An approach to constructing reversible multi-qubit benchmarks with provably minimal implementations

This paper reports on a method of the construction of new difficult benchmarks for reversible logic synthesis. It is shown how to extrapolate 3- and 4-variable reversible functions implemented by gate count minimal circuits having regular structure. In this way sequences of reversible functions of an arbitrary number of variables have been constructed for which we have built minimal circuits implementing them. For two example sequences of functions we applied the synthesis tool Revkit trying different synthesis algorithms. The outcome shows a large gap between the circuits synthesized by the tool and the ones proved minimal by construction.