Study on Implementation of Shor’s Factorization Algorithm on Quantum Computer

Songyuan Chen, Haosen Chen, Xin Tang +2 more

Adjie Wahyu Wicaksono, Arya Wicaksana

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.

Daniel Neuenschwander

Anocha Yimsiriwattana, Samuel J. Lomonaco Jr. A

We present a distributed implementation of Shor’s quantum factoring algorithm on a distributed quantum network model. This model provides a means for small capacity quantum computers to work together in such a way as to simulate a large capacity quantum computer. In this paper, entanglement is used as a resource for implementing non-local operations between two or more quantum computers. These non-local operations are used to implement a distributed factoring circuit with polynomially many gates. This distributed version of Shor’s algorithm requires an additional overhead of O((log N) 2) communication complexity, where N denotes the integer to be factored. Keywords: Shor’s algorithm, factoring algorithm, distributed quantum algorithms, quantum circuit. 1.

Xiang-Qun Fu, Wan‐Su Bao, Chun Hua Zhou

 Fu, Xiang-Qun, Bao +3 more