  We present a systematic and realistic simulation for single and double
phosphorous donors in a silicon-based quantum computer design. A two-valley
equation is developed to describe the ground state of phosphorous donors in
strained silicon quantum well (QW), with the central cell effect treated by a
model impurity potential. We find that the increase of quantum well confinement
leads to shrinking charge distribution in all 3 dimensions. Using an
unrestricted Hartree-Fock method with Generalized Valence Bond (GVB)
single-particle wave functions, we are able to solve the two-electron
Sch${\ddot o}$dinger equation with quantum well confinement and realistic gate
potentials. The effects of QW width, gate voltages, donor separation, and donor
position are calculated and analyzed. The gate tunability and gate fidelity are
defined and evaluated, for a typical QC design. Estimates are obtained for the
duration of $\sqrt{SWAP}$ gate operation and the required accuracy in voltage
control. A strong exchange oscillation is observed as both donors are shifted
along [001] axis but with their separation unchanged. Applying a gate potential
tends to suppress the oscillation. The exchange oscillation as a function of
donor position along [100] axis is found to be completely suppressed as the
donor separation is decreased. The simulation presented in this paper is of
importance to the practical design of an exchange-based silicon quantum
computer.
