However, a form of non-superpositional quantum computation is possible. Non-superpositional quantum computation uses quantum systems to implement standard computational architectures in a way that does indeed involve superposed states, but does not exploit them for computational parallelism in the way that, e.g., Shor's algorithm does. Thus, it does not have the disadvantages of that approach: it can proceed even if the superpositional state cannot be maintained, and it can be generalized to implement any computation whatsoever. But so also it does not have the parallel advantages of superpositional quantum computation. Nevertheless, as the rest of this paper will attempt to show, non-superpositional quantum computation has its own advantages and theoretical interest.
First, mention can be made of the more mundane computational advantages of quantum computation in general: advanatages of size and speed. Non-superpositional quantum computers (NSQC's) have the potential to be very small indeed, allowing a lot of computational power in a very small space. This is not just because of the fact that quanta are small; it is also because of the nature of the physical forces involved. The biggest stumbling block, in conventional hardware design, to greater and greater scales of component integration is not the size of the components, but the density of connections. Communication in classical computers is via wires, and as components get smaller, there is geometrically less surface area of the component to which one can attach connecting wires. Also, wires have to be insulated from each other, which takes up more space. We will see below that in an NSQC, not only are the components small, but they communicate, not with wires, but with forces. In a conventional computer or network, this communication would require wire connectivity between the relevant components, which would limit the scale of integration.
Furthermore, in NSQC's, the non-locality of quantum interactions means that this communication is instantaneous. This increase in speed may or may not be dramatic for the short distances involved in conventional ways of thinking of nano-scale integration. But one can imagine a macro-spatially extended array of NSQC processors, which could communicate instantaneously (or near-instantaneously if relativistic considerations demand such a restriction) across substantial distances.