Lecturer: Ivan Damgård
Welcome! You have reached the page with supplementary information on the course in Quantum Information
Processing. Having come so far, you have probably read the official description of the course. Otherwise, you
can find it below. The home page for the course can be found here.
This page is meant to help answer some questions you may have on the course. If you have additional
questions, you are always welcome to come and see one of us in our offices (Turing, 2. floor) or send mail
to (ivan (at) cs.au.dk).
Quantum Information (QI) generally means information encoded in the state of very small
physical systems. So small, in fact, that the laws of quantum mechanics govern its behavior.
This means that QI, unlike its classical counterpart, cannot be copied or be measured completely
reliably, but can on the other hand exist in superposition of several different states. This opens
the way to forms of communication and computing that are not possible with classical means:
a quantum computer can efficiently solve problems that are exceedingly difficult with conventional
methods, and quantum cryptography makes it possible to exchange secret keys efficiently under the
nose of an all powerful adversary.
Thus QI Processing unifies in a unique way mathematics, physics and computer science. While
some of the possibilities in QI processing are still science fiction, others - in particular quantum
key exchange - can be implemented with today's technology. Several such experiments have been
run in the local physics department.
No prior knowledge of quantum mechanics will be assumed, the course will introduce the basics of
quantum physics needed. We shall also introduce the basics of quantum information theory which,
in some sense, provides the foundations for both quantum computing and quantum cryptography.
We will then cover the most important quantum algorithms including efficient algorithms for solving
the factoring and discrete log problem and quantum searching. The course ends with quantum cryptography.
Q:
Don't you have to know a lot of quantum physics to follow the course?
A:
No. The quantum physics we need will be introduced during the course.
Q:
Isn't quantum physics very strange and hard to understand?
A:
It is true that quantum physics predicts that nature behaves in ways that seem quite strange and
counterintuitive, based on our everyday experience. But from a mathematical point of view,
things are - in a sense - very simple: quantum mechanics is a mathematical model of the world.
And this model is not all that complicated, it is completely based on linear algebra. So if you
know about vectorspaces, matrices, scalar products etc., you will see nothing that is new. So
the model itself is not very hard to understand. It is only when we consider what this model
predicts about the real world that strange things begin to happen. On the other hand, these
strange things are exactly what is new and fascinating about quantum information!
Q:
What kind of math do I have to know to follow the course?
A:
Linear algebra is essential. So is knowledge of complex numbers. The course in
linear algebra from the bachelor programme contains all you need (and more).
Q:
Course material?
A:
See the home page of the course.
Q:
What about the exam?
A:
You have to hand in and have approved a certain number of exercises during the course.
The exam is oral, you draw one out of a number of previously published subjects and
we talk about this subject for about 20 minutes.