Generalizing the Concept of Scalable Reversible Circuit Synthesis for Multiple-Valued Logic

Research on reversible circuits has gained significance due to its application in quantum computations and many further areas such as the design of encoders. At the same time, the use of multiple-valued logic gained importance since this reduces the number of required entities in physical systems (e.g. in a future quantum computer). While most research is still conducted in the Boolean domain, there exist only few approaches which realize reversible circuits for multiple-valued logic. Moreover, most of the previously proposed solutions for synthesis of multiple-valued reversible circuits are not scalable and consider ternary (i.e. 3-valued circuits) only. Instead of overcoming these issues by developing new synthesis approaches for multiple-valued reversible circuits from scratch, we propose to utilize the recent accomplishments in the design of Boolean reversible circuits and to generalize them for multiple-valued logic. To this end, we discuss how to generalize Quantum Multiple-valued Decision Diagram based (QMDD-based) synthesis – a synthesis approach for Boolean reversible circuits which has been proven to be scalable and which has been used in several recently developed design flows. The discussions eventually show how to bridge the development gap between Boolean and multiple-valued logic for reversible circuits.