Random Forest (RF) is a popular tree-ensemble method for supervised learning, prized for its ease of use and flexibility. Online RF models require to account for new training data to maintain model accuracy. This is particularly important in applications where data is periodically and sequentially generated over time in data streams, such as auto-driving systems, and credit card payments. In this setting, performing periodic model retraining with the old and new data accumulated is beneficial as it fully captures possible drifts in the data distribution over time. However, this is unpractical with state-of-the-art classical algorithms for RF as they scale linearly with the accumulated number of samples. We propose QC-Forest, a classical-quantum algorithm designed to time-efficiently retrain RF models in the streaming setting for multi-class classification and regression, achieving a runtime poly-logarithmic in the total number of accumulated samples. QC-Forest leverages Des-q, a quantum algorithm for single tree construction and retraining proposed by Kumar et al. by expanding to multi-class classification, as the original proposal was limited to binary classes, and introducing an exact classical method to replace an underlying quantum subroutine incurring a finite error, while maintaining the same poly-logarithmic dependence. Finally, we showcase that QC-Forest achieves competitive accuracy in comparison to state-of-the-art RF methods on widely used benchmark datasets with up to 80,000 samples, while significantly speeding up the model retrain.
Random Forest (RF) is a popular tree-ensemble method for supervised learning, prized for its ease of use and flexibility. Online RF models require to account for new training data to maintain model accuracy. This is particularly important in applications where data is periodically and sequentially generated over time in data streams, such as auto-driving systems, and credit card payments. In this setting, performing periodic model retraining with the old and new data accumulated is beneficial as it fully captures possible drifts in the data distribution over time. However, this is unpractical with state-of-the-art classical algorithms for RF as they scale linearly with the accumulated number of samples. We propose QC-Forest, a classical-quantum algorithm designed to time-efficiently retrain RF models in the streaming setting for multi-class classification and regression, achieving a runtime poly-logarithmic in the total number of accumulated samples. QC-Forest leverages Des-q, a quantum algorithm for single tree construction and retraining proposed by Kumar et al. by expanding to multi-class classification, as the original proposal was limited to binary classes, and introducing an exact classical method to replace an underlying quantum subroutine incurring a finite error, while maintaining the same poly-logarithmic dependence. Finally, we showcase that QC-Forest achieves competitive accuracy in comparison to state-of-the-art RF methods on widely used benchmark datasets with up to 80,000 samples, while significantly speeding up the model retrain.
Decision trees are widely adopted machine learning models due to their simplicity and explainability. However, as training data size grows, standard methods become increasingly slow, scaling polynomially with the number of training examples. In this work, we introduce Des-q, a novel quantum algorithm to construct and retrain decision trees for regression and binary classification tasks. Assuming the data stream produces small, periodic increments of new training examples, Des-q significantly reduces the tree retraining time. Des-q achieves a logarithmic complexity in the combined total number of old and new examples, even accounting for the time needed to load the new samples into quantum-accessible memory. Our approach to grow the tree from any given node involves performing piecewise linear splits to generate multiple hyperplanes, thus partitioning the input feature space into distinct regions. To determine the suitable anchor points for these splits, we develop an efficient quantum-supervised clustering method, building upon the q-means algorithm introduced by Kerenidis et al. We benchmark the simulated version of Des-q against the state-of-the-art classical methods on multiple data sets and observe that our algorithm exhibits similar performance to the state-of-the-art decision trees while significantly speeding up the periodic tree retraining.
Abstract Decision trees are widely used in machine learning for their simplicity in construction and interpretability. However, as data sizes grow, traditional methods for constructing and retraining decision trees become increasingly slow, scaling polynomially with the number of training examples. We introduce a novel quantum algorithm, Des-q, for constructing and retraining decision trees in regression and binary classification. Assuming the data stream produces small increments of new training examples, Des-q significantly reduces the tree retraining time, achieving poly-logarithmic time complexity in the number of examples, even accounting for the time needed to load the new examples into quantum-accessible memory. Our approach involves building a decision tree algorithm to perform k-piecewise linear tree splits at each internal node. These splits simultaneously generate multiple hyperplanes, dividing the feature space into k distinct regions. To determine the k suitable anchor points for these splits, we develop an efficient quantum-supervised clustering method, building upon the q-means algorithm by Kerenidis et al. Des-q first efficiently estimates each feature weight using a novel quantum technique to estimate the Pearson correlation. Subsequently, we employ weighted distance estimation to cluster the training examples in k disjoint regions based on nearest-neighbor matching and then proceed to expand the tree using the same procedure. We benchmark the performance of the simulated version of our algorithm against the state-of-the-art classical decision tree on multiple data sets with numerical features. Further, we showcase that the proposed algorithm exhibits similar performance to the state-of-the-art decision tree while significantly speeding up the periodic tree retraining.
