Despite the seemingly endless upwards spiral of modern VLSI technology, many experts are predicting a hard,wall for CMOS in about a decade. Given this, researchers continue to look at alternative technologies, one of which is based on quantum riots, called quantum cellular automata. While the first such devices have been fabricated, little is known about how to design complete systems of them. This paper summarizes one of the first such studies, namely an attempt to design a complete, albeit simple, CPU in the technology. The projections are striking: a projected 10 to 1 increase in circuit density when compared to a CMOS equivalent, but a design approach,which is radically different from conventional "logic" design, especially in timing considerations.