The role of coherence theory in attractor quantum neural networks

TL;DR

This paper explores how coherence theory explains the functioning of attractor quantum neural networks, linking network depth to decoherence and showing potential performance improvements using entanglement or coherence.

Contribution

It introduces a coherence-theoretic framework for aQNNs, relating network properties to quantum coherence and decoherence, and analyzes the impact of noise and resource enhancement.

Findings

aQNNs are linked to non-coherence-generating channels

Network depth correlates with decohering power

Performance can be improved with entanglement or coherence

Abstract

We investigate attractor quantum neural networks (aQNNs) within the framework of coherence theory. We show that: i) aQNNs are associated to non-coherence-generating quantum channels; ii) the depth of the network is given by the decohering power of the corresponding quantum map; and iii) the attractor associated to an arbitrary input state is the one minimizing their relative entropy. Further, we examine faulty aQNNs described by noisy quantum channels, derive their physical implementation and analyze under which conditions their performance can be enhanced by using entanglement or coherence as external resources.