  Coherent rotations of single spin-based qubits may be accomplished
electrically at fixed Zeeman energy with a qubit defined solely within a single
electrostatically-defined quantum dot; the $g$-factor and the external magnetic
field are kept constant. All that is required to be varied are the voltages on
metallic 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-dimensional
potential well. Rotations are created by altering the direction of the
pseudomagnetic field through changes in the shape of the confinement potential.
By deriving an exact analytic solution to the long-range Coulomb interaction
matrix elements, we calculate explicitly the range of magnitudes and directions
the pseudomagnetic field can take. Numerical estimates are given for {GaAs}.
