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Joint International Conference on Information Sciences

Pattern Classification Using a Quantum System

Dan A. Ventura

Published Jan 1, 2002• 5 citations
OpenAlex

Abstract

We consider and compare three approaches to quantum pattern classification, presenting empirical results from simulations.

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Pattern classification represents a challenging problem in machine learning and data science research domains, especially when there is a limited availability of training samples. In recent years, artificial neural network (ANN) algorithms have demonstrated astonishing performance when compared to traditional generative and discriminative classification algorithms. However, due to the complexity of classical ANN architectures, ANNs are sometimes incapable of providing efficient solutions when addressing complex distribution problems. Motivated by the mathematical definition of a quantum bit (qubit), we propose a novel autonomous perceptron model (APM) that can solve the problem of the architecture complexity of traditional ANNs. APM is a nonlinear classification model that has a simple and fixed architecture inspired by the computational superposition power of the qubit. The proposed perceptron is able to construct the activation operators autonomously after a limited number of iterations. Several experiments using various datasets are conducted, where all the empirical results show the superiority of the proposed model as a classifier in terms of accuracy and computational time when it is compared with baseline classification models.

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Although quantum neural networks (QNNs) have shown promising results in solving simple machine learning tasks recently, the behavior of QNNs in binary pattern classification is still underexplored. In this work, we find that QNNs have an Achilles’ heel in binary pattern classification. To illustrate this point, we provide a theoretical insight into the properties of QNNs by presenting and analyzing a new form of symmetry embedded in a family of QNNs with full entanglement , which we term negational symmetry . Due to negational symmetry, QNNs can not differentiate between a quantum binary signal and its negational counterpart. We empirically evaluate the negational symmetry of QNNs in binary pattern classification tasks using Google’s quantum computing framework. Both theoretical and experimental results suggest that negational symmetry is a fundamental property of QNNs, which is not shared by classical models. Our findings also imply that negational symmetry is a double-edged sword in practical quantum applications.
The problem of pattern classification in quantum data has been of great importance over the past few years. This study investigates the effect of deploying Grover’s, the partial diffusion, and the fixed-phase algorithms separately to amplify the amplitudes of a desired pattern in an unstructured dataset. These quantum search operators were applied to symmetric and antisymmetric input superpositions on a three-qubit system for 20 iterations each. After each iteration, different probabilities of classification were calculated in order to determine the accuracy of classification for each of the three quantum search operators. The results indicated that, in the case of applying the three quantum search operators to incomplete superposition input states, the partial diffusion operator outperformed the other operators with a probability of correct classification that reached 100% in certain iterations. It also showed that the classification accuracy of the fixed-phase operator exceeded the accuracy of the other two operators by 40% in most cases when the input state was a uniform superposition, and some of the basis states were phase-inverted.
Pattern classification represents a challenging problem in machine learning and data science research domains, especially when there is a limited availability of training samples. In recent years, artificial neural network (ANN) algorithms have demonstrated astonishing performance when compared to traditional generative and discriminative classification algorithms. However, due to the complexity of classical ANN architectures, ANNs are sometimes incapable of providing efficient solutions when addressing complex distribution problems. Motivated by the mathematical definition of a quantum bit (qubit), we propose a novel autonomous perceptron model (APM) that can solve the problem of the architecture complexity of traditional ANNs. APM is a nonlinear classification model that has a simple and fixed architecture inspired by the computational superposition power of the qubit. The proposed perceptron is able to construct the activation operators autonomously after a limited number of iterations. Several experiments using various datasets are conducted, where all the empirical results show the superiority of the proposed model as a classifier in terms of accuracy and computational time when it is compared with baseline classification models.