Quantum Computations: Fundamentals And Algorithms

Basic concepts of quantum theory of information, principles of quantum calculations and the possibility of creation on this basis unique on calculation power and functioning principle device, named quantum computer, are briefly reviewed. The main blocks of quantum logic, schemes of implementation of quantum calculations, as well as some known today effective quantum algorithms, called to realize advantages of quantum calculations upon classical, are concerned. Among them special place is taken by Shor's algorithm of number factorization, Grover's algorithm of unsorted database search and, finally, the most promising in application methods of quantum phenomena simulation, particularly quantum chaos. The most perspective methods of experimental realization of quantum computer, namely nuclear-magnetic resonance and trapped ions realizations, are discussed. Phenomena of decoherence, its influence on quantum computer stability and methods of quantum error correction are described.
Comment: 6 pages, presented at "Quantum Electrodynamics and Statistical Physics", 2nd Int. Conf., Sept. 19-23, 2006 Kharkov, Ukraine. For extended 28pp. (10pt,wide) version in Russian "Topological Methods In Quantum Computations" (J.KNU,2007) see http://www.math.rutgers.edu/~duplij/publications/Duplij-Shapoval_TOPOLOGICAL-QUANTUM-COMPUTERS.pdf