Progress towards constructing sequences of benchmarks for quantum Boolean circuits synthesis

In this paper, a method for constructing sequences of reversible functions of large number of variables is presented. First, by using our database of all minimal reversible circuits for 3-variable reversible functions, and our tool for designing minimal circuits for 4-variable reversible functions, circuits with structural regularities are searched for. The aim is to find a pair, 3- and 4-variable functions, having similar permutation cycle structures, for which there exist minimal circuits with the same kind of structural regularity. After finding such a pair we are extrapolating the selected structural regularities to circuits of higher number of inputs. Then, cycle structure properties of the functions implemented by the extrapolated circuits are checked for similarity to the previously found pair. In this way, we have found many sequences of reversible functions having similar properties. The approach is promising for constructing benchmarks of large size for which minimal or nearly minimal circuits are known.