Hopfield Network and Adiabatic Quantum Computation

Masamichi Akazawa

Catherine C. McGeoch

Christian Bauckhage, Ramsés J. Sánchez, Rafet Sifa

Our goal with this paper is to elucidate the close connection between Hopfield networks and adiabatic quantum computing. Focusing on their use in problem solving, we point out that the energy functions minimized by Hopfield networks are essentially identical to those minimized by adiabatic quantum computers. To practically illustrate this, we consider a simple textbook problem, namely the k-rooks problem, and discuss how to set it up for solution via a Hopfield network or adiabatic quantum computing.

Ray LaPierre

Evgenii V. Burlakov

Adiabatic quantum computing is successfully used to solve discrete optimization problems. The classical Hopfield neural network can also be applied to such problems but is primarily used for pattern recognition and reconstruction. Since its dynamics are deterministic, this can adversely affect its performance: the network sometimes gets trapped in local energy minima. This paper proposes a novel approach in which the Hopfield neural network learning rule (Hebbian rule) is combined with forward and reverse quantum annealing. This enables the use of adiabatic quantum annealers for pattern recognition, providing an alternative to traditional approaches.

Wolfgang Scherer