### Quantum Computers

#### Course Description

#### General Competencies

Students will be able to understand basic quantum mechanical principles and calculation techniques closely connected with a (quantum) information processing. They will be able to solve problems within the mathematical and physical framework of quantum information formation and its transmission. A good theoretical and practical knowledge about quantum states, entanglement principles and quantum algorithms will be given. A review of teleportation and the quantum cryptography will be given.

#### Learning Outcomes

- Explain simple quantum systems.
- Apply quantum mechanics to elementary processes. Explain a qubit state.
- Explain 1/2 and 1 spin states, a linear and circular polarization and its relation to a qubit.
- Explain a notion of an operator, Hermitean and unitary operator and Hilbert space of states.
- Apply matrix repesentation of an operator on a different quantum mechanical situations with qubits.
- Explain trace of an operator, eignevalues and diagonalization of an operator.
- Relate a notion of an operator with mean value calculation in QM and pure and mixed states.
- Explain onequbit and multiplequbit states. Explain tensor product of states and operators.
- Explain quantum gates and quantum circuits. Explain no-cloning theorem and teleportation.
- Apply quantum gates to quantum algorithms (Deutsch, Jozsa, Shor, Grover)

#### Forms of Teaching

**Lectures**Lectures with AV support.

**Exams**Midterm, homework assignments, final exam.

**Exercises**Problems and examples are solved in lectures.

**Consultations**Weekly consultations

**Seminars**Special topics presented shortly during lectures.

#### Grading Method

Continuous Assessment | Exam | |||||
---|---|---|---|---|---|---|

Type | Threshold | Percent of Grade | Comment: | Percent of Grade | ||

Homeworks | 0 % | 10 % | 0 % | 10 % | ||

Mid Term Exam: Written | 0 % | 40 % | 0 % | |||

Final Exam: Written | 0 % | 50 % | ||||

Exam: Written | 0 % | 40 % | ||||

Exam: Oral | 50 % |

#### Week by Week Schedule

- Classical information theory. Probability theory.
- Vector spaces. Basis. Orthogonalization.
- Dirac bra and ket notation. Schroedinger equation. Operators. Quantum mechanical postulates. Qubits and quantum states. Multiqubit states. Tensor product of states and operators.
- Hermitian and unitary operators. Hilbert space of states. Different bases in a vector space. Transformations.
- Probability density operator. Quantum theory of measurement. Pure states. Mixed states. Diagonalization of an operator.
- Pauli representation. Spin states and classical and quantum representation. Light polarization.
- Bell's Theorem. Entangled states.
- Midterm exam
- Classical logic gates. Unitary transformations. Single-qubit gates. Universal gates.
- Basic quantum circuit digrams
- Composition and decomposition of quantum gates. No-cloning theorem.
- Quantum algorithms. Deutsch and Deutsch-Jozsa algorithm. Quantum Fourier transform.
- Shor algorithm. Quantum searching.
- Review of teleportation and quantum cryptography. Possible realization of quantum computers.
- Final exam

#### Study Programmes

Control Engineering and Automation -> Electrical Engineering and Information Technology (Profile)

Electrical Engineering Systems and Technologies -> Electrical Engineering and Information Technology (Profile)

Electrical Power Engineering -> Electrical Engineering and Information Technology (Profile)

Electronic and Computer Engineering -> Electrical Engineering and Information Technology (Profile)

Electronics -> Electrical Engineering and Information Technology (Profile)

Information Processing -> Information and Communication Technology (Profile)

Telecommunication and Informatics -> Information and Communication Technology (Profile)

Wireless Technologies -> Information and Communication Technology (Profile)

Software Engineering and Information Systems -> Computing (Profile)

Computer Engineering -> Computing (Profile)

Computer Science -> Computing (Profile)

#### Literature

*Quantum Computation and Quantum Information*, Cambridge Univ. Press

*Classical and Quantum Computation*, American Math. Society

*Feynman Lectures on Computation*, Addison-Wesley Publ. Comp.

*Quantum Computing, A Gentle Introduction*, The MIT Press

*Quantum Computing Explained*, Wiley-Interscience

#### Lecturers in Charge

#### Grading System

**4**ECTS

**L3**English Level

**L1**e-Learning

**45**Lecturers

**0**Exercises

**0**Laboratory exercises

#### Grading

**90**Excellent

**80**Very Good

**70**Good

**60**Acceptable