Adiabatic quantum optimization for associative memory recall

Abstract

Hopfield networks are a variant of associative memory that recall patterns stored in the couplings of an Ising model. Stored memories are conventionally accessed as fixed points in the network dynamics that correspond to energetic minima of the spin state. We show that memories stored in a Hopfield network may also be recalled by energy minimization using adiabatic quantum optimization (AQO). Numerical simulations of the underlying quantum dynamics allow us to quantify AQO recall accuracy with respect to the number of stored memories and noise in the input key. We investigate AQO performance with respect to how memories are stored in the Ising model according to different learning rules. Our results demonstrate that AQO recall accuracy varies strongly with learning rule, a behavior that is attributed to differences in energy landscapes. Consequently, learning rules offer a family of methods for programming adiabatic quantum optimization that we expect to be useful for characterizing AQO performance.

Recall Performance for Content-Addressable Memory Using Adiabatic Quantum Optimization

“…We previously verified the principles of CAM recall by adiabatic quantum optimization using numerical simulations to investigate the pure-state dynamics of a small memory system [28]. Through simulations of the quantum dynamics, we showed that specific key-value associations could be recovered when the ground state of an encoded Ising model Hamiltonian was prepared by adiabatic quantum optimization.…”

“…In this scenario, the input value is then recalled as opposed to stored memory. This critical value can be calculated based on the Hamming distance between the stored memories [28,34]. For a given problem instance, we recover the lowest energy eigenstate of H θ using AQO.…”

“…As a specific example, we consider the application of adiabatic quantum optimization to the problem of recall in a content-addressable memory system [28]. Content-addressable memory (CAM) represents a memory structure in which key-value data is recalled based on its value as opposed to its key [29].…”

“…CAM recall using adiabatic quantum computing is based on finding the energetic minimum of a Ising model constructed from a database of known key-value pairs [28]. Under ideal conditions, the energetic minimum within this Ising model energy landscape encodes the association between a sought-after key-value pair.…”

Identifying the minor set cover of dense connected bipartite graphs via random matching edge sets

“…The full embedding of a problem graph in the hardware graph is found by first embedarXiv:1612.07366v1 [math-ph] 21 Dec 2016 ding into a chosen virtual hardware or one of its minors. Our choice of a bipartite virtual representation for the hardware is motivated in part by the simplicity of the structure as well as its balance between size and order of the virtual representation, and additionally for its connection to associative memory recall and other variants of machine learning applications [21]. We note that alternative virtual representations are equally valid, e.g., a square grid.…”