ABSTRACT Ensemble learning plays a central role in improving the generalization of machine learning models, yet its full potential remains underexplored in the quantum domain. In this work, we propose a Quantum Ensemble Learning (QEL) algorithm that leverages the parallelism of quantum computing to construct diverse classifiers in a shallow‐circuit ensemble. The method uses a control‐qubit‐based sampling strategy to create superpositions of training subsamples, enabling simultaneous evaluation of multiple weak learners. The algorithm proceeds through four stages: quantum state preparation, superposition‐based sampling, learning via quantum interference, and final measurement. Our framework is flexible and allows different quantum classifiers to be used as base learners. We demonstrate this by implementing a robust QSVM‐based ensemble with quantum feature extraction using PauliFeatureMaps. Unlike classical methods, this technique adds classifiers to time complexity additively rather than multiplicatively due to the parallelism of quantum computing. To demonstrate the workflow of the proposed algorithm, we include a step‐by‐step example using the XOR problem. Simulation results further validate the effectiveness of the QEL framework—enhanced by the integration of a Quantum Support Vector Machine (QSVM) classifier with quantum feature extraction—showing improved classification accuracy compared to existing algorithms across several UCI benchmark datasets using IBM Qiskit.
ABSTRACT Ensemble learning plays a central role in improving the generalization of machine learning models, yet its full potential remains underexplored in the quantum domain. In this work, we propose a Quantum Ensemble Learning (QEL) algorithm that leverages the parallelism of quantum computing to construct diverse classifiers in a shallow‐circuit ensemble. The method uses a control‐qubit‐based sampling strategy to create superpositions of training subsamples, enabling simultaneous evaluation of multiple weak learners. The algorithm proceeds through four stages: quantum state preparation, superposition‐based sampling, learning via quantum interference, and final measurement. Our framework is flexible and allows different quantum classifiers to be used as base learners. We demonstrate this by implementing a robust QSVM‐based ensemble with quantum feature extraction using PauliFeatureMaps. Unlike classical methods, this technique adds classifiers to time complexity additively rather than multiplicatively due to the parallelism of quantum computing. To demonstrate the workflow of the proposed algorithm, we include a step‐by‐step example using the XOR problem. Simulation results further validate the effectiveness of the QEL framework—enhanced by the integration of a Quantum Support Vector Machine (QSVM) classifier with quantum feature extraction—showing improved classification accuracy compared to existing algorithms across several UCI benchmark datasets using IBM Qiskit.
In this Letter, we propose a quantum machine learning scheme for the classification of classical nonlinear data. The main ingredients of our method are variational quantum perceptron (VQP) and a quantum generalization of classical ensemble learning. Our VQP employs parameterized quantum circuits to learn a Grover search (or amplitude amplification) operation with classical optimization, and can achieve quadratic speedup in query complexity compared to its classical counterparts. We show how the trained VQP can be used to predict future data with O(1) {query} complexity. Ultimately, a stronger nonlinear classifier can be established, the so-called quantum ensemble learning (QEL), by combining a set of weak VQPs produced using a subsampling method. The subsampling method has two significant advantages. First, all T weak VQPs employed in QEL can be trained in parallel, therefore, the query complexity of QEL is equal to that of each weak VQP multiplied by T. Second, it dramatically reduce the {runtime} complexity of encoding circuits that map classical data to a quantum state because this dataset can be significantly smaller than the original dataset given to QEL. This arguably provides a most satisfactory solution to one of the most criticized issues in quantum machine learning proposals. To conclude, we perform two numerical experiments for our VQP and QEL, implemented by Python and pyQuil library. Our experiments show that excellent performance can be achieved using a very small quantum circuit size that is implementable under current quantum hardware development. Specifically, given a nonlinear synthetic dataset with 4 features for each example, the trained QEL can classify the test examples that are sampled away from the decision boundaries using 146 single and two qubits quantum gates with 92% accuracy.
