Quantum Hopfield neural network

TL;DR

This paper explores a quantum algorithm for Hopfield neural networks, enabling exponential storage capacity and logarithmic computational complexity, with applications in pattern recognition and genetic sequence identification.

Contribution

It introduces a quantum encoding method for Hopfield networks that significantly enhances storage capacity and computational efficiency.

Findings

Exponential network storage in polynomial quantum bits

Logarithmic complexity in data dimension

Successful application to genetic sequence recognition

Abstract

Quantum computing allows for the potential of significant advancements in both the speed and the capacity of widely used machine learning techniques. Here we employ quantum algorithms for the Hopfield network, which can be used for pattern recognition, reconstruction, and optimization as a realization of a content-addressable memory system. We show that an exponentially large network can be stored in a polynomial number of quantum bits by encoding the network into the amplitudes of quantum states. By introducing a classical technique for operating the Hopfield network, we can leverage quantum algorithms to obtain a quantum computational complexity that is logarithmic in the dimension of the data. We also present an application of our method as a genetic sequence recognizer.