Decision diagrams for the design of reversible and quantum circuits

Reversible circuits found great interest in the past as an alternative computation paradigm which can be beneficial e.g. for encoder circuits, low power design, adiabatic circuits, verification, and much more. Besides that, reversible circuits provide the basis for many components of quantum circuits, which by themselves emerged as a very promising computing technology that, particularly these days, gains more and more relevance. All that led to a steadily increasing demand for methods that efficiently and correctly design such circuits. Decision diagrams play an important role in the design of conventional circuitry. In the meantime, also their benefits for the design of the newly emerging reversible and quantum circuits become evident. In this overview paper, we review and illustrate past work on decision diagrams for such circuits and sketch corresponding design methods relying on them. By this, we demonstrate how broadly decision diagrams can be employed in this area and what benefits they yield for these emerging technologies.