Decision Diagrams for Quantum Computing

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.