Nuclear-spin qubit interactions in a heterostructure can be mediated via the bound outer electrons of impurity atoms whose nuclear spins 1/2 are the qubits. These outer electrons, in turn, interact via the two-dimensional electron gas in the quantum Hall effect regime. We devised a quantum computing scheme, based on this mechanism, with qubit separation of order 0.1 µm, attainable with the present-day semiconductor device technologies, and retaining all the gate-control and measurement aspects of earlier nuclear-spin quantum computing proposals.