<p>This paper presents a generalized framework for implementing Shor’s algorithm using two distinct approaches: the conventional and iterative methods. We propose a novel quantum circuit design that generalizes and optimizes the modular exponentiation function, enabling its efficient execution on current quantum hardware. The implementations are evaluated through simulations using a quantum computing framework, demonstrating significant reductions in qubit requirements and improved scalability. Furthermore, by integrating variational quantum algorithms and tensor network techniques into the circuit design, the proposed approach reduces gate count and resource usage, moving toward the practical realization of the Shor’s algorithm on near-term quantum devices.</p>