  The silicon-based quantum computer proposal has been one of the intensely
pursued ideas during the past three years. Here we calculate the donor electron
exchange in silicon and germanium, and demonstrate an atomic-scale challenge
for quantum computing in Si (and Ge), as the six (four) conduction band minima
in Si (Ge) lead to inter-valley electronic interferences, generating strong
oscillations in the exchange splitting of two-donor two-electron states. Donor
positioning with atomic scale precision within the unit cell thus becomes a
decisive factor in determining the strength of the exchange coupling--a
fundamental ingredient for two-qubit operations in a silicon-based quantum
computer.
