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.