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arXiv:2207.11449

Generating quantum feature maps for SVM classifier

Bang-Shien Chen, Jann–Long Chern

Published Jul 23, 2022• 5 citations
arXivHTMLPDF

Abstract

We present and compare two methods of generating quantum feature maps for quantum-enhanced support vector machine, a classifier based on kernel method, by which we can access high dimensional Hilbert space efficiently. The first method is a genetic algorithm with multi-objective fitness function using penalty method, which incorporates maximizing the accuracy of classification and minimizing the gate cost of quantum feature map circuit. The second method uses variational quantum circuit, focusing on how to contruct the ansatz based on unitary matrix decomposition. Numerical results and comparisons are presented to demonstrate how the fitness fuction reduces gate cost while remaining high accuracy and conducting circuit through unitary matrix obtains even better performance. In particular, we propose some thoughts on reducing and optimizing the gate cost of a circuit while remaining perfect accuracy.

DOI
10.48550/arxiv.2207.11449

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We present and compare two methods of generating quantum feature maps for quantum-enhanced support vector machine, a classifier based on kernel method, by which we can access high dimensional Hilbert space efficiently. The first method is a genetic algorithm with multi-objective fitness function using penalty method, which incorporates maximizing the accuracy of classification and minimizing the gate cost of quantum feature map circuit. The second method uses variational quantum circuit, focusing on how to contruct the ansatz based on unitary matrix decomposition. Numerical results and comparisons are presented to demonstrate how the fitness fuction reduces gate cost while remaining high accuracy and conducting circuit through unitary matrix obtains even better performance. In particular, we propose some thoughts on reducing and optimizing the gate cost of a circuit while remaining perfect accuracy.
Good feature maps are crucial for machine learning kernel methods for effective mapping of non-linearly separable input data into a higher dimension feature space, thus allowing the data to be linearly separable in feature space. Recent works have proposed automating the task of quantum feature map circuit design with methods such as variational ansatz parameter optimization and genetic algorithms. A problem commonly faced by genetic algorithm methods is the high cost of computing the genetic cost function. To mitigate this, this work investigates the suitability of two metrics as alternatives to test set classification accuracy. Accuracy has been applied successfully as a genetic algorithm cost function for quantum feature map design in previous work. The first metric is kernel-target alignment, which has previously been used as a training metric in quantum feature map design by variational ansatz training. Kernel-target alignment is a faster metric to evaluate than test set accuracy and does not require any data points to be reserved from the training set for its evaluation. The second metric is an estimation of kernel-target alignment which further accelerates the genetic fitness evaluation by an adjustable constant factor. The second aim of this work is to address the issue of the limited gate parameter choice available to the genetic algorithm. This is done by training the parameters of the quantum feature map circuits output in the final generation of the genetic algorithm using COBYLA to improve either kernel-target alignment or root mean squared error. This hybrid approach is intended to complement the genetic algorithm structure optimization approach by improving the feature maps without increasing their size. Eight new approaches are compared to the accuracy optimization approach across nine varied binary classification problems from the UCI machine learning repository, demonstrating that kernel-target alignment and its approximation produce feature map circuits enabling comparable accuracy to the original approach, with larger margins on training data that improve further with variational training.
Abstract We propose a new technique for the automatic generation of optimal ad-hoc ansätze for classification by using quantum support vector machine. This efficient method is based on non-sorted genetic algorithm II multiobjective genetic algorithms which allow both maximize the accuracy and minimize the ansatz size. It is demonstrated the validity of the technique by a practical example with a non-linear dataset, interpreting the resulting circuit and its outputs. We also show other application fields of the technique that reinforce the validity of the method, and a comparison with classical classifiers in order to understand the advantages of using quantum machine learning.
