Quantum machine learning is considered one of the current research fields with great potential. In recent years, Havl\'{\i}\ifmmode \check{c}\else \v{c}\fi{}ek et al. [Nature (London) 567, 209 (2019)] have proposed a quantum machine learning algorithm with quantum-enhanced feature spaces, which effectively addressed a binary classification problem and offered a potential pathway to achieving quantum advantage. However, a straightforward binary classification algorithm falls short in solving multiclass classification problems. In this paper, we propose a quantum algorithm that rigorously demonstrates that quantum kernel methods enhance the efficiency of multiclass classification in real-world applications, providing quantum-enhanced performance. To demonstrate this, we design six distinct quantum kernels within the quantum algorithm to map input data into quantum state spaces and estimate the corresponding quantum kernel matrices. The results from quantum simulations reveal that the quantum algorithm outperforms its classical counterpart in handling six real-world multiclass classification problems. Furthermore, we leverage a variety of performance metrics to comprehensively evaluate the classification and generalization performance of the quantum algorithm. The results demonstrate that the quantum algorithm achieves superior classification and better generalization performance relative to classical counterparts.
Quantum machine learning is considered one of the current research fields with great potential. In recent years, Havl'{\i}\ifmmode \check{c}\else \v{c}\fi{}ek et al. [Nature (London) 567, 209 (2019)] have proposed a quantum machine learning algorithm with quantum-enhanced feature spaces, which effectively addressed a binary classification problem and offered a potential pathway to achieving quantum advantage. However, a straightforward binary classification algorithm falls short in solving multiclass classification problems. In this paper, we propose a quantum algorithm that rigorously demonstrates that quantum kernel methods enhance the efficiency of multiclass classification in real-world applications, providing quantum-enhanced performance. To demonstrate this, we design six distinct quantum kernels within the quantum algorithm to map input data into quantum state spaces and estimate the corresponding quantum kernel matrices. The results from quantum simulations reveal that the quantum algorithm outperforms its classical counterpart in handling six real-world multiclass classification problems. Furthermore, we leverage a variety of performance metrics to comprehensively evaluate the classification and generalization performance of the quantum algorithm. The results demonstrate that the quantum algorithm achieves superior classification and better generalization performance relative to classical counterparts.
The functional characterization of different neuronal types has been a longstanding and crucial challenge. With the advent of physical quantum computers, it has become possible to apply quantum machine learning algorithms to translate theoretical research into practical solutions. Previous studies have shown the advantages of quantum algorithms on artificially generated datasets, and initial experiments with small binary classification problems have yielded comparable outcomes to classical algorithms. However, it is essential to investigate the potential quantum advantage using real-world data. To the best of our knowledge, this study is the first to propose the utilization of quantum systems to classify neuron morphologies, thereby enhancing our understanding of the performance of automatic multiclass neuron classification using quantum kernel methods. We examined the influence of feature engineering on classification accuracy and found that quantum kernel methods achieved similar performance to classical methods, with certain advantages observed in various configurations.
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.
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 kernel methods have emerged as a promising approach for leveraging high-dimensional feature spaces in machine learning, particularly in domains where classical kernel methods face scalability limitations. In this work, we present the first large-scale study of fidelity-quantum-kernel support vector machines for hyperspectral data classification without requiring heavy prior feature selection or dimensionality reduction. By simulating quantum kernels using tensor network contraction techniques and GPU acceleration, we overcome the computational bottlenecks traditionally associated with quantum models, achieving quadratic scaling O(n^2) in the number of qubits. Our approach enables the evaluation of quantum kernels on hyperspectral data with hundreds of spectral bands, aligning quantum feature spaces with real-world remote sensing applications. We provide an in-depth analysis of kernel bandwidth optimization, demonstrating its crucial role in mitigating exponential concentration effects and ensuring the model's ability to generalize. Experimental results on binary classification (Indian Pines and Methane Detection) and multiclass classification (Indian Pines) demonstrate that quantum kernels achieve competitive performance compared to a broad range of state-of-the-art classical baselines. As illustrative cases, on four 50-band splits selected from Indian Pines, the quantum model achieved a 78.0 pm6.2% accuracy for a binary classification task compared to 72.0 pm5.0% for the standard radial basis function (RBF) kernel. For a four-class classification task, the quantum kernel reached 83.3 pm3.1% accuracy, outperforming several state-of-the-art baselines. On five 75-band splits selected from the Methane Detection dataset, the quantum approach yielded 58.5\pm5.0% accuracy versus 55.1\pm2.5% for the classical counterpart...
In this work, we studied the use of Quantum Machine Learning (QML) algorithms for binary classification and compared their performance with classical Machine Learning (ML) methods. QML merges principles of Quantum Computing (QC) and ML, offering improved efficiency and potential quantum advantage in data-driven tasks and when solving complex problems. In binary classification, where the goal is to assign data to one of two categories, QML uses quantum algorithms to process large datasets efficiently. Quantum algorithms like Quantum Support Vector Machines (QSVM) and Quantum Neural Networks (QNN) exploit quantum parallelism and entanglement to enhance performance over classical methods. This study focuses on two common QML algorithms, Quantum Support Vector Classifier (QSVC) and QNN. We used the Qiskit software and conducted the experiments with three different datasets. Data preprocessing included dimensionality reduction using Principal Component Analysis (PCA) and standardization using scalers. The results showed that quantum algorithms demonstrated competitive performance against their classical counterparts in terms of accuracy, while QSVC performed better than QNN. These findings suggest that QML holds potential for improving computational efficiency in binary classification tasks. This opens the way for more efficient and scalable solutions in complex classification challenges and shows the complementary role of quantum computing.
Quantum kernel methods are a promising branch of quantum machine learning, but their per- formance across data types and encoding choices remains incompletely understood. To address this gap, we developed an algorithmic framework for variational quantum kernels utilizing resource- efficient ansätze for complex classification tasks and introduced a parameter scaling technique to accelerate convergence. We conducted a comprehensive benchmark of this framework on eight chal- lenging, real-world and high-dimensional datasets covering tabular, image, time series, and graph data. Our results show that the proposed quantum kernel demonstrated competitive classification accuracy compared to standard classical kernels in classical simulation, such as the radial basis function (RBF) kernel. This work demonstrates that properly designed quantum kernels can func- tion as versatile, high-performance tools, laying a foundation for quantum-enhanced applications in machine learning. Further research is needed to fully assess the practical performance of quantum methods.