## Admission Requirements

In order to be able to follow the course, familiarity with complex numbers and linear algebrais necessary and sufficient.

## Description

It is well known that quantum computers (when they become available) will greatly outperform classical computers on certain computational problems. The most prominent example is Shor's quantum algorithm for factoring integers, which threatens most of the cryptography in use. In this course, we give an introduction to quantum computing and to the mathematics behind. In the first part of the course, the basic mathematical theory for describing "quantum information" and studying its behavior is introduced. The second part briefly addresses the basic theory of quantum computation, like how to formalize what a quantum algorithm is and how to measure its complexity, but then the main goal is to introduce and analyze various quantum algorithms, and to understand (to some extent) their "common denominator". The algorithms discussed range from the early simple examples by Deutsch etc., but also include the more sophisticated algorithms that are relevant for the design of the next generation of cryptographic schemes, like Grover's and Shor's algorithm. On the way, it will be necessary to briefly look into representation theory of finite groups and into the theory of continued fractions.

## Course objectives

The objectives of this course are to understand the state vector formalism of quantum information science, and to understand how (and why) the most prominent quantum algorithms work.

## Mode of instruction

Lectures, take-home exercises, some home study

## Assessment method

Oral exam. The take-home exercises do not contribute to the final grade.

## Literature

Lecture notes will be handed out.

## Website

a self crafted course page will be made available. Please see the Brightspace page for the link.

## Contact

Email: serge[dot]fehr[at]cwi[dot]nl