Scalability of Shor's algorithm with a limited set of rotation gates

Abstract

Scalability of Shor's algorithm with a limited set of rotation gates was investigated. Shor's algorithm was revised with emphasis on extracting useful output from the quantum period finding (QPF) subroutine. It was found that the length of the longest factorable integer can be related to the maximum acceptable runs of quantum period finding and the smallest accurately implementable controlled rotation gate. It was suggested that integers thousands of digits in length can be factored provided controlled rotations can be implemented.