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Summary form only given. We give a theoretical description of how a prototype quantum computer using a single dot would function. The basic element of a quantum computer is represented by a quantum unit of information, or qubit. In our case, the presence and absence of the exciton in a quantum dot constitutes a qubit and the up and down spin excitons in the same dot yield two qubits with a strong mutual interaction. With laser control of these two excitons in a dot, we have the makings of a two-qubit quantum computer.