Random logic networks: From classical Boolean to quantum dynamics

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