18 months. The doubling trend continues to this day and, by crude extrapolation, predicts that the computers of 2020 might be approaching the one-atom-per-bit level. Physical systems such as atoms, however, behave in ways that are very d- ferent from everyday objects. In fact they are governed by the laws of quantum mechanics rather than classical mechanics. In the early 1980¿s some foresighted physicists,suchesCharlesBennett(ourconferenceChairperson),RolfLandauer, Paul Benio, David Deutsch, and Richard Feynman, began to question what it would mean for a computer to operate at the one-atom-per-bit scale. The - ementary operations of such a computer would need to be described in terms of quantum mechanics. Recently, physicists and computer scientists have come to appreciate that certain quantum e ects, in particular superposition, int- ference, entanglement, non-locality, indeterminism, and non-clonability, allow entirely new kinds of tasks to be performed.