Outgoing inspection of the production line is very important for many manufacturing companies. In recent years, two class classification of good and defective products must be carried out efficiently as the number of small-quantity, high-mix products have been increasing. The support vector machine with kernel method (kernel learning) is the most popular method in two class classification used in factories. Quantum kernel learning is one of the most promising applications of quantum technology. In this study, we propose an analysis method that allows us to know the difference between classical and quantum machine learning by plotting false positive rate (FPR) and true positive rate (TPR) on Receiver Operating Characteristic (ROC) space. Quantum machine learning uses quantum data with feature maps. We compared quantum and classical data using a small-sized existing datasets. First, it was not possible to confirm that the quantum data incorporating quantum entanglement could achieve the effect in this study. Next, when we examined the learning process of quantum data with Pauli feature map and classical data, we observed differences in the initial learning process. Based on these results, in contrast to the commonly used ROC curve, we plotted the FPR and TPR separately on the ROC space according to the training size. Plotting on ROC space in this experiment shows that quantum kernel learning is a method to reduce only FPR from high FPR and TPR. We found that the kernel learning process using quantum data is different from one using classical data.
Outgoing inspection of the production line is very important for many manufacturing companies. In recent years, two class classification of good and defective products must be carried out efficiently as the number of small-quantity, high-mix products have been increasing. The support vector machine with kernel method (kernel learning) is the most popular method in two class classification used in factories. Quantum kernel learning is one of the most promising applications of quantum technology. In this study, we propose an analysis method that allows us to know the difference between classical and quantum machine learning by plotting false positive rate (FPR) and true positive rate (TPR) on Receiver Operating Characteristic (ROC) space. Quantum machine learning uses quantum data with feature maps. We compared quantum and classical data using a small-sized existing datasets. First, it was not possible to confirm that the quantum data incorporating quantum entanglement could achieve the effect in this study. Next, when we examined the learning process of quantum data with Pauli feature map and classical data, we observed differences in the initial learning process. Based on these results, in contrast to the commonly used ROC curve, we plotted the FPR and TPR separately on the ROC space according to the training size. Plotting on ROC space in this experiment shows that quantum kernel learning is a method to reduce only FPR from high FPR and TPR. We found that the kernel learning process using quantum data is different from one using classical data.
Abstract For many manufacturing companies, the production line is very important. In recent years, the number of small-quantity, high-mix products have been increasing, and the identification of good and defective products must be carried out efficiently. At that time, machine learning is a very important issue on shipping inspection using small amounts of data. Quantum machine learning is one of most exciting prospective applications of quantum technologies. SVM using kernel estimation is one of most popular methods for classifiers. Our purpose is to search quantum advantage on classifier to enable us to classifier in inspection test for small size datasets. In this study, we made clear the difference between classical and quantum kernel learning in initial state and propose analysis of learning process by plotting ROC space. To meet the purpose, we investigated the effect of each feature map compared to classical one, using evaluation index. The simulation results show that the learning model construction process between quantum and classical kernel learning is different in initial state. Moreover, the result indicates that the learning model of quantum kernel is the method to decrease the false positive rate (FPR) from high FPR, keeping high true positive rates on several datasets. We demonstrate that learning process on quantum kernel is different from classical one in initial state and plotting to ROC space graph is effective when we analyse the learning model process.
Abstract Quantum machine learning is one of most exciting prospective applications of quantum technologies. Quantum kernel SVM is one of most popular methods for classifiers. However, there are few reports that show the quantum advantage in learning model construction compared with classical learning models. In this work, we investigated the process of learning model construction of quantum machine learning by using an evaluation index and ROC space graph. The behaviour between quantum and classical machine learning is different, and the quantum learning model is the method to decrease the false positive rate from high false and true positive rates that is based on quantum superposition. In summary, we have demonstrated the effect of quantum superposition on quantum machine learning for the first time from actual experimental results. This truth supports that quantum machine learning can build an outline of learning models faster than classical methods even if the number of original data is smaller.
