Adiabatic Quantum Optimization for Associative Memory Recall

TL;DR

This paper explores using adiabatic quantum optimization to recall memories in Hopfield networks, analyzing how different learning rules affect recall accuracy and energy landscape complexity.

Contribution

It introduces a quantum approach to associative memory recall and examines how learning rules influence AQO performance and computational complexity.

Findings

AQO recall accuracy depends on the number of stored memories and input noise.

Performance varies significantly with different memory storage learning rules.

Learning rules indirectly affect the energy landscape and computational efficiency.

Abstract

Hopfield networks are a variant of associative memory that recall information stored in the couplings of an Ising model. Stored memories are fixed points for the network dynamics that correspond to energetic minima of the spin state. We formulate the recall of memories stored in a Hopfield network using energy minimization by adiabatic quantum optimization (AQO). Numerical simulations of the quantum dynamics allow us to quantify the AQO recall accuracy with respect to the number of stored memories and the noise in the input key. We also investigate AQO performance with respect to how memories are stored in the Ising model using different learning rules. Our results indicate that AQO performance varies strongly with learning rule due to the changes in the energy landscape. Consequently, learning rules offer indirect methods for investigating change to the computational complexity of the recall task and the computational efficiency of AQO.