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This talk will describe the simulation, design and optimization of a qubit

for use in quantum communication or quantum computation. The qubit is

realized as the spin of a single trapped electron in a semi-conductor

quantum dot. The quantum dot and a quantum wire are formed by the

combination of quantum wells and gates. The design goal for this system is a

"double pinchoff", in which there is a single trapped electron in the dot

and a single (or small number of) conduction states in the wire. Because of

considerable experimental uncertainty in the system parameters, the optimal

design should be "robust", in the sense that it is far away from

unsuccessful designs. We use a Poisson-Schrodinger model for the

electrostatic potential and electron wave function and a semi-analytic

solution of this model. Through a Monte Carlo search, aided by an analysis

of singular points on the design boundary, we find successful designs and

optimize them to achieve maximal robustness.