Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics

Probability Theory

The quantum mechanics-based algorithms and protocols can play an important role in our nowadays used technical solutions. Quantum computing and quantum communications is no longer belongs to the world of scientific laboratories since more and more products are offered by different companies in the market. This course gives an overview on different areas of quantum computing and communication including qubits, quantum registers, quantum gates and different quantum algorithms (Grover, Deutsch-Jozsa, Shor, etc.) and protocols (including quantum teleportation and quantum key distribution).

Week 1: Introduction

Motivation of quantum computing. Moore's law and quantum mechanics. Application possibilities of quantum computing. Quantum interferometer.

Week 2: Basics of quantum computing

Hilbert space and quantum mechanics. Notation. Complex probability amplitudes. Postulates of quantum mechanics.

Week 3: Quantum bit, quantum register

Quantum bit and quantum register. Superposition. Representation with the Bloch sphere. Elementary quantum gates and their descriptions.

Week 4: Entanglement

Entanglement and its effects. Entanglement with the environment.

Week 5: Basics of quantum computing (2)

Measurement: connection between quantum and classical world. Measurement techniques. Projective measurement. POVM. Connection between the measurements.

Week 6: Basics of quantum computing (3)

General description of quantum interferometer. No Cloning Theorem. Creating unitary quantum bit using elementary quantum gates

Week 7: Early quantum protocols

Superdense coding. Quantum teleportation

Week 8: Quantum parallelism

Basics of quantum parallelism. Deustch-Jozsa algorithm.

Week 9: Quantum parallelism (2)

Simon's algoritmus. Application of quantum parallelism

Week 10: Quantum solutions of infocommunications problems (1)

Quantum cryptography and quantum key distribution. BB84 protocol. B92 protocol.

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Week 11: Application of quantum cryptography

Overview of fiber based quantum key distribution systems. Application of quantum communications in space communication.

Week 12: Quantum solutions of infocommunications problems (2)

Efficient searching in an unsorted database. Grover's algorithm

Week 13: Quantum solutions of infocommunications problems (3)

Prim factorization, order finding, Shor's algorithm

Week 14: Quantum computers: state of the art

State of art of quantum computers: photons, electron spins, atoms. Existing architecture and current research directions.

The English course is offered as an online course:
- Lectures are available as video recordings (access details will be
  provided).
- Concerning the laboratory exercise (single occasion, see Week 4
  in course program) there are two options
  Option 1  Online (remote) laboratory exercise, instructor's
            support in on demand.
  Option 2  In person laboratory (lab is at the department) for
            those who would like to attend in person, registration
            is required in advance.
- 3 online classroom tests are organized online in dedicated
  time slots according to the course time-table (30 minutes at the
  beginning of the specified schedule)
    1st test on week  5,
    2nd test on week  9,
    3rd test on week 14.

Fulfilling the requirements of 1 homework project and 3 short classroom tests.

The final grade is calculated as follows: result of 1 homework project (40 percent) and results of 3 short classroom tests (20 percent each).

Short classroom tests cannot be repeated. Homework project can be submitted later until the supplement week according to the related university regulations.

Ad hoc meetings with the lecturer.

Slides are available on the course web site with further recommended readings.

S. Imre, F. Balázs: Quantum Computing and Communications - An Engineering Approach, Published by John Wiley and Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, 2005, ISBN 0-470-86902-X, 283 oldal (néhány példányban kölcsönözhető).