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arXiv:2110.01443

Development and Training of Quantum Neural Networks, Based on the Principles of Grover's Algorithm

C. B. Pronin, Andrey Vladimirovich Ostroukh

Published Oct 1, 2021• 1 citation
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Abstract

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.

DOI
10.48550/arxiv.2110.01443

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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.
В данной работе рассматривается возможность создания квантовых нейронных сетей, обучаемых с помощью алгоритма Гровера. Цель данной работы заключается в совмещении процесса обучения нейронной сети, производимого с помощью алгоритма Гровера, и функциональной структуры нейронной сети, интерпретированной в виде квантовой схемы. В качестве простого примера нейронной сети, для рассмотрения концепции, был предложен персептрон с одним обучаемым параметром – весом синапса, входящего в скрытый нейрон. This paper discusses the possibility of creating quantum neural networks trained using Grover’s algorithm. The purpose of this work is to combine the learning process of the neural network, produced using Grover’s algorithm, and the functional structure of the neural network, interpreted as a quantum circuit. As a simple example of a neural network, to consider the concept, a perceptron was proposed with one learning parameter – the weight of a synapse entering 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.
This paper showcases a method of parametric synthesis of quantum circuits for training perceptron neural networks. Synapse weights are found using Grover's algorithm with a modified oracle function. The results of running these parametrically synthesized circuits for training perceptrons of three different topologies are described. The circuits were run on a 100-qubit IBM quantum simulator. The synthesis of quantum circuits is carried out using quantum synthesizer "Naginata", which was developed in the scope of this work, the source code of which is published and further documented on GitHub. The article describes the quantum circuit synthesis algorithm for training single-layer perceptrons. At the moment, quantum circuits are created mainly by manually placing logic elements on lines that symbolize quantum bits. The purpose of creating Quantum Circuit Synthesizer "Naginata" was due to the fact that even with a slight increase in the number of operations in a quantum algorithm, leads to the significant increase in size of the corresponding quantum circuit. This causes serious difficulties both in creating and debugging these quantum circuits. The purpose of our quantum synthesizer is enabling users an opportunity to implement quantum algorithms using higher-level commands. This is achieved by creating generic blocks for frequently used operations such as: the adder, multiplier, digital comparator (comparison operator), etc. Thus, the user could implement a quantum algorithm by using these generic blocks, and the quantum synthesizer would create a suitable circuit for this algorithm, in a format that is supported by the chosen quantum computation environment. This approach greatly simplifies the processes of development and debugging a quantum algorithm.
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 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.