In both the search for ever smaller and faster computational devices,
and the search for a computational understanding of biological systems
such as the brain, one is naturally led to consider the possibility of
computational devices the size of cells, molecules, atoms, or on even
smaller scales. Indeed, it has been pointed out [Braunstein, 1995]
that if trends over the last forty years continue, we may reach
atomic-scale computation by the year 2010 [Keyes, 1988]. This move
down in scale takes us from systems that can be understood (to a good
enough approximation) using classical mechanics alone, to those which
require a quantum mechanical understanding. Thus, it should not be
surprising to find that the idea of *quantum computation* is not
new (see, e.g., [Deutsch, 1985] and [Feynman, 1982]). However, most
if not all work so far has been understandably speculative.

This paper continues in this speculative vein, but tries to be
concrete in describing what an implementation of a quantum
computational system might be like. There are two ways in which the
focus here differs from other considerations of quantum computation
First, the focus is on quantum *learning*: quantum computers that
modify themselves in order to improve their performance in some way.
The type of learning that is considered here is that family of
algorithms loosely known as *neural networks*, *
connectionism*, or *parallel distributed processing*. Second, in
order to investigate the possibilities for quantum learning, a
distinction is made between two types of quantum computation:
superpositional and non-superpositional.

- 1.1 Superpositional quantum computation
- 1.2 Non-superpositional quantum computation
- 1.3 Quantum learning

Wed Nov 20 01:10:59 GMT 1996