Quantum machine learning has shown advantages in many ways compared to classical machine learning. In machine learning, a difficult problem is how to learn a model with high robustness and strong generalization ability from a limited feature space. Combining multiple models as base learners, ensemble learning (EL) can effectively improve the accuracy, generalization ability and robustness of the final model. The key to EL lies in two aspects, the performance of base learners and the choice of the combination strategy. Recently, quantum EL (QEL) has been studied. However, existing combination strategies in QEL are inadequate in considering the accuracy and variance among base learners. This paper presents a hybrid EL framework that combines quantum and classical advantages. More importantly, we propose an efficient combination strategy for improving the accuracy of classification in the framework. We verify the feasibility and efficiency of our framework and strategy by using the MNIST dataset. Simulation results show that the hybrid EL framework with our combination strategy not only has a higher accuracy and lower variance than the single model without the ensemble, but also has a better accuracy than the majority voting and the weighted voting strategies in most cases.
Ensemble Learning, a technique that combines multiple base models to enhance performance and reduce variance, is a well-established approach in machine learning. In recent years, quantum machine learning has emerged as a field aiming to accelerate classical machine learning through quantum algorithms. In this paper, we introduce a quantum ensemble learning framework, with a particular focus on utilizing the parallel amplitude amplification (parallel AA) technique when employing a quantum support vector machine (QSVM) as the base learner. This approach reduces complexity compared to classical ensemble techniques, making it a promising advancement in the field of quantum machine learning. It demonstrates significant improvements in time complexity and maintains competitive accuracy when compared to classical bagging, including support vector machine (SVM) and least squares support vector machine (LS-SVM).
Abstract Ensemble methods in machine learning aim to improve prediction accuracy by combining multiple models. This is achieved by ensuring diversity among predictors to capture different data aspects. Homogeneous ensembles use identical models, achieving diversity through different data subsets, and weighted-average ensembles assign higher influence to more accurate models through a weight learning procedure. We propose a method to achieve a weighted homogeneous quantum ensemble using quantum classifiers with indexing registers for data encoding. This approach leverages instance-based quantum classifiers, enabling feature and training point subsampling through superposition and controlled unitaries, and allowing for a quantum-parallel execution of diverse internal classifiers with different data compositions in superposition. The method integrates a learning process involving circuit execution and classical weight optimization, for a trained ensemble execution with weights encoded in the circuit at test-time. Empirical evaluation demonstrate the effectiveness of the proposed method, offering insights into its performance.
Abstract Ensemble methods aggregate predictions from multiple models, typically demonstrating improved accuracy and reduced variance compared to individual classifiers. However, they often come with significant memory usage and computational time requirements. A novel quantum algorithm that leverages quantum superposition, entanglement, and interference to construct an ensemble of classification models using bagging as an aggregation strategy is introduced. Through the generation of numerous quantum trajectories in superposition, the authors achieve B transformations of the training set with only operations, allowing an exponential enlargement of the ensemble size while linearly increasing the depth of the corresponding circuit. Moreover, when assessing the algorithm's overall cost, the authors demonstrate that the training of a single weak classifier contributes additively to the overall time complexity, as opposed to the multiplicative impact commonly observed in classical ensemble methods. To illustrate the efficacy of the authors’ approach, experiments on reduced real‐world datasets utilising the IBM qiskit environment to demonstrate the functionality and performance of the proposed algorithm are introduced.
Abstract A powerful way to improve performance in machine learning is to construct an ensemble that combines the predictions of multiple models. Ensemble methods are often much more accurate and have a lower variance than the individual classifiers that make them up, but have high requirements in terms of memory and computational time. In fact, a large number of alternative algorithms is usually adopted, each requiring to query all available data. We propose a new quantum algorithm that exploits quantum superposition, entanglement and interference to build an ensemble of classification models. Thanks to the generation of the several quantum trajectories in superposition, we obtain B transformations of the quantum state which encodes the training set in only log ( B ) operations. This implies an exponential growth of the ensemble size while increasing linearly the depth of the correspondent circuit. Furthermore, when considering the overall cost of the algorithm, we show that the training of a single weak classifier impacts additively to the overall time complexity rather than multiplicatively, as it usually happens in classical ensemble methods. We also present small-scale experiments on real-world datasets, defining a quantum version of the cosine classifier and using the IBM qiskit environment to show how the algorithms work.