  Due to the significant progress made in the implementation of quantum
hardware, efficient methods and tools to design corresponding algorithms become
increasingly important. Many of these tools rely on functional representations
of certain building blocks or even entire quantum algorithms which, however,
inherently exhibit an exponential complexity. Although several alternative
representations have been proposed to cope with this complexity, the
construction of those representations remains a bottleneck. In this work, we
propose solutions for efficiently constructing representations of quantum
functionality based on the idea of conducting as many operations as possible on
as small as possible intermediate representations -- using Decision Diagrams as
a representative functional description. Experimental evaluations show that
applying these solutions allows to construct the desired representations
several factors faster than with state-of-the-art methods. Moreover, if
repeating structures (which frequently occur in quantum algorithms) are
explicitly exploited, exponential improvements are possible -- allowing to
construct the functionality of certain algorithms within seconds, whereas the
state of the art fails to construct it in an entire day.
