Paper Key : IRJ************748
Author: Nitish
Date Published: 02 Jul 2024
Abstract
In the rapidly evolving field of quantum computing, Shor's and Grover's algorithms are celebrated achievements leveraging quantum mechanics to solve problems beyond classical computational capabilities. This paper conducts a comparative analysis of Shor's algorithm, known for factorizing large composite numbers, and Grover's algorithm, adept at searching unstructured databases and optimizing problem-solving. The research explores theoretical foundations, practical implementations, and real-world implications. Shor's algorithm utilizes Quantum Fourier Transform and modular arithmetic, promising exponential speedup for factoring, impacting classical cryptographic systems like RSA. Grover's algorithm, employing amplitude amplification and quantum oracle operations, offers quadratic speedup for searches, valuable beyond prime factorization. Implemented using IBM Qiskit, Shor's algorithm focuses on factorizing, demonstrating quantum phase estimation and period finding. Grover's algorithm applies to dataset searches adapted for prime factorization. Methodology includes quantum circuit design, parameter tuning, and simulations on quantum hardware. Results assess execution times, accuracy, and reliability, highlighting strengths and limitations. Shor's algorithm excels in specific problems but faces scalability issues. Grover's algorithm, versatile yet limited by quadratic speedup, finds broad application. Discussions include cryptographic implications, need for new protocols, and Grover's applications in database search, optimization, and machine learning. Addressing hardware challenges like qubit fidelity and gate errors, future research aims to enhance quantum algorithm robustness. This study underscores quantum algorithmstransformative potential, guiding advancements in quantum computing applications and theory
DOI Requested