  We formulate a new concept for computing with quantum cellular automata
composed of arrays of nanostructured superconducting devices. The logic states
are defined by the position of two trapped flux quanta (vortices) in a 2x2
blind-hole-matrix etched on a mesoscopic superconducting square. Such small
computational unit-cells are well within reach of current fabrication
technology. In an array of unit-cells, the vortex configuration of one cell
influences the penetrating flux lines in the neighboring cell through the
screening currents. Alternatively, in conjoined cells, the information transfer
can be strengthened by the interactions between the supercurrents in adjacent
cells. Here we present the functioning logic gates based on this fluxonic
cellular automata (FCA), where the logic operations are verified through
theoretical simulations performed in the framework of the time-dependent
Ginzburg-Landau theory. The input signals are defined by current loops placed
on top of the two diagonal blind holes of the input cell. For given
current-polarization, external flux lines are attracted or repelled by the
loops, forming the '0' or '1' configuration. The read-out technology may be
chosen from a large variety of modern vortex imaging methods, transport and
LDOS measurements.