Classification is a common task in machine learning. Random features (RFs) stand as a central technique for scalable learning algorithms based on kernel methods, and more recently proposed optimized random features, sampled depending on the model and the data distribution, can significantly reduce and provably minimize the required number of features. However, existing research on classification using optimized RFs has suffered from computational hardness in sampling each optimized RF; moreover, it has failed to achieve the exponentially fast error-convergence speed that other state-of-the-art kernel methods can achieve under a low-noise condition. To overcome these slowdowns, we here construct a classification algorithm with optimized RFs accelerated by means of quantum machine learning (QML) and study its runtime to clarify overall advantage. We prove that our algorithm can achieve the exponential error convergence under the low-noise condition even with optimized RFs; at the same time, our algorithm can exploit the advantage of the significant reduction of the number of features without the computational hardness owing to QML. These results discover a promising application of QML to acceleration of the leading kernel-based classification algorithm without ruining its wide applicability and the exponential error-convergence speed.
The research article presents a Quantum-Enhanced Hybrid Machine Learning Model (QEHMLM) designed to accelerate data classification in Large-Scale Big Data Environments (LSBDE). The proposed framework integrates Quantum Computing (QC) with Classical Machine Learning Techniques (CMLT) including Support Vector Machine (SVM), Random Forest (RF), and Neural Network (Artificial-ANN) to overcome the computational and scalability limitations of classical approaches when processing High-Dimensional Datasets (HDD). The model leverages quantum feature encoding, entanglement-based transformations, and classical optimization to enhance accuracy and convergence speed. Simulations conducted using IBM Qiskit and TensorFlow Quantum on the Mobile Telecom Network Traffic Dataset validate the industrial applicability of the suggested approach in Applied Operational environment. The QEHMLM achieves notable improvements, recording 97% accuracy, 95% F1-score, and nearly 20% reduction in computational time compared to classical counterparts. These outcomes confirm that Hybrid Quantum-Classical Systems (HQCS) provide a scalable, efficient, and high-performance paradigm for next-generation Big Data analytics and intelligent computational ecosystems.
This study investigates the application of machine learning techniques for predicting gate depth in quantum computational systems, focusing on the relationship between quantum circuit parameters and computational performance. Using a dataset of 50 observations encompassing qubit count, gate depth, entanglement rate, and logical error rate, we developed and compared Linear Regression (LR) and Random Forest Regression (RFR) models for gate depth prediction. The research addresses critical challenges in quantum fault tolerance and circuit optimization, which are essential for achieving scalable quantum computation. Our analysis revealed strong negative correlation (-0.65) between qubit count and logical error rate, while gate depth showed moderate positive correlation (0.62) with error rates. The Random Forest model demonstrated superior performance with R² values of 0.96068 on training data and 0.87262 on testing data, significantly outperforming Linear Regression (R²: 0.87552 training, 0.60257 testing). Error metrics further confirmed RFR's superiority, achieving RMSE of 2.33 (training) and 2.97 (testing) compared to LR's 4.15 and 5.25 respectively. The study highlights the importance of quantum error correction mechanisms and the inherent trade-offs between circuit complexity and computational reliability. Both models showed expected performance degradation from training to testing, with RFR maintaining better generalization capabilities. These findings contribute to the development of typed models for quantum mechanics in computational applications, offering insights into quantum circuit optimization and fault-tolerant design. The research demonstrates that ensemble methods like Random Forest provide more robust predictions for quantum system parameters, supporting the advancement of practical quantum computing implementations and algorithm development. KeyWords: Quantum Computation, Gate Depth Prediction, Random Forest Regression, Quantum Error Correction, Machine Learning, Fault Tolerance.
Quantum Machine Learning (QML) has emerged as a paradigm that combines the computational advantages of quantum computing with the predictive capabilities of machine learning to address complex data classification problems. As data dimensionality increases rapidly and classical learning algorithms face scalability constraints, QML leverages quantum parallelism, entanglement, and high-dimensional Hilbert space representations to enhance learning performance. This paper reviews and analyses advanced QML algorithms, including Quantum Support Vector Machines (QSVM), Variational Quantum Circuits (VQC), Quantum Neural Networks (QNN), and Quantum Kernel Estimation, for optimizing both binary and multi-class classification tasks under high-complexity conditions. The proposed QML framework is evaluated on benchmark datasets like MNIST, the Breast Cancer Wisconsin (BCW) dataset, and synthetic nonlinear datasets, and is compared against classical machine learning baselines, including Support Vector Machines (SVM), Random Forests (RF), and Deep Neural Networks (DNN). The results demonstrate notable improvements in classification accuracy (up to 96.8%), decision margins, and computational efficiency in quantum-suitable data regimes, while also highlighting current limitations related to noise, circuit depth, and hardware constraints. Overall, the study presents a unified QML framework, theoretical formulations, and experimental evaluations that illustrate the potential of quantum algorithms for next-generation classification tasks.