  The quantum multicomputer consists of a large number of small nodes and a
qubus interconnect for creating entangled state between the nodes. The primary
metric chosen is the performance of such a system on Shor's algorithm for
factoring large numbers: specifically, the quantum modular exponentiation step
that is the computational bottleneck. This dissertation introduces a number of
optimizations for the modular exponentiation. My algorithms reduce the latency,
or circuit depth, to complete the modular exponentiation of an n-bit number
from O(n^3) to O(n log^2 n) or O(n^2 log n), depending on architecture.
Calculations show that these algorithms are one million times and thirteen
thousand times faster, when factoring a 6,000-bit number, depending on
architecture. Extending to the quantum multicomputer, five different qubus
interconnect topologies are considered, and two forms of carry-ripple adder are
found to be the fastest for a wide range of performance parameters. The links
in the quantum multicomputer are serial; parallel links would provide only very
modest improvements in system reliability and performance. Two levels of the
Steane [[23,1,7]] error correction code will adequately protect our data for
factoring a 1,024-bit number even when the qubit teleportation failure rate is
one percent.
