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Research on Compact Quantum Classifier Based on Kernel Method

Ruihong Jia, Guang Yang, Min Nie, Yun Zhang

Published Mar 10, 2023• 0 citations
Publisher

Abstract

Kernel method is widely used in machine learning. At present, the connection between kernel methods and quantum computing has been gradually established, which provides a new algorithm idea for the field of quantum machine learning. Research shows that the construction of minimized quantum circuits can be reliably performed on Noisy Intermediate-Scale Quantum (NISQ) devices. This paper proposes a compact quantum classifier based on kernel method. By introducing the compact amplitude encoding, the data label of the phase corresponding to the quantum state is encoded. Compared with the proposed classifier based on quantum kernel method, it can reduce 2 quantum registers, further reduce the circuit depth, and thus reduce the algorithm complexity. The double qubit measurement is simplified to single qubit measurement. In addition, this model achieves the optimal variance in quantum circuit parameters, which can effectively save computational resources. Experimental simulation shows that the expected value measurement in the proposed classifier model is closer to the theoretical value, and the classification accuracy is more accurate. At the same time, the system model has low entanglement, which can effectively reduce the cost of the whole preparation.

DOI
10.1145/3589572.3589592

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Kernel method is widely used in machine learning. At present, the connection between kernel methods and quantum computing has been gradually established, which provides a new algorithm idea for the field of quantum machine learning. Research shows that the construction of minimized quantum circuits can be reliably performed on Noisy Intermediate-Scale Quantum (NISQ) devices. This paper proposes a compact quantum classifier based on kernel method. By introducing the compact amplitude encoding, the data label of the phase corresponding to the quantum state is encoded. Compared with the proposed classifier based on quantum kernel method, it can reduce 2 quantum registers, further reduce the circuit depth, and thus reduce the algorithm complexity. The double qubit measurement is simplified to single qubit measurement. In addition, this model achieves the optimal variance in quantum circuit parameters, which can effectively save computational resources. Experimental simulation shows that the expected value measurement in the proposed classifier model is closer to the theoretical value, and the classification accuracy is more accurate. At the same time, the system model has low entanglement, which can effectively reduce the cost of the whole preparation.
Abstract Quantum computing opens exciting opportunities for kernel-based machine learning methods, which have broad applications in data analysis. Recent works show that quantum computers can efficiently construct a model of a classifier by engineering the quantum interference effect to carry out the kernel evaluation in parallel. For practical applications of these quantum machine learning methods, an important issue is to minimize the size of quantum circuits. We present the simplest quantum circuit for constructing a kernel-based binary classifier. This is achieved by generalizing the interference circuit to encode data labels in the relative phases of the quantum state and by introducing compact amplitude encoding, which encodes two training data vectors into one quantum register. When compared to the simplest known quantum binary classifier, the number of qubits is reduced by two and the number of steps is reduced linearly with respect to the number of training data. The two-qubit measurement with post-selection required in the previous method is simplified to single-qubit measurement. Furthermore, the final quantum state has a smaller amount of entanglement than that of the previous method, which advocates the cost-effectiveness of our method. Our design also provides a straightforward way to handle an imbalanced data set, which is often encountered in many machine learning problems.
To witness quantum advantages in practical settings, substantial efforts are required not only at the hardware level but also on theoretical research to reduce the computational cost of a given protocol. Quantum computation has the potential to significantly enhance existing classical machine learning methods, and several quantum algorithms for binary classification based on the kernel method have been proposed. These algorithms rely on estimating an expectation value, which in turn requires an expensive quantum data encoding procedure to be repeated many times. In this work, we calculate explicitly the number of repetition necessary for acquiring a fixed success probability and show that the Hadamard-test and the swap-test circuits achieve the optimal variance in terms of the quantum circuit parameters. The variance, and hence the number of repetition, can be further reduced only via optimization over data-related parameters. We also show that the kernel-based binary classification can be performed with a single-qubit measurement regardless of the number and the dimension of the data. Finally, we show that for a number of relevant noise models the classification can be performed reliably without quantum error correction. Our findings are useful for designing quantum classification experiments under limited resources, which is the common challenge in the noisy intermediate-scale quantum era.
