We present a theoretical study of locally interconnected tunneling arrays operating in the Coulomb blockade regime. In these arrays bits of information are represented by single electrons and useful behaviors can be obtained if the size of a ‘‘dressed’’ electron on the array, i.e., an excess electron plus its polarization cloud, is small. Under this condition, we demonstrate (using simple quasistatic tunneling theory) that linear tunneling arrays can be made to act as charge‐coupled devices for single electrons. Such devices could potentially be applied to computational and/or signal processing applications. As a simplest example, we show that these linear arrays can be made to simulate a random walk. These initial results illuminate some of the requirements on locally interconnected quantum device arrays if they are to do useful computation. More speculatively, they suggest that Coulomb blockade‐based arrays could be the basis for future very high‐powered digital processors. For such hardware to be practical, however, ways of dealing with device nonuniformities (particularly associated with ‘‘polarization charge’’) must be found. ©1995 American Institute of Physics.