Quadratic Sieve Factorization Quantum Algorithm and its Simulation

TL;DR

This paper introduces a quantum version of the Quadratic Sieve factorization algorithm, simulates it using Mathematica, and demonstrates its potential efficiency advantages over classical methods.

Contribution

It presents the design and simulation of a quantum variant of the Quadratic Sieve, a significant classical factorization algorithm, showcasing its improved computational complexity.

Findings

Quantum Quadratic Sieve is more efficient than classical versions

Simulation confirms feasibility of quantum implementation

Potential to impact cryptography by faster factorization

Abstract

Quantum computing is a winsome field that concerns with the behaviour and nature of energy at the quantum level to improve the efficiency of computations. In recent years, quantum computation is receiving much attention for its capability to solve difficult problems efficiently in contrast to classical computers. Specifically, some well-known public-key cryptosystems depend on the difficulty of factoring large numbers, which takes a very long time. It is expected that the emergence of a quantum computer has the potential to break such cryptosystems by 2020 due to the discovery of powerful quantum algorithms (Shor's factoring, Grover's search algorithm and many more). In this paper, we have designed a quantum variant of the second fastest classical factorization algorithm named "Quadratic Sieve". We have constructed the simulation framework of quantized quadratic sieve algorithm using high-level programming language Mathematica. Further, the simulation results are performed on a classical computer to get a feel of the quantum system and proved that it is more efficient than its classical variants from computational complexity point of view.