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

Larissa Cherckesova,Olga Safaryan,Pavel Razumov,Yuriy Ivanov,Ivan Smirnov,Irina Pilipenko,V Breskich,Y Dreizis,A Zheltenkov

doi:10.1051/e3sconf/202022401016

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%.

Highlights

Today, the field of quantum computations is gradually becoming the leader of information technology and calculations
Scientific researchers are paying increasing attention to super-modern computational model based on the notion of qubit designed to supplant the long–known model that has been used in almost all computer hardware and based on the notion of bit, developed by A
Based on the foregoing, it is necessary to prove the advantage of the quantum algorithm over the algorithms of other computational models

Summary

Introduction

The field of quantum computations is gradually becoming the leader of information technology and calculations. Scientific researchers are paying increasing attention to super-modern computational model based on the notion of qubit (quantum bit) designed to supplant the long–known model that has been used in almost all computer hardware and based on the notion of bit, developed by A. Quantum bit is kind of quantum system, which before the measurement is in arbitrary linear superposition of two basic quantum states, and as a result of the measurement, it takes one of two possible values with certain probability. On one hand, this element is the same bit, because it takes two values, and on other, it is quantum, since these two values are. One of the clearest examples of such problems is the problem of the certain number factorization, the solution of which is to find the divisors of this number [4]

Purpose of Investigations

Theoretical Preconditions and Research Methods

Findings

Conclusion