  This thesis deals with a series of quantum computer implementation issues
from the Kane 31P in 28Si architecture to Shor's integer factoring algorithm
and beyond. The discussion begins with simulations of the adiabatic Kane CNOT
and readout gates, followed by linear nearest neighbor implementations of
5-qubit quantum error correction with and without fast measurement. A linear
nearest neighbor circuit implementing Shor's algorithm is presented, then
modified to remove the need for exponentially small rotation gates. Finally, a
method of constructing optimal approximations of arbitrary single-qubit
fault-tolerant gates is described and applied to the specific case of the
remaining rotation gates required by Shor's algorithm.
