  In this article initial steps in an analysis of cyclic networks of quantum
logic gates is given. Cyclic networks are those in which the qubit lines are
loops. Here we have studied one and two qubit systems plus two qubit cyclic
systems connected to another qubit on an acyclic line. The analysis includes
the group classification of networks and studies of the dynamics of the qubits
in the cyclic network and of the perturbation effects of an acyclic qubit
acting on a cyclic network. This is followed by a discussion of quantum
algorithms and quantum information processing with cyclic networks of quantum
gates, and a novel implementation of a cyclic network quantum memory. Quantum
sensors via cyclic networks are also discussed.
