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Quantum algorithm for the implementation of a perceptron

Riccardo Bon

Published Nov 25, 2019• 0 citations
OpenAlex

Abstract

Quantum information and quantum computers have enabled us to write algorithms, - quantum algorithms - that in some cases display a speedup with respect to their classical counterpart. As machine learning is becoming of upmost importance not only for our every-day-life and for scientific research, it is natural to inquire if we could use methods from quantum information to speed up machine learning’s processes. In this Thesis, we review a model of a quantum perceptron, a key component for modern neural networks, and simulate its time evolution to characterize behavior.

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Quantum information and quantum computers have enabled us to write
algorithms, - quantum algorithms - that in some cases display a speedup
with respect to their classical counterpart. As machine learning is
becoming of upmost importance not only for our every-day-life and for
scientific research, it is natural to inquire if we could use methods
from quantum information to speed up machine learning’s processes. In
this Thesis, we review a model of a quantum perceptron, a key component
for modern neural networks, and simulate its time evolution to
characterize behavior.
Abstract Artificial neural networks are the heart of machine learning algorithms and artificial intelligence. Historically, the simplest implementation of an artificial neuron traces back to the classical Rosenblatt’s “perceptron”, but its long term practical applications may be hindered by the fast scaling up of computational complexity, especially relevant for the training of multilayered perceptron networks. Here we introduce a quantum information-based algorithm implementing the quantum computer version of a binary-valued perceptron, which shows exponential advantage in storage resources over alternative realizations. We experimentally test a few qubits version of this model on an actual small-scale quantum processor, which gives answers consistent with the expected results. We show that this quantum model of a perceptron can be trained in a hybrid quantum-classical scheme employing a modified version of the perceptron update rule and used as an elementary nonlinear classifier of simple patterns, as a first step towards practical quantum neural networks efficiently implemented on near-term quantum processing hardware.
Quantum machine learning emerges from the symbiosis of quantum mechanics and machine learning. In particular, the latter gets displayed in quantum sciences as: (i) the use of classical machine learning as a tool applied to quantum physics problems, (ii) or the use of quantum resources such as superposition, entanglement, or quantum optimization protocols to enhance the performance of classification and regression tasks compare to their classical counterparts. This paper reviews examples in these two scenarios. On the one hand, the application of classical neural network to design a new quantum sensing protocol. On the other hand, the design of a quantum neural network based on the dynamics of a quantum perceptron optimized with the aid of shortcuts to adiabaticity gives rise to a short operation time and robust performance. These examples demonstrate the mutual reinforcement of both neural networks and quantum physics.
This Ph.D. thesis provides a comprehensive review of the state-of-the-art in the field of Variational Quantum Algorithms and Quantum Machine Learning, including numerous original contributions. The first chapters are devoted to a brief summary of quantum computing and an in-depth analysis of variational quantum algorithms. The discussion then shifts to quantum machine learning, where an introduction to the elements of machine learning and statistical learning theory is followed by a review of the most common quantum counterparts of machine learning models. Next, several novel contributions to the field based on previous work are presented, namely: a newly introduced model for a quantum perceptron with applications to recognition and classification tasks; a variational generalization of such a model to reduce the circuit footprint of the proposed architecture; an industrial use case of a quantum autoencoder followed by a quantum classifier used to analyze classical data from an industrial power plant; a study of the entanglement features of quantum neural network circuits; and finally, a noise deconvolution technique to remove a large class of noise when performing arbitrary measurements on qubit systems.
For the past two decades, researchers have attempted to create a Quantum Neural Network (QNN) by combining the merits of quantum computing and neural computing. In order to exploit the advantages of the two prolific fields, the QNN must meet the non-trivial task of integrating the unitary dynamics of quantum computing and the dissipative dynamics of neural computing. At the core of quantum computing and neural computing lies the qubit and perceptron, respectively. We see that past implementations of the quantum perceptron model have failed to fuse the two elegantly. This was due to a slow learning rule and a disregard for the unitary requirement. In this paper, we present a quantum perceptron that can compute functions uncomputable by the classical perceptron while analytically solving for parameters and preserving the unitary and dissipative requirements.
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.
Quantum Machine Learning (QML) represents a promising frontier of research where the principles of quantum mechanics are combined with machine learning to offer potentially superior performance over classical counterparts. This review article explores the current advancements in QML, specifically focusing on the performance improvement and comparison between standard classical algorithms and their quantum implementations. We initiate with an overview of fundamental quantum algorithms that have found applicability within machine learning contexts, such as quantum principal component analysis and quantum support vector machines. The review then delves into a critical assessment of these quantum approaches, highlighting case studies where quantum implementations have demonstrated computational speedups or improved accuracy. Furthermore, we investigate the inherent challenges and limitations that currently hinder the widespread adoption of QML technologies, including the issues of decoherence, error rates, and quantum resource requirements. In addition, the review provides insights into the current state of quantum hardware and its scalability for machine learning tasks. Throughout, comparisons are made to outline scenarios in which quantum machine learning presents a genuine advantage over classical techniques, supported by performance metrics and benchmark datasets. The article concludes by discussing future directions in QML research, with an emphasis on algorithmic innovation and hardware improvement, to realize the full potential of quantum-enhanced machine learning.