Prime number factorization is a problem in computer science where the solution to that problem takes super-polynomial time classically. Shor’s quantum factoring algorithm is able to solve the problem in polynomial time by harnessing the power of quantum computing. The implementation of the quantum algorithm itself is not detailed by Shor in his paper. In this paper, an approach and experiment to implement Shor’s quantum factoring algorithm are proposed. The implementation is done using Python and a quantum computer simulator from ProjectQ. The testing and evaluation are completed in two computers with different hardware specifications. User time of the implementation is measured in comparison with other quantum computer simulators: ProjectQ and Quantum Computing Playground. This comparison was done to show the performance of Shor’s algorithm when simulated using different hardware. There is a 33% improvement in the execution time (user time) between the two computers with the accuracy of prime factorization in this implementation is inversely proportional to the number of qubits used. Further improvements upon the program that has been developed for this paper is its accuracy in terms of finding the factors of a number and the number of qubits used, as previously mentioned.

Quantum algorithms are well-known for their quadratic if not exponential speedup over their classical counterparts. The two widely-known quantum algorithms are Shor's quantum factoring algorithm and Grover's quantum search algorithm. Shor's quantum factoring algorithm could perform integer factorization in O(logN). Grover's quantum search algorithm could solve the unsorted search problem in O(√N). However, both algorithms are introduced as theoretical concepts in the original papers due to the limitations of quantum technology at that time. In this paper, an improved way is presented to realize the two algorithms into a web application using state-of-the-art quantum technology. The web-app is designed and built considering the uses of a quantum simulator and libraries provided by ProjectQ and Rigetti Forest. The result shows that both algorithms are realizable into web-applications.