Problem Solving with Hopfield Networks and Adiabatic Quantum Computing

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.