A quantum diffusion network

TL;DR

This paper introduces a quantum-thermal hybrid version of Wong's diffusion network, analyzing its convergence and discussing auxiliary functions, aiming to enhance performance over traditional thermal annealing methods.

Contribution

It presents a novel joint quantum and thermal diffusion network model and studies its convergence properties, extending Wong's classical diffusion network with quantum annealing concepts.

Findings

Convergence properties of the quantum-thermal diffusion network are established.

Different auxiliary functions, including kinetic types, are analyzed for the network.

The model potentially improves performance over classical thermal annealing methods.

Abstract

Wong's diffusion network is a stochastic, zero-input Hopfield network with a Gibbs stationary distribution over a bounded, connected continuum. Previously, logarithmic thermal annealing was demonstrated for the diffusion network and digital versions of it were studied and applied to imaging. Recently, "quantum" annealed Markov chains have garnered significant attention because of their improved performance over "pure" thermal annealing. In this note, a joint quantum and thermal version of Wong's diffusion network is described and its convergence properties are studied. Different choices for "auxiliary" functions are discussed, including those of the kinetic type previously associated with quantum annealing.