Spec. course "Quantum computing"

Lecturer: Prof. O.N.Granichin

Students: 5 year, computer science department

Summary:

"Computer science" will be significantly changed because size of elementary units of modern computers decrease on 10-30% per year. After several years we'll have elementary units of computer device by 100-200 A (0,01-0.02 micron). This kind of device will not be capable to operate with usual bits {0,1}. Internal nature of information will be changed. The new devices will operate with "wave function" instead "digit". The new point of view on the process of calculation needs in new math basement. On the one hand, it causes the replacement basic classical (not quantum) algorithms, and, on the other hand, enables closely to be risen to the solution of problems of “artificial intelligence”.

Themes of the course:

1. Perspectives of development of computer facilities. Specialized devices for the fast solution of many-dimensional problems.
2. Model of quantum calculations.
3. Quantum parallelism. Deutsch problem.
4. Search in a data base (Grover’s algorithm).
5. P.Shor’s algorithm of a factorization.
6. Teleportation of quantum bits.
7. Randomized algorithms of stochastic approximation for the solving of multidimensional optimization problems.

References:

1. Bennet C.H., Shor P.W. ” Quantum information theory” IEEE Transactions on Information Theory, 1988, vol.44, p.2724—2742.
2. Shor P.W. “Quantum computing”. In: Proceedings of the 9-th Int. Math. Congress. Berlin, 1998, www.math.nine.edu/documenta/xvol-icm/Fields/Fields.html.
3. Preskill J. “Quantum Information and Computation”, http://www.theory.caltech.edu/~preskill/ph229.
4. Granichin O.N. “Randomized algorithms for stochastic approximation under arbitrary disturbances” Automation and Remote Control, 2002, v.63, No.2, pp.209-219.
5. Faddeev L.D., Yakubovskii O.A. “ The lectures on a quantum mechanics for the student - mathematicians ”. L.: LSU, 1980, 200p.