Quantum computing has opened new possibilities for solving problems that are intractable with classical computing. One of the most representative examples is Shor’s algorithm, which enables the factorization of large integers in polynomial time, thus challenging the security of many current cryptographic systems that rely on the difficulty of this problem. Its operation is based on fundamental tools such as the Quantum Fourier Transform (QFT) and phase estimation, which leverage the nature of quantum parallelism and interference to efficiently find solutions.

The interest in studying these algorithms lies not only in their potential impact, but also in their structure, as they help us understand how the power of qubits can be harnessed to solve complex algebraic problems. This project aims to delve deeper into the theoretical analysis and practical implementation of these algorithms, using simulators like Qiskit to experiment with quantum circuits, given that real devices such as the Gemini SpinQ still have limitations in the number of qubits available.

Understanding how and why these algorithms work allows us to develop a stronger intuition about the principles of quantum computing and its applications, as well as to open the door to exploring new quantum algorithms and their implementation on increasingly accessible hardware.