In this paper, a scalable Quantum Machine Learning (QML) algorithm is introduced to perform large-scale data classification and optimization with limited quantum resources. The method combines the amplitude-based encoding of quantum features with quantum circuits with parameters and hybrid optimization with RMSProp to lead to a high quality of accuracy and scalability in comparison with traditional machine learning models. The model has been run on 16-qubit NISQ processors with Qiskit and PennyLane frameworks and compared to the classical neural and kernel-based systems. Findings show that the suggested approach had a mean classification accuracy of 96.42 % better than classical models by an average of 5.2 % and with the same level of computation efficiency. The quantum kernel and entanglement optimization drastically enhanced high-dimensional similarity measurement and the noise mitigation strategies inherent in it also increased fidelity to 0.93. A test of the scalability of the system was a stable performance with sizes of up to 10,000 samples in datasets, with a sub-linear increase in time. These results confirm that quantum-enhanced architectures have the ability to learn complicated patterns and still be resource-efficient. The article forms a solid basis of the application of QML to other fields, including bioinformatics, finance, and IoT analytics where the dimensions of data and computation requirements are intensive.
Quantum machine learning has emerged as a promising frontier, leveraging the principles of quantum computing to enhance classical algorithms. This paper proposes an optimized Quantum Support Vector Classifier (QSVC) for the classification of the MNIST dataset (a benchmark in handwritten digit recognition). We employ a Chebyshev Parameterized Quantum Circuit (PQC) with an increased number of qubits and layers, and utilize an existing projected quantum kernel method to effectively capture the complex patterns in the data. To enhance model robustness, data augmentation techniques are applied, and dimensionality reduction is performed using Principal Component Analysis (PCA). The proposed QSVC demonstrates competitive accuracy on both the training and testing datasets, highlighting the potential of quantum kernel methods in practical machine learning applications. A comparative analysis with classical Support Vector Machines (SVM) demonstrates the feasibility of quantum methods for high-dimensional classification tasks. Additionally, we investigate the impact of varying the number of qubits in the quantum circuit, providing in-depth insights into the scalability and performance trade-offs of quantum kernel methods.
Quantum processors may enhance machine learning by mapping high-dimensional data onto quantum systems for processing. Conventional feature maps, for encoding data onto a quantum circuit are currently impractical, as the number of entangling gates scales quadratically with the dimension of the dataset and the number of qubits. In this work, we introduce a quantum feature map designed to handle high-dimensional data with a significantly reduced number of qubits and entangling operations. Our approach preserves essential data characteristics while promoting computational efficiency, as evidenced by extensive experiments on benchmark datasets that demonstrate a marked improvement in both accuracy and resource utilization when using our feature map as a kernel for characterization, as compared to state-of-the-art quantum feature maps. Our noisy simulation results, combined with lower resource requirements, highlight our map's ability to function within the constraints of noisy intermediate-scale quantum devices. Through numerical simulations and small-scale implementation on a superconducting circuit quantum computing platform, we demonstrate that our scheme performs on par or better than a set of classical algorithms for classification. While quantum kernels are typically stymied by exponential concentration, our approach is affected with a slower rate with respect to both the number of qubits and features, which allows practical applications to remain within reach. Our findings herald a promising avenue for the practical implementation of quantum machine learning algorithms on near future quantum computing platforms.
In the current era, known as Noisy Intermediate-Scale Quantum (NISQ), encoding large amounts of data in the quantum devices is challenging and the impact of noise significantly affects the quality of the obtained results. A viable approach for the execution of quantum classification algorithms is the introduction of a well-known machine learning paradigm, namely, the ensemble methods. Indeed, the ensembles combine multiple internal classifiers, which are characterized by compact sizes due to the smaller data subsets used for training, to achieve more accurate and robust prediction performance. In this way, it is possible to reduce the qubit requirements with respect to a single larger classifier while achieving comparable or improved performance. In this work, we present an implementation and an extensive empirical evaluation of ensembles of quantum instance-based classifiers for binary classification, with the purpose of providing insights into their effectiveness, limitations, and potential for enhancing the performance of basic quantum models. In particular, three classical ensemble methods and three quantum instance-based classifiers have been taken into account here. Hence, the scheme that has been implemented (in Python) has a hybrid nature. The results (obtained on real-world datasets) have shown an accuracy advantage for the ensemble techniques with respect to the single quantum classifiers, and also an improvement in robustness. In fact, ensembles have proven effective not only in mitigating unsuitable data normalizations but also in reducing the impact of noise on quantum classifiers, enhancing their stability.