## Mathematical Physics (MAP): Quantum Information and Quantum Computation

**
Instructor**: Dr. Máté Matolcsi

**Text**: M.A. Nielsen, I.L. Chuang: Quantum Information and Quantum Computation (Cambridge University Press, 2000).

**Prerequisites**:
Basics of linear algebra (matrices), and probability theory.

**Course description**:
What is a quantum-bit, and how would a quantum computer operate? Would it be more powerful than the classical computers of today? How could it break the currently used codes of cryptography? How does quantum-cryptography come to the rescue? How do quantum-teleportation and superdense coding work? This course offers an introduction to quantum information theory and the questions above will be discussed, with the answers often being much easier to understand than you would think -- but not always...

The emphasis will be on the mathematical, information-theoretical aspects (but not directly on physics). In the first part
of the course the necessary mathematical tools are introduced, while
in the second part the above questions are
discussed.

If you are interested about the essence of quantum-physics, read this short summary
(written by Dr. Mihaly Weiner, a previous instructor) in a "Q&A" format.

**Topics**:

*1st part (the mathematical tools)*:

Finite dimensional Hilbert spaces, orthogonal projections, operator
norms, normal operators, self-adjoint operators, unitary operators, spectral
resolution, positive operators, tensorial products,
pure states, measurable quantities, operations between measurable quantities.

*2nd part (applications)*:

Quantum-bits (also known as q-bits) and quantum-computers, the "EPR" paradox, quantum cryptography (the protocol of
Bennett and Brassard), superdense coding, teleportation, no-clone theorem, an example of an algorithm
for a quantum computer (e.g. Shor's algorithm for factorizing numbers).