  We investigate dynamical properties of a quantum generalization of classical
reversible Boolean networks. The state of each node is encoded as a single
qubit, and classical Boolean logic operations are supplemented by controlled
bit-flip and Hadamard operations. We consider synchronous updating schemes in
which each qubit is updated at each step based on stored values of the qubits
from the previous step. We investigate the periodic or quasiperiodic behavior
of quantum networks, and we analyze the propagation of single site
perturbations through the quantum networks with input degree one. A
non-classical mechanism for perturbation propagation leads to substantially
different evolution of the Hamming distance between the original and perturbed
states.
