Quantum Algorithms

Full course description

This course will provide a thorough examination of the most important Quantum Algorithms. We will see how the quantum mechanical formalism gives rise to a new algorithmic design paradigm with the potential of performing certain computational tasks faster than we could do using a classical computer. The course will start with some basic algorithms like Bernstein-Vazirani and Simon’s algorithm, then we will move on to Quantum Fourier Transform and Phase Estimation. Then, a thorough discussion of Shor’s celebrated algorithm for factoring will follow, together with a detailed coverage of Grover’s unstructured search algorithm, its optimality, adaptations, and applications. Further, we will move on to the HHL algorithm for solving systems of linear equations, a crucial component of many quantum algorithms, including Machine Learning quantum algorithms. In the last part of the course, we will present algorithms for quantum simulation, discuss quantum walks, and basics of quantum complexity theory by introducing and discussing the BQP and QMA complexity classes.