Speed improvement of the quantum factorization algorithm of P. Shor by upgrade its classical part

¹ Don state technical University, Rostov–on–Don, 1, Gagarin square, Russia
² Southern Federal University, Taganrog, Taganrog, 44, per. Nekrasovsky, Rostov region, Russia
³ Institute of artificial intelligence problems, 118B, Artyom street, Donetsk, Ukraine

^* Corresponding author: chia2002@inbox.ru

Abstract

This report discusses Shor’s quantum factorization algorithm and ρ–Pollard’s factorization algorithm. Shor’s quantum factorization algorithm consists of classical and quantum parts. In the classical part, it is proposed to use Euclidean algorithm, to find the greatest common divisor (GCD), but now exist large number of modern algorithms for finding GCD. Results of calculations of 8 algorithms were considered, among which algorithm with lowest execution rate of task was identified, which allowed the quantum algorithm as whole to work faster, which in turn provides greater potential for practical application of Shor’s quantum algorithm. Standard quantum Shor’s algorithm was upgraded by replacing the binary algorithm with iterative shift algorithm, canceling random number generation operation, using additive chain algorithm for raising to power. Both Shor’s algorithms (standard and upgraded) are distinguished by their high performance, which proves much faster and insignificant increase in time in implementation of data processing. In addition, it was possible to modernize Shor’s quantum algorithm in such way that its efficiency turned out to be higher than standard algorithm because classical part received an improvement, which allows an increase in speed by 12%.