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Wave Electronics and its Application in Information and Telecommunication Systems (WECONF)

Application of a Quantum Annealer for Pattern Recognition

Evgenii V. Burlakov

Published May 12, 2025• 1 citation
Publisher

Abstract

Adiabatic quantum computing is successfully used to solve discrete optimization problems. The classical Hopfield neural network can also be applied to such problems but is primarily used for pattern recognition and reconstruction. Since its dynamics are deterministic, this can adversely affect its performance: the network sometimes gets trapped in local energy minima. This paper proposes a novel approach in which the Hopfield neural network learning rule (Hebbian rule) is combined with forward and reverse quantum annealing. This enables the use of adiabatic quantum annealers for pattern recognition, providing an alternative to traditional approaches.

DOI
10.1109/weconf65186.2025.11016976

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Adiabatic quantum computing is successfully used to solve discrete optimization problems. The classical Hopfield neural network can also be applied to such problems but is primarily used for pattern recognition and reconstruction. Since its dynamics are deterministic, this can adversely affect its performance: the network sometimes gets trapped in local energy minima. This paper proposes a novel approach in which the Hopfield neural network learning rule (Hebbian rule) is combined with forward and reverse quantum annealing. This enables the use of adiabatic quantum annealers for pattern recognition, providing an alternative to traditional approaches.
This study compares three discrete-variable models: the fully connected Ising model, the quadratic unconstrained binary optimization model, and the Hopfield neural network. The analysis evaluates their potential interchangeability in solving optimization and pattern recognition tasks, as well as their applicability to quantum computing. A novel method for pattern storage and recognition is proposed, based on the dynamics of forward and reverse quantum annealing. This method has been successfully tested on a D-Wave adiabatic quantum computer. An optimal annealing parameter was empirically determined, maximizing recognition accuracy while minimizing annealing time. The study also highlights limitations related to the size and noise levels of the patterns, imposed by the quantum processor's architectural constraints. Finally, conclusions are drawn regarding the effectiveness implications of the proposed approach.
Abstract Quantum computing is a new mode that follows the laws of quantum mechanics. It performs computational tasks based on the control of quantum units. From the view of computable problems, quantum computers can only solve the problems that traditional computers can solve, but considering the efficiency of computation, due to the existence of quantum superposition, some known quantum algorithms are exponentially faster than traditional general-purpose computers. In this article, we combine quantum computing with a classical neural network to design a quantum Hopfield network. Each neuron is initialized to a specified state and evolved into a steady state. The output result is one of patterns in a training set. We also present an application of this protocol in image recognition. The simulation results show that this network works in the quantum environment and the output images are correct, therefore the feasibility of this protocol is verified.
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.
Quantum machine learning has the potential to enable advances in artificial intelligence, such as solving problems intractable on classical computers. Some fundamental ideas behind quantum machine learning are similar to kernel methods in classical machine learning. Both process information by mapping it into high-dimensional vector spaces without explicitly calculating their numerical values. We explore a setup for performing classification on labeled classical datasets, consisting of a classical neural network connected to a quantum annealer. The neural network programs the quantum annealer's controls and thereby maps the annealer's initial states into new states in the Hilbert space. The neural network's parameters are optimized to maximize the distance of states corresponding to inputs from different classes and minimize the distance between quantum states corresponding to the same class. Recent literature showed that at least some of the "learning" is due to the quantum annealer, connecting a small linear network to a quantum annealer and using it to learn small and linearly inseparable datasets. In this study, we consider a similar but not quite the same case, where a classical fully-fledged neural network is connected with a small quantum annealer. In such a setting, the fully-fledged classical neural-network already has built-in nonlinearity and learning power, and can already handle the classification problem alone, we want to see whether an additional quantum layer could boost its performance. We simulate this system to learn several common datasets, including those for image and sound recognition. We conclude that adding a small quantum annealer does not provide a significant benefit over just using a regular (nonlinear) classical neural network.
There is increasing interest in quantum computing, because of its enormous computing potential. A small number of powerful quantum algorithms have been proposed to date; however, the development of new quantum algorithms for practical use remains essential. Parallel computing with a neural network has successfully realized certain unique functions such as learning and recognition; therefore, the introduction of certain neural computing techniques into quantum computing to enlarge the quantum computing application field is worthwhile. In this paper, a novel quantum associative memory (QuAM) is proposed, which is achieved with a quantum neural network by employing adiabatic Hamiltonian evolution. The memorization and retrieval procedures are inspired by the concept of associative memory realized with an artificial neural network. To study the detailed dynamics of our QuAM, we examine two types of Hamiltonians for pattern memorization. The first is a Hamiltonian having diagonal elements, which is known as an Ising Hamiltonian and which is similar to the cost function of a Hopfield network. The second is a Hamiltonian having non-diagonal elements, which is known as a neuro-inspired Hamiltonian and which is based on interactions between qubits. Numerical simulations indicate that the proposed methods for pattern memorization and retrieval work well with both types of Hamiltonians. Further, both Hamiltonians yield almost identical performance, although their retrieval properties differ. The QuAM exhibits new and unique features, such as a large memory capacity, which differs from a conventional neural associative memory.