Quantum-like states on complex synchronized networks

TL;DR

This paper introduces a model for quantum-like states in complex networks, demonstrating how classical systems can exhibit quantum-like processing capabilities with potential applications in computing and brain function.

Contribution

It proposes a framework for QL states in complex networks, especially using $k$-regular random graphs, and explores their properties and potential advantages.

Findings

Networks can host robust QL states that process information in a quantum-like manner.

Emergent classical states exhibit properties analogous to quantum states.

Potential for QL advantage in computation and implications for brain function are discussed.

Abstract

Recent work has exposed the idea that interesting quantum-like probability laws, including interference effects, can be manifest in classical systems. Here we propose a model for quantum-like (QL) states and QL bits. We suggest a way that huge, complex systems can host robust states that can process information in a QL fashion. Axioms that such states should satisfy are proposed. Specifically, it is shown that building blocks suited for QL states are networks, possibly very complex, that we defined based on $k$-regular random graphs. These networks can dynamically encode a lot of information that is distilled into the emergent states we can use for QL like processing. Although the emergent states are classical, they have properties analogous to quantum states. Concrete examples of how QL functions are possible are given. The possibility of a `QL advantage' for computing-type operations and the potential relevance for new kinds of function in the brain are discussed and left as open questions.