Systematic Literature Review on Problem Solving with Quantum Algorithms

Abstract

Quantum computing is a high-powered computational model that possess the capability to solve problems that are non-detectable by traditional algorithms. These algorithms primarily exploit well-known rules and principles of quantum mechanics i.e., superposition and entanglement to implement and deploy solutions for sophisticated tasks. Its applications have revolutionized various domains like optimization, cryptography, machine learning, and simulation. With the increasing research in this significant computational field, it is becoming more essential to critically assess that how quantum algorithms are being employed in real-world problem-solving contexts. The comprehensive literature review that has been conducted in this study is primarily based upon the critical assessment of four key quantum algorithms, which are 1) Shor's Algorithm, 2) Grover's Algorithm, 3) the Quantum Approximate Optimization Algorithm (QAOA), and the 4) Quantum Fourier Transform (QFT). We have primarily focused upon their uses in secure communication, machine learning, chemistry, cryptography, and optimization.  30 excellent studies published between 2015 and 2024 were found through a systematic search of IEEE Xplore, SpringerLink, ScienceDirect, arXiv, and Google Scholar. Our results identify major patterns in the usage of algorithms like Grover's, Shor's, QAOA, and VQE and elucidate their applications in tackling theoretical and pragmatic problems. Unlike previous reviews that concentrate narrowly on algorithm design or on particular areas, this SLR presents a wide but organized synthesis that highlights problem-driven applications. Moreover, we have also highlighted the primary research gaps in this area and also suggested possible future directions for further investigation. This review provides a basis for researchers who would like to apply quantum algorithms to new or interdisciplinary problems.