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International Conference on Quantum Communications, Networking, and Computing (QCNC)

Grover’s Algorithm for Neural Networks

Andrew Haverly, Shahram Rahimi, M. A. Novotny

Published Mar 31, 2025• 2 citations
Publisher

Abstract

This paper introduces an application of Grover’s algorithm to optimize neural network training by eliminating the computationally demanding backward propagation. It clarifies previous assertions regarding training neural networks with Grover’s algorithm. The paper introduces parallel data training and training on exponentially seeded datasets. A quantum binary neural network is created to more efficiently implement neural networks on quantum computers. This trained discriminatory quantum binary neural network is shown to behave as a generative quantum binary neural network. We present methods that both simplify and enhance the process of neural network development and training through Grover’s algorithm. The quantum binary neural network has the potential to far outpace classical neural network training in terms of training time and energy.

DOI
10.1109/qcnc64685.2025.00111

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This paper introduces an application of Grover’s algorithm to optimize neural network training by eliminating the computationally demanding backward propagation. It clarifies previous assertions regarding training neural networks with Grover’s algorithm. The paper introduces parallel data training and training on exponentially seeded datasets. A quantum binary neural network is created to more efficiently implement neural networks on quantum computers. This trained discriminatory quantum binary neural network is shown to behave as a generative quantum binary neural network. We present methods that both simplify and enhance the process of neural network development and training through Grover’s algorithm. The quantum binary neural network has the potential to far outpace classical neural network training in terms of training time and energy.
Binary Neural Networks (BNNs) are the result of a simplification of network parameters in Artificial Neural Networks (ANNs). The computational complexity of training ANNs increases significantly as the size of the network increases. This complexity can be greatly reduced if the parameters of the network are binarized. Binarization, which is a one bit quantization, can also come with complications including error and information loss. The implementation of BNNs on quantum hardware could potentially provide a computational advantage over its classical counterpart. This is due to the fact that binarized parameters fit nicely to the nature of quantum hardware. Quantum superposition allows the network to be trained more efficiently, without using back propagation techniques, with the application of Grover's Algorithm for the training process. This paper looks into two BNN designs that utilize only quantum hardware, as opposed to hybrid quantum-classical implementations. It also provides practical implementations for both of them. Looking into their scalability, improvements on the design are proposed to reduce complexity even further.
This paper is about studying the application of quantum computing to develop machine learning methods, in order to optimize the time of calculation for processing extensive amounts of data, thanks to the use of the quantum superposition state of information, which enables to apply parallel computation for processing different parts of data simultaneously. In fact, we introduce a quantum approach, using Grover's algorithm, to search for the optimal parameters of a perceptron classifier as a fundamental element for developing a quantum neural network, with the proposition of the training process and the comparison with the related works. The proposed approach enables yielding the optimal parameters of a perceptron classifier with one application of Grover's search method rather than applying the iterative approaches that were previously introduced in the literature.
This paper highlights the possibility of creating quantum neural networks that are trained by Grover's Search Algorithm. The purpose of this work is to propose the concept of combining the training process of a neural network, which is performed on the principles of Grover's algorithm, with the functional structure of that neural network, interpreted as a quantum circuit. As a simple example of a neural network, to showcase the concept, a perceptron with one trainable parameter - the weight of a synapse connected to a hidden neuron.
This paper highlights a practical research of the possibility of forming quantum circuits for training neural networks. The demonstrated quantum circuits were based on the principles of Grover's Search Algorithm. The perceptron was chosen as the architecture for the example neural network. The multilayer perceptron is a popular neural network architecture due to its scalability and applicability for solving a wide range of problems. Large scale neural networks can require significant computing resources for training purposes, therefore Grover’s quantum search algorithm could be used as a way to speed up this process, thanks to its ability of simultaneously processing multiple input values of a given function.
Abstract Training of neural networks (NNs) has emerged as a major consumer of both computational and energy resources. Quantum computers were coined as a root to facilitate training, but no experimental evidence has been presented so far. Here we demonstrate that quantum annealing platforms, such as D-Wave, can enable fast and efficient training of classical NNs, which are then deployable on conventional hardware. From a physics perspective, NN training can be viewed as a dynamical phase transition: the system evolves from an initial spin glass state to a highly ordered, trained state. This process involves eliminating numerous undesired minima in its energy landscape. The advantage of annealing devices is their ability to rapidly find multiple deep states. We found that this quantum training achieves superior performance scaling compared to classical backpropagation methods, with a clearly higher scaling exponent (1.01 vs. 0.78). It may be further increased up to a factor of 2 with a fully coherent quantum platform using a variant of the Grover algorithm. Furthermore, we argue that even a modestly sized annealer can be beneficial to train a deep NN by being applied sequentially to a few layers at a time.
The performance of a neural network for a given task is largely determined by the initial calibration of the network parameters. Yet, it has been shown that the calibration, also referred to as training, is generally NP-complete. This includes networks with binary weights, an important class of networks due to their practical hardware implementations. We therefore suggest an alternative approach to training binary neural networks. It utilizes a quantum superposition of weight configurations. We show that the quantum training guarantees with high probability convergence towards the globally optimal set of network parameters. This resolves two prominent issues of classical training: (1) the vanishing gradient problem and (2) common convergence to suboptimal network parameters. Moreover we achieve a provable polynomial---sometimes exponential---speedup over classical training for certain classes of tasks. We design an explicit training algorithm and implement it in numerical simulations.