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Промышленные АСУ и контроллеры.

Creation and Training of Quantum Neural Networks Based on Grover’s Algorithm

Пронин Цезарь Борисович, Andrey Vladimirovich Ostroukh

Published Nov 26, 2021• 1 citation
Publisher

Abstract

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.

DOI
10.25791/asu.11.2021.1328

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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.
Целью данной работы, является практическое исследование возможности формирования квантовых схем для машинного обучения нейронных сетей. За основу демонстрируемых квантовых схем были взяты принципы работы квантового алгоритма Гровера (Grover’s Search Algorithm). За архитектуру примера обучаемой нейронной сети был взят персептрон. Многослойный персептрон является достаточно популярной архитектурой нейронной сети за счет масштабируемости и возможности применения для решения широкого спектра задач. The purpose of this work is a practical study of the possibility of forming quantum schemes for machine learning neural networks. The principles of operation of the Grovers Search Algorithm (Grover’s Search Algorithm) were taken as the basis of the quantum schemes. For the architecture of an example of a trained neural network was taken by Perseceptron. The multilayer perceptron is a fairly popular neural network architecture due to scalability and the possibility of applying a wide range of tasks.
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.
A consolidated review of studies, forming a single line of work on constructing and applying quantum circuits for machine learning: From the Deutsch-Jozsa Algorithm to Training Quantum Neural Networks Based on Grover’s Algorithm. The matrix formalism of transformations in quantum circuits is summarised, and the Deutsch-Jozsa algorithm is implemented step by step by manual matrix calculation, matching the Quirk simulation. Reversible quantum analogues of classical logic elements (NOT, AND, OR, XOR) and circuits — a full adder and a 2-bit multiplier — are constructed; a reversible multiplier is used as an oracle function of Grover's algorithm. A principle for building mathematical oracle functions that rotate only the amplitude of the solution while uncomputing auxiliary operations is formulated, and the gain of Grover iterations over brute-force search is estimated (about 326 times for a 16-qubit register). A concept of quantum circuits for perceptron training with an oracle built from the activation function is proposed; training of a single-weight quantum perceptron is demonstrated. Circuit optimisation by composing gate sequences into a single operation and debugging Grover's algorithm on IBM Q prototypes, which revealed noise growth with circuit depth, are reported. Limitations (2-3-qubit registers, simulators and NISQ devices, arithmetic bit width) and further research directions are discussed.
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.