  We consider the task of breaking down a quantum computation given as an
isometry into C-NOTs and single-qubit gates, while keeping the number of C-NOT
gates small. Although several decompositions are known for general isometries,
here we focus on a method based on Householder reflections that adapts well in
the case of sparse isometries. We show how to use this method to decompose an
arbitrary isometry before illustrating that the method can lead to significant
improvements in the case of sparse isometries. We also discuss the classical
complexity of this method and illustrate its effectiveness in the case of
sparse state preparation by applying it to randomly chosen sparse states.
