Quantum Computing

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Quantum computing represents a new programming paradigm. The safety of nowadays encypering techniques is based on enormous computation complexity of classical mathematical problems. This safety may be broken by quantum computers.

The ``building stones'' of a quantum computer and quantum computers will be developed during the course. We will design fast factorization algorithms, fast database search, etc.

Requirements:

Syllabus of lectures:

1. Introduction (basic quantum gates, Deutsch's algorithm)

2. A brief intro to Computer Science (Turing machines, logical gates, Church-Turing Thesis)

3. Computational complexity (complexity classes, computationally hard problems)

4. Mathematical tools of Quantum Mechanics (linear spaces, linear operators)

5. Postulates of Quantum Mechanics

6. Superdense coding

7. Quantum gates

8. Classical encyphering protocols (RSA, Diffie and Hellman key exchange, safety and attacks)

9. Fourier Transform

10. Shor's factorization algorithm

11. Shor's algorithm for discrete logarithm

12. Quantum search

13. Searching the database

14. Spare lecture

Syllabus of tutorials:

Study Objective:

Study materials:

1. Michael A. Nielsen, Isaac L. Chuang: Quantum Computation and Quantum Information, Cambridge University Press, 2000

2. web pages http://www.iqi.caltech.edu/

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Doctoral studies, daily studies (compulsory elective course)
• Doctoral studies, combined studies (compulsory elective course)
• Doctoral studies, structured daily studies (compulsory elective course)
• Doctoral studies, structured combined studies (compulsory elective course)