (quantum computer) based on the hyperfine interactions between the conduction electrons and nuclear spins embedded in a two-dimensional electron system in the quantum-Hall regime. Nuclear spins can be controlled individually by electromagnetic pulses. Their interactions, which are of the spin-exchange RKKY type, can be effectively switched on and off pair-wise dynamically, for nearest neighbors, by controlling impurities. We also propose the way to feed in the initial data and explore possibilities for reading off the final results. Owing to rapid advances in the experimental facilities, the proposed quantum-computer realization will likely be experimentally accessible in near future.