Quantum Hopfield Neural Networks: A New Approach and Its Storage Capacity

At the interface between quantum computing and machine learning, the field of quantum machine learning aims to improve classical machine learning algorithms with the help of quantum computers. Examples are Hopfield neural networks, which can store patterns and thereby are used as associative memory. However, the storage capacity of such classical networks is limited. In this work, we present a new approach to quantum Hopfield neural networks with classical inputs and outputs. The approach is easily extendable to quantum inputs or outputs. Performance is evaluated by three measures of error rates, introduced in this paper. We simulate our approach and find increased storage capacity compared to classical networks for small systems. We furthermore present classical results that indicate an increased storage capacity for quantum Hopfield neural networks in large systems as well.