1 Algorithms for Quantum Systems — Quantum Algorithms

Since the presentation of polynomial time quantum algorithms for discrete log and factoring [Sho94] it is generally accepted that quantum computers may—at least for some problems— outperform classical ones. But the field of quantum information processing does not only have implications for computational problems. Using quantum mechanical systems for information processing naturally leads to the problem of finding efficient ways to control quantum mechanical systems. Here we address several algorithmic aspects of quantum information processing in different areas. First, the state of the art of quantum signal transforms which are at the core of a huge class of quantum algorithms, namely hidden subgroup problems, is presented. Second, we discuss aspects of quantum error-correcting codes, in particular an interesting view on stabilizer codes which relates them to simple interaction Hamiltonians. The efficient implementation of unitary operations by given Hamiltonians is investigated next. Finally, results on the simulation of one quantum mechanical system by another are discussed.