Quantum Algorithms Spring 2026

Course Description

Remarkable results from the last three decades have given evidence that computers based on quantum mechanical principles could profoundly alter the nature of information processing. Efficient algorithms for breaking widely used cryptographic systems, query efficient strategies for database searches, techniques like teleportation and superdense coding, and provably secure schemes for cryptographic key distribution have demonstrated how differently quantum information behaves, and how these properties can be exploited to solve certain computational tasks better than known classically.

This course focuses on the algorithmic aspects of quantum computing. We develop a quantum model of computation, and discuss known paradigms of efficient quantum computation, including amplitude amplification, phase estimation, quantum walks, and quantum signal processing. We apply the paradigms to computational problems such as satisfiability, the hidden subgroup problem (including integer factoring and discrete log), simulation, and solving systems of linear equations.

Prerequisites

Knowledge of linear algebra (eigenvalues and eigenvectors) at the level of Math 341, probability theory at the level of Math 431, and theoretical computer science at the level of CS 577 or CS 520. No knowledge of quantum physics is assumed.

Text

There is no required text. Lecture notes will be made available.

Lectures

TR 2:30-3:45pm in 2534 Engineering Hall.

Instructor

Dieter van Melkebeek