Quantum Algorithms

Quantum algorithms — a new topic in both informatics and physics has become a central theme of one of the most challenging areas of interdisciplinary research of modern science. This seemingly esoteric area of research which has been stimulated by Feynman in 1980 and Benioff, who was the first to suggest quantum-mechanical evolution for computation in 1982, has become a serious challenge after Shor’s publication of the “Algorithms for quantum computation: Discrete logarithms and factoring” in 1994. This breakthrough in theoretical computer science has stimulated a new field of physics, especially on the experimental side, namely the investigation of controlled quantum systems which is motivated by the promise that algorithmic processing of quantum information may provide an exponential gain in speed and space over classical computers. As a consequence of this joint research there has been a surprising progress during the last years towards new algorithms and especially complexity bounds for certain problems. However, up to today there are no exact theorems available on the relation between quantum complexity classes and classical complexity classes. Quantum algorithms rely on three effects: