Based on Lie group machine learning theory and noncommutative features of quantum group, this paper proposes a symmetrical linear transform learning al- gorithm on quantum group and have it applied on DNA sequence classification. The comparing between quantum group classifier and the widely used SVM is also presented.
Abstract Quantum machine learning, an emerging field at the intersection of quantum computing and classical machine learning, has shown great promise in enhancing computational capabilities beyond classical bounds. A key element in this area of research is the utilization of Quantum Kernel Estimators, traditionally grounded in the symmetries of SU(2) groups associated with qubits. This study extends the conceptual framework of Quantum Kernel Estimators to incorporate a broader spectrum of symmetry groups. By harnessing the various structures of Lie groups, we develop novel quantum-inspired feature maps that offer more flexible and potentially powerful ways to encode and compress classical data into quantum states. We present a comprehensive theoretical introduction for this approach, followed by a methodology that integrates the developed feature maps into kernel-based quantum classifiers. Our results, derived from a series of computational experiments across various datasets, demonstrate the efficacy of this approach in comparison to traditional quantum and classical machine learning models. The findings not only underline the versatility of Lie-group theory in enhancing quantum machine learning algorithms but also open new avenues for exploring complex symmetries in quantum information processing. This research bridges a gap between the study of symmetries and machine learning, paving the way for more sophisticated quantum algorithms capable of tackling complex, high-dimensional data in ways previously unattainable.
In this article, we investigate the applicability of quantum machine learning for classification tasks using two quantum classifiers from the Qiskit Python environment: the variational quantum circuit and the quantum kernel estimator (QKE). We provide a first evaluation on the performance of these classifiers when using a hyperparameter search on six widely known and publicly available benchmark datasets and analyze how their performance varies with the number of samples on two artificially generated test classification datasets. As quantum machine learning is based on unitary transformations, this paper explores data structures and application fields that could be particularly suitable for quantum advantages. Hereby, this paper introduces a novel dataset based on concepts from quantum mechanics using the exponential map of a Lie algebra. This dataset will be made publicly available and contributes a novel contribution to the empirical evaluation of quantum supremacy. We further compared the performance of VQC and QKE on six widely applicable datasets to contextualize our results. Our results demonstrate that the VQC and QKE perform better than basic machine learning algorithms, such as advanced linear regression models (Ridge and Lasso). They do not match the accuracy and runtime performance of sophisticated modern boosting classifiers such as XGBoost, LightGBM, or CatBoost. Therefore, we conclude that while quantum machine learning algorithms have the potential to surpass classical machine learning methods in the future, especially when physical quantum infrastructure becomes widely available, they currently lag behind classical approaches. Our investigations also show that classical machine learning approaches have superior performance classifying datasets based on group structures, compared to quantum approaches that particularly use unitary processes. Furthermore, our findings highlight the significant impact of different quantum simulators, feature maps, and quantum circuits on the performance of the employed quantum estimators. This observation emphasizes the need for researchers to provide detailed explanations of their hyperparameter choices for quantum machine learning algorithms, as this aspect is currently overlooked in many studies within the field. To facilitate further research in this area and ensure the transparency of our study, we have made the complete code available in a linked GitHub repository.
Quantum machine learning (QML) models are aimed at learning from data encoded in quantum states.Recently, it has been shown that models with little to no inductive biases (i.e., with no assumptions about the problem embedded in the model) are likely to have trainability and generalization issues, especially for large problem sizes.As such, it is fundamental to develop schemes that encode as much information as available about the problem at hand.In this work we present a simple, yet powerful, framework where the underlying invariances in the data are used to build QML models that, by construction, respect those symmetries.These so-called group-invariant models produce outputs that remain invariant under the action of any element of the symmetry group G associated with the dataset.We present theoretical results underpinning the design of G-invariant models, and exemplify their application through several paradigmatic QML classification tasks, including cases when G is a continuous Lie group and also when it is a discrete symmetry group.Notably, our framework allows us to recover, in an elegant way, several well-known algorithms for the literature, as well as to discover new ones.Taken together, we expect that our results will help pave the way towards a more geometric and group-theoretic approach to QML model design.
Quantum computing is the application of Quantum mechanical resources to solve computational problems more precisely, quickly, and effectively than classical computers. Machine learning is all about discovering patterns and relationships in data. Quantum Machine Learning (QML) blends Machine Learning (ML) and Quantum Computing (QC) technologies. QML approaches may be utilized efficiently for data classification problems. Quantum Feature Maps (QFMs) are used for transferring non-linear classical data from lower input space to higher dimensional Hilbert space. Calculating the inner product between data points for classification purposes is exceedingly costly when Hilbert Space is vast. Quantum Kernel Techniques, which are immediate results of QFMs, are used to overcome this problem. In general, we cannot claim that QFMs are superior than Classical Feature Maps (CFMs); yet, there are datasets for which QFMs perform better while CFMs are less effective. It gives us the motivation behind using QFM for classification. In this paper, we proposed two new non-linear encoding functions based quantum kernels for data classification in the range [0, 2π]. The make_moons and make_circles datasets are utilized in this article to perform binary classifications using Qiskit and Sklearn. Construction of quantum kernels is performed, and Support Vector Machines (SVM) are then applied for classification. We have compared the results of our two newly proposed non-linear encoding functions to those mentioned in the literature. Our classifier's performance is approximately comparable or in some cases better to that of existing classifiers in literature.
In this study, the performance of classical and quantum machine learning models was compared using the Breast Cancer dataset, which consists of diagnostic data aimed at classifying breast tumor types. Breast cancer, being one of the most common and life-threatening cancers in women, requires accurate diagnostic tools for early detection and effective treatment. The primary objective of this study is to evaluate the accuracy of quantum-assisted models through quantum feature selection methods. Initially, classical machine learning algorithms such as Support Vector Machines (SVM), Decision Trees, Random Forests, and Logistic Regression were applied to the dataset for baseline analysis. Subsequently, a quantum feature map was constructed using the Cirq library, enabling feature transformation based on this map. The classification was performed using the SVM model with the quantum-transformed features. The Logistic Regression and SVM models demonstrated the highest performance among classical machine learning models, achieving an accuracy rate of 96.49%, followed by Random Forest at 94.74% and Decision Tree at 92.11%. In the context of quantum feature transformation, the model utilizing the top five selected features achieved an accuracy rate of 94.74%, in contrast to 98.25% for the model trained with all features. These findings underscore the potential of quantum feature maps in enhancing model performance compared to classical techniques. The results suggest that quantum computing may offer significant advantages when integrated into machine learning frameworks, particularly in domains such as medical diagnostics, where high accuracy is crucial.