Computing circuits could be simplified in that signal paths could be crossed.

Integrated circuits of a proposed type based on quantum-dot cellular automata (QCA) would implement permutation matrices. These circuits would serve as prototype building blocks for demonstrating the feasibility of quantum-dot-based computing and for the further development of increasingly complex and increasingly capable quantum-dot-based computing circuits. Permutation matrices were chosen as part of the basis of this development because (1) they play a major role in fast transforms (e.g., the fast Fourier, cosine, and Hartley transforms) that arise in the processing of signals and images and that are amenable to parallel computing by application-specific integrated circuits and (2) in principle, they could be implemented directly in the patterns of circuits of the proposed type.