  Simulating quantum circuits on classical computers is a notoriously hard, yet
increasingly important task for the development and testing of quantum
algorithms. In order to alleviate this inherent complexity, efficient data
structures and methods such as tensor networks and decision diagrams have been
proposed. However, their efficiency heavily depends on the order in which the
individual computations are performed. For tensor networks the order is defined
by so-called contraction plans and a plethora of methods has been developed to
determine suitable plans. On the other hand, simulation based on decision
diagrams is mostly conducted in a straight-forward, i.e., sequential, fashion
thus far. In this work, we study the importance of the path that is chosen when
simulating quantum circuits using decision diagrams and show, conceptually and
experimentally, that choosing the right simulation path can make a vast
difference in the efficiency of classical simulations using decision diagrams.
We propose an open-source framework (available at github.com/cda-tum/ddsim)
that not only allows to investigate dedicated simulation paths, but also to
re-use existing findings, e.g., obtained from determining contraction plans for
tensor networks. Experimental evaluations show that translating strategies from
the domain of tensor networks may yield speedups of several factors compared to
the state of the art. Furthermore, we design a dedicated simulation path
heuristic that allows to improve the performance even further -- frequently
yielding speedups of several orders of magnitude. Finally, we provide an
extensive discussion on what can be learned from tensor networks and what
cannot.
