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.
- 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 with AV support.Exams
Midterm, homework assignments, final exam.Exercises
Problems and examples are solved in lectures.Consultations
Special topics presented shortly during lectures.
|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