We aim to use quantum machine learning to detect various anomalies in image inspection by using small size data. Assuming the possibility that the expressive power of the quantum kernel space is superior to that of the classical kernel space, we are studying a quantum machine learning model. Through trials of image inspection processes not only for factory products but also for products including agricultural products, the importance of trials on real data is recognized. In this study, training was carried out on SVMs embedded with various quantum kernels on a small number of agricultural product image data sets collected in the markets. The quantum kernels prepared in this study consisted of a smaller number of rotating gates and control gates. The F1 scores for each quantum kernel showed a significant effect of using CNOT gates. After confirming the results with a quantum simulator, the usefulness of the quantum kernels was confirmed on a quantum computer. Learning with SVMs embedded with specific quantum kernels showed significantly higher values of the AUC compared to classical kernels. The reason for the lack of learning in quantum kernels is considered to be due to kernel concentration or exponential concentration similar to the Baren plateau. The reason why the F1 score does not increase as the number of features increases is suggested to be due to exponential concentration, while at the same time it is possible that only certain features have discriminative ability. Furthermore, it is suggested that controlled Toffoli gate may be a promising quantum kernel component.
Quantum-enhanced machine learning is a rapidly evolving field that aims to leverage the unique properties of quantum mechanics to enhance classical machine learning. However, the practical applicability of these methods remains an open question, particularly beyond the context of specifically crafted toy problems, and given the current limitations of quantum hardware. This study focuses on quantum kernel methods in the context of classification tasks. In particular, it examines the performance of quantum kernel estimation and quantum kernel training (QKT) in connection with two quantum feature mappings, namely, ZZFeatureMap and CovariantFeatureMap. Remarkably, these feature maps have been proposed in the literature under the conjecture of possible near-term quantum advantage and have shown promising performance in ad hoc datasets. This study aims to evaluate their versatility and generalization capabilities in a more general benchmark, encompassing both artificial and established reference datasets. Classical machine learning methods, specifically support vector machines and logistic regression, are also incorporated as baseline comparisons. Experimental results indicate that quantum methods exhibit varying performance across different datasets. Despite outperforming classical methods in ad hoc datasets, mixed results are obtained for the general case among standard classical benchmarks. The experimental data call into question a general added value of applying QKT optimization, for which the additional computational cost does not necessarily translate into improved classification performance. Instead, it is suggested that a careful choice of the quantum feature map in connection with proper hyperparameterization may prove more effective.
The support vector machine algorithm with a quantum kernel estimator (QSVM-Kernel), as a leading example of a quantum machine learning technique, has undergone significant advancements. Nevertheless, its integration with classical data presents unique challenges. While quantum computers primarily interact with data in quantum states, embedding classical data into quantum states using feature mapping techniques is essential for leveraging quantum algorithms Despite the recognized importance of feature mapping, its specific impact on data classification outcomes remains largely unexplored. This study addresses this gap by comprehensively assessing the effects of various feature mapping methods on classification results, taking medical data analysis as a case study. In this study, the QSVM-Kernel method was applied to classification problems in two different and publicly available medical datasets, namely, the Wisconsin Breast Cancer (original) and The Cancer Genome Atlas (TCGA) Glioma datasets. In the QSVM-Kernel algorithm, quantum kernel matrices obtained from 9 different quantum feature maps were used. Thus, the effects of these quantum feature maps on the classification results of the QSVM-Kernel algorithm were examined in terms of both classifier performance and total execution time. As a result, in the Wisconsin Breast Cancer (original) and TCGA Glioma datasets, when Rx and Ry rotational gates were used, respectively, as feature maps in the QSVM-Kernel algorithm, the best classification performances were achieved both in terms of classification performance and total execution time. The contributions of this study are that (1) it highlights the significant impact of feature mapping techniques on medical data classification outcomes using the QSVM-Kernel algorithm, and (2) it also guides undertaking research for improved QSVM classification performance.
A basic idea of quantum computing is surprisingly similar to that of kernel methods in machine learning, namely, to efficiently perform computations in an intractably large Hilbert space. In this Letter we explore some theoretical foundations of this link and show how it opens up a new avenue for the design of quantum machine learning algorithms. We interpret the process of encoding inputs in a quantum state as a nonlinear feature map that maps data to quantum Hilbert space. A quantum computer can now analyze the input data in this feature space. Based on this link, we discuss two approaches for building a quantum model for classification. In the first approach, the quantum device estimates inner products of quantum states to compute a classically intractable kernel. The kernel can be fed into any classical kernel method such as a support vector machine. In the second approach, we use a variational quantum circuit as a linear model that classifies data explicitly in Hilbert space. We illustrate these ideas with a feature map based on squeezing in a continuous-variable system, and visualize the working principle with two-dimensional minibenchmark datasets.