## Admission requirements

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

## Description

It is 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.

The course consists of regular lecturers in which we look at Quantum Computing through the eyes of a computer scientist. This means that after the presentation of some necessary basic knowledge, several topics are addressed like architecture, algorithms, programming languages, cryptography, and hardware. This results in knowledge of an exiting research field, of which it is clear that despite the progress made, many hurdles still have to be taken.

## 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.

## Timetable

The most recent timetable can be found on the students' website.

## Mode of instruction

Video lectures and assignments.

## Assessment method

Written exam to be provided online.

## Reading List

References:

Eleanor Rieffel and Wolfgang Polak, Quantum Computing, the MIT Press, 2011, isbn 978-0-262-01506-6

Michael A. Nielsen and Isaac L. Chung, Quantum Computing and Quantum Information, reprinted 2012, Cambridge University Press, isbn 978-1-10700-217-3

Quantum Computer Science: An Introduction” by David N. Mermin, 2007, Cambridge University Press.

Adiabatic Quantum Computation and Quantum Annealing: Theory and Practice, by Catherine C. McGeoch

Handouts

## Registration

- You have to sign up for courses and exams (including retakes) in uSis. Check this link for information about how to register for courses.

## Contact

Lecturer: F. Neukart

f.neukart@liacs.leidenuniv.nl