Quantum computers and algorithms for such computers are among the most important, interesting, and promising innovations in information and communication technology today. This course is an introduction to quantum algorithms which
(1)    covers fundamental and the theory behind them,
(2)    is rigorous from a mathematics, physics, and computer science perspective,
(3)    is self-contained, i.e., requires only basic knowledge from mathematics such as calculus and linear algebra.

 

The syllabus of the course is as follows.
(1)    Basic concepts of quantum algorithms using the Deutsch algorithm as an example
(2)    Classical computability and complexity theory with a focus on reversible computation.
(3)    Finite-dimensional Hilbert spaces
(4)    Quantum Postulates and quantum computation
(5)    The algorithms of Deutsch-Josza and Simon
(6)    Shors's algorithm I: the quantum Fourier transform
(7)    Shor's algorithm II: factoring and computing discrete logarithms
(8)    Grover's algorithm and outlook

 

In the lectures, I will present the important concepts and results and selected proofs. All proofs are explained in detail in my lecture notes of which all participants will receive a copy and which will appear as a textbook later this year. After each lecture I will propose exercises which the participants are invited to solve. Solutions for the exercises are discussed in the exercise session. The participants are encouraged to present their solutions. The grade for the course will depend on these presentations and a final exam that depending on the number of participants may be written or oral.