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Coherent rotations of single spin-based qubits may be accomplishedelectrically at fixed Zeeman energy with a qubit defined solely within a singleelectrostatically-defined quantum dot; the $g$-factor and the external magneticfield are kept constant. All that is required to be varied are the voltages onmetallic gates which effectively change the shape of the elliptic quantum dot.The pseudospin-1/2 qubit is constructed from the two-dimensional $S=1/2$,$S_z=-1/2$ subspace of three interacting electrons in a two-dimensionalpotential well. Rotations are created by altering the direction of thepseudomagnetic field through changes in the shape of the confinement potential.By deriving an exact analytic solution to the long-range Coulomb interactionmatrix elements, we calculate explicitly the range of magnitudes and directionsthe pseudomagnetic field can take. Numerical estimates are given for {GaAs}.

Coherent rotations of a single spin-based qubit in a single quantum dot at fixed Zeeman energy