  A quantum computer consists of a set of quantum bits upon which operations
called gates are applied to perform computations. In order to perform quantum
algorithms, physicists would like to design arbitrary gates to apply to quantum
bits. However, the physical limitations of the quantum computing device
restrict the set of gates that physicists are able to apply. Thus, they must
compose a sequence of gates from the permitted gate set, which approximates the
gate they wish to apply - a process called quantum compiling.
  Austin Fowler proposes a method that finds optimal gate sequences in
exponential time, but which is tractable for common problems. In this paper, I
present several optimizations to this algorithm. While my optimizations do not
improve its overall exponential behavior, they improve its empirical
performance by one to two orders of magnitude.
