The shortest path method for quantum Boolean circuits construction

Abstract

At present, only the exhaustive synthesis algorithm can find all the optimal quantum Boolean circuits. It is more difficult to synthesize a more complicated quantum Boolean circuit. In this paper, we use the method of circuit bipartition to partition a more complicated quantum Boolean circuit into simpler circuits in order to reduce the difficulty of the more complicated quantum Boolean circuit synthesis. And find these partitioned quantum Boolean circuits by searched the database of quantum Boolean circuits according the method of the shortest path in the circuit. Finally, combine these partitioned circuits to become the more complicated quantum Boolean circuit. This approach can significantly reduce the synthesis complexity of a more complicated quantum Boolean circuit. We can see that the results are very close to the optimal circuits according to the experimental results of all the 3-variable reversible functions.