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.