Optimizing Shor’s algorithm through approximate fractions for quantum factorization

This paper presents a way to increase the success of Shor's algorithm by applying a well-known procedure to the results. The work leverages the continued fractions algorithm, a key component of Shor’s algorithm, to find close approximations when the initial estimation is insufficient. Factorization may still be achieved with these close fractions if their denominators are multiples of the exact fraction denominator. By implementing this approach with Qiskit and Beauregard’s version of Shor’s algorithm, we demonstrate a significant enhancement in its success rate in a quantum computer.