Random logic networks: from classical Boolean to quantum dynamics

TL;DR

This paper explores the quantum extension of classical Boolean networks by encoding nodes as qubits and analyzing their dynamic behaviors, including perturbation propagation, revealing non-classical mechanisms.

Contribution

It introduces a quantum generalization of classical Boolean networks with new dynamics and perturbation propagation mechanisms, expanding understanding of quantum network behavior.

Findings

Quantum networks exhibit non-classical perturbation propagation.

Quantum dynamics differ significantly from classical Boolean networks.

Analysis of periodic and quasiperiodic behaviors in quantum networks.

Abstract

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.