Abstract Kernel methods are an import class of techniques in machine learning. To be effective, good feature maps are crucial for mapping non-linearly separable input data into a higher dimensional (feature) space, thus allowing the data to be linearly separable in feature space. Previous work has shown that quantum feature map design can be automated for a given dataset using NSGA-II, a genetic algorithm, while both minimizing circuit size and maximizing classification accuracy. However, the evaluation of the accuracy achieved by a candidate feature map is costly. In this work, we demonstrate the suitability of kernel-target alignment as a substitute for accuracy in genetic algorithm-based quantum feature map design. Kernel-target alignment is faster to evaluate than accuracy and does not require some data points to be reserved for its evaluation. To further accelerate the evaluation of genetic fitness, we provide a method to approximate kernel-target alignment. To improve kernel-target alignment and root mean squared error, the final trainable parameters of the generated circuits are further trained using COBYLA to determine whether a hybrid approach applying conventional circuit parameter training can easily complement the genetic structure optimization approach. A total of eight new approaches are compared to the original across nine varied binary classification problems from the UCI machine learning repository, showing that kernel-target alignment and its approximation produce feature map circuits enabling comparable accuracy to the previous work but with larger margins on training data (in excess of 20% larger) that improve further with circuit parameter training.
Quantum Support Vector Machines (QSVM) is one of the most promising frameworks in quantum machine learning, yet their performance depends on the design of the feature map. Conventional approaches rely on fixed quantum circuits, which often fail to generalize across datasets. To address this limitation, we propose GA-QSVM, a hybrid framework that employs Genetic Algorithms (GA) to automatically optimize feature maps. The proposed method introduces a configurable framework that flexibly defines the evolutionary parameters, enabling the construction of adaptive circuits. Experimental evaluation of datasets, including Digits, Fashion, Wine, and Breast Cancer, demonstrates that GA-QSVMs achieve a comparable accuracy compared to classical SVMs and standard QSVMs. Furthermore, transfer learning results indicate that GA-QSVM's circuits generalize effectively across datasets. These findings highlight the potential of evolutionary strategies to automate and enhance kernel design for future quantum machine learning applications.
The current development of Support Vector Machines (SVM) has reached a bottleneck, with issues such as long training times and weak interpretability when dealing with large-scale, multi-dimensional data. This paper introduces the concept of Quantum Support Vector Machines (QSVM) and achieves efficient solutions through quantum algorithms such as the HHL algorithm. The research designs a computational architecture that combines classical and quantum computing, utilizing the Pauli decomposition of Hermitian matrices to simulate the quantum simulation of Hamiltonian quantities and implementing the quantum simulation of unitary operators. Based on the conclusions, a complete quantum linear solver circuit is designed, achieving exponential growth in computational complexity. Experiments using the Iris dataset demonstrate the excellent classification performance of QSVM, which outperform classical SVM in classification accuracy, computational time complexity, and memory requirements. More efficient quantum mapping algorithms and quantum circuit optimization methods are implemented, providing new ideas and methods for the application of SVM to large-scale datasets.
Abstract Feature selection is critical in machine learning to reduce dimensionality and improve model accuracy and efficiency. The exponential growth in feature space dimensionality for modern datasets directly results in ambiguous samples and redundant features, which can severely degrade classification accuracy. Quantum machine learning offers potential advantages for addressing this challenge. In this paper, we propose a novel method, quantum support vector machine feature selection (QSVMF), integrating quantum support vector machines with multi-objective genetic algorithm. QSVMF optimizes multiple simultaneous objectives: maximizing classification accuracy, minimizing selected features and quantum circuit costs, and reducing feature covariance. We apply QSVMF for feature selection on a breast cancer dataset, comparing the performance of QSVMF against classical approaches with the selected features. Experimental results show that QSVMF achieves superior performance. Furthermore, the Pareto front solutions of QSVMF enable analysis of accuracy versus feature set size trade-offs, identifying extremely sparse yet accurate feature subsets. We contextualize the biological relevance of the selected features in terms of known breast cancer biomarkers. This work highlights the potential of quantum-based feature selection to enhance machine learning efficiency and performance on complex real-world data.