Quantum algorithms for algebraic problems

Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for classical computers. Understanding what other computational problems can be solved significantly faster using quantum algorithms is one of the major challenges in the theory of quantum computation, and such algorithms motivate the formidable task of building a large-scale quantum computer. This article reviews the current state of quantum algorithms, focusing on algorithms with superpolynomial speedup over classical computation, and in particular, on problems with an algebraic flavor.Comment: 52 pages, 3 figures, to appear in Reviews of Modern Physic

Distinctions between short- and long-term human growth studies

It is known what the aim is in a complete long-term growth study; the final height is the outcome measure, although the annual height velocity values provide additional information. Strictly, short-term growth studies are also defined in terms of minimum length of observation, i.e. one month, as well as the type of measurement errors to be considered. The poor correlation between short- and long-term growth velocity values has led to the conclusion that the short-term study cannot be interpreted in long-term perspectives, and vice versa. There is a need to debate the way in which results of short-term studies should be interpreted. This is especially important when short-term growth is taken as the outcome measure in a controlled study. Our proposal is that such studies must include information about the growth achieved for a period after the treatment has ended in order to describe possible compensatory growth. Without weighing in some long-term consequences, we may incorrectly document short-term growth as a positive or negative effect of a certain treatment.link_to_subscribed_fulltex