Description:

Quantum theory brought new ideas to the theory of information leading which ultimately lead to the theory of quantum information, computation and communication. The lecture introduces the basic concepts of quantum information e.g. quantum algorithms (Shor?s and Grover?s), entanglement, quantum teleportation, quantum cryptography and quantum error correction. It also provides an introduction to modern parts of quantum information, e.g. measurement-based and adiabatic quantum computation and quantum walks.

Contents:

1. Qubit, Bloch sphere, von Neumann entropy
2. Quantum correlations, entanglement and its measures, reduced density operator
3. Quantum teleportation, quantum key distribution
4. Quantum gates and circuits, Deutsch algorithm, universal quantum gates
5. Shor?s factorization, quantum Fourier transformation
6. Grover?s search algorithm
7. Quantum operations, decoherence, POVM measurements
8. Quantum state discrimination
9. Quantum error correction
10. Measurement-based and adiabatic quantum computation
11. Realizations of quantum computing
12. Quantum walks

Seminar contents:

Outline of the exercises:
Solving problems to illustrate the theory from the lecture.

Recommended literature:

Key references:
[1] M. A. Nielsen, I. L. Chuang, Quantum computation and quantum information, Cambridge Univ. Press, 2013.
[2] J. A. A. Bergou, M. Hillery, Introduction to the Theory of Quantum Information Processing, Springer, 2015.

Recommended references:
[3] M. Dušek, Koncepční otázky kvantové teorie, Olomouc, 2002. (in Czech)
[4] G. Alber, Quantum Information, Springer, Berlin 2002.
[5] D. Bruss, G. Leuchs, Lectures on Quantum Information, Wiley-VCH, Weinheim, 2007.

Keywords:

Qubit, quantum gate, entanglement, Shor?s algorithm, Grover?s algorithm, state discrimination, quantum walks

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar