Course: Introduction to Quantum Theory for Informatics

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Course title Introduction to Quantum Theory for Informatics
Course code KMI/PGSKT
Organizational form of instruction Lecture
Level of course Doctoral
Year of study not specified
Semester Winter and summer
Number of ECTS credits 12
Language of instruction Czech, English
Status of course unspecified
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Řeháček Jaroslav, prof. Mgr. Ph.D.
Course content
1. Historical survey of quantum mechanics: de Broglie waves, Heisenberg's matrices of infinite order, Schrödinger wave equation, Born's interpretation of wave, Born's postulates, Copenhagen interpretation 2. Quantum mechanics: definition, physics view of quantum mechanics postulates 3. Experiment in quantum mechanics: Heisenberg uncertainty principle, measuring, difference from classical mechanics 4. Non-locality, decoherence, non-determinism, paradoxes of quantum mechanics (EPR and Bell's inequalities, Schrödinger's cat) 5. Finite dimensional complex Hilbert space - 1st part: Dirac's notation, linear dependence, orthonormal basis, Gram - Schmidt orthogonal process, inner product, vector norm, metric 6. Finite dimensional complex Hilbert space - 2nd part: operators (normal, self-adjoint, positive definite, positive semi-definite), unitary mapping 7. Finite dimensional complex Hilbert space - 3rd part: Hermitian operator, commutator, anticommutator, eigenvectors and eigenvalues of an operator, tensor product of vectors and operators, tensor product properties 8. The density operator 9. Postulates of quantum mechanics using density operator and vectors in Hilbert space 10. Quantum bit - 1st part: Stern - Gerlach experiment, mathematical model, geometrical visualization, non-cloning theorem, physical realization 11. Quantum bit - 2nd part: quantum bit transformation, state of quantum bit (pure, mixed, entanglement), teleportation, Superdense coding 12. Quantum bit - 3rd part: estimation and discrimination of quantum states

Learning activities and teaching methods
Dialogic Lecture (Discussion, Dialog, Brainstorming)
  • Preparation for the Exam - 50 hours per semester
Learning outcomes
Introduction to formalism of quantum mechanics. Broadening the knowledge of linear algebra. Gaining background for the follow-up course on the theory of quantum information processing.
On successful completion of this module, students should be able to know and understand the syllabus topics and be able to use the acquired knowledge in solving problems.
Prerequisites
No prior requirements.

Assessment methods and criteria
Oral exam, Student performance

Sufficient knowledge of the syllabus topics.
Recommended literature
  • Blank J., Exner P., Havlíček M. (1993). Lineární operátory v kvantové fyzice. Karolinum, Praha.
  • Formánek J. (2004). Úvod do kvantové teorie, část I. Academia, Praha.
  • Formánek J. (2004). Úvod do kvantové teorie, část II. Academia, Praha.
  • Messiah A. (2000). Quantum Mechanics. Dover, New York.
  • Sakurai J. J. (1995). Modern Quantum Mechanics, revised edition. Addison-Wesley, New York.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester