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.
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 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.
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.
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 data encoding circuits used in quantum support vector machine (QSVM) kernels play a crucial role in their classification accuracy. However, manually designing these circuits poses significant challenges in terms of time and performance. To address this, we leverage the GASP (Genetic Algorithm for State Preparation) framework for gate sequence selection in QSVM kernel circuits. We explore supervised and unsupervised kernel loss functions' impact on encoding circuit optimisation and evaluate them on diverse datasets for binary and multiple-class scenarios. Benchmarking against classical and quantum kernels reveals GA-generated circuits matching or surpassing standard techniques. We analyse the relationship between test accuracy and quantum kernel entropy, with results indicating a positive correlation. Our automated framework reduces trial and error, and enables improved QSVM based machine learning performance for finance, healthcare, and materials science applications.
Indoor localization using Received Signal Strength Indication (RSSI) is a notoriously challenging problem due to signal noise from multipath fading and interference. Although quantum machine learning (QML) presents a new paradigm for tackling such problems, the design of effective quantum feature maps remains a significant bottleneck. This paper introduces a novel approach for automated quantum feature map design using a Hierarchical Genetic Algorithm (HGA). We propose a sequential Hybrid Quantum-Classical Neural Network (HQNN) architecture where the initial quantum feature map is not handcrafted but is evolved by the HGA. The chromosome for the GA represents a hierarchical sequence of parametric and nonparametric quantum gate layers, allowing for the discovery of complex data-encoding structures. We evaluated the performance of our approach on wireless indoor user localization datasets. The results are compared with a standard HQNN using a ‘ZZFeatureMap’ proposed in a prior work, demonstrating the potential and challenges of evolutionary quantum circuit design. Our findings indicate that while the HGA effectively explores a vast search space of quantum circuits and improves against the benchmark in majority of cases, achieving superior performance on sparse, high-interference datasets requires careful consideration of the fitness landscape and generalization capabilities of the evolved feature maps.
Abstract The quest for effective quantum feature maps for data encoding presents significant challenges, particularly due to the flat training landscapes and lengthy training processes associated with parameterized quantum circuits. To address the gap between training-free search evaluation and downstream task performance, we propose Quantum Proxy-assisted Feature Search (QuProFS) framework that employs circuit-based heuristics focused on trainability, hardware robustness, generalization ability, expressivity, complexity, and kernel-target alignment. By ranking circuit architectures with various proxies, we reduce evaluation costs and incorporate hardware-aware circuits to enhance robustness against noise. We evaluate QuProFS on binary classification tasks using a quantum support vector machine on nine benchmark datasets, including Breast Cancer, MNIST-2, Fashion-MNIST-2, Coset-10, Two Curves, Hidden Manifold, Linearly Separable, Bars-and-Stripes, and Hyperplane, using both quantum simulators and IBM Quantum hardware. Compared with existing quantum architecture search methods, QuProFS achieves the highest accuracy on the majority of benchmark datasets while reducing architecture search time by up to 2 × . Furthermore, QuProFS achieves classification performance comparable to strong classical machine learning baselines on several benchmark datasets, demonstrating an efficient and scalable strategy for quantum feature map optimization.