  Quantum computing promises to solve some important problems faster than
conventional computations ever could. Currently available NISQ devices on which
first practical applications are already executed demonstrate the potential --
with future fault-tolerant quantum hardware for more demanding applications on
the horizon. Nonetheless, the advantages in computing power come with
challenges to be addressed in the design automation and software development
community. In particular, non-quantum representations of states and operations,
which provide the basis, e.g., for quantum circuit simulation or verification,
require an exponential amount of memory. We propose to use decision diagrams as
data structure to conquer the exponential memory requirements in many cases. In
this chapter, we review the fundamentals on decision diagrams and highlight
their applicability in the tasks of quantum circuit simulation with and without
errors as well as in verification of quantum circuits. The tools presented here
are all available online as open source projects.
