This paper presents a hybrid quantum logistic regression model for binary data classification that combines classical logistic regression methods with quantum computing to improve efficiency and speed up the learning process. Quantum computing is used to represent and process feature and weight vectors as quantum states and to efficiently compute the dot product underlying the logistic function. The use of normalized amplitude coding allows for compact representation of feature vectors and weights, reducing the number of qubits required and potentially speeding up computations for high-dimensional classification problems where classical methods may encounter scalability limitations. The quantum dot product computation is performed using the Hadamard test, which provides a statistical estimate of the probability of measuring an auxiliary qubit. The auxiliary qubit is first put into a superposition state, and after performing controlled unitary operations, amplitude interference is formed, which depends on the scalar product of the feature vector and weight coefficients. The obtained measurement probability is used to estimate the scalar product of the feature vectors and weights. The classical part of the model provides for the execution of operations that are difficult to implement on modern quantum devices, in particular, vector normalization, application of the sigmoid function to estimate the probability of an object belonging to a certain class, calculation of the loss function and iterative update of weight coefficients by the gradient descent method. The purpose of classification is to predict the binary class for an unknown sample based on the training sample. To demonstrate the model, a numerical example is given with a step-by-step calculation of one iteration of logistic regression training. In addition, computer modeling of the hybrid algorithm training process was performed, taking into account the influence of noise on the results of quantum state measurements. A quantum noise model was developed based on the probability of confidence in the measurement result, which is interpreted as an assessment of its reliability in a Bernoulli experiment. Comparison of the obtained results with the classical approach confirms the practical suitability of the hybrid algorithm for binary classification problems. The hybrid model preserves the key properties of classical logistic regression – parameter interpretability and optimization stability, while allowing for the use of quantum advantages for compact data encoding and scalar product computation. This makes the study of hybrid logistic regression relevant for the development of machine learning algorithms on modern quantum platforms.
This paper presents a hybrid quantum logistic regression model for binary data classification that combines classical logistic regression methods with quantum computing to improve efficiency and speed up the learning process. Quantum computing is used to represent and process feature and weight vectors as quantum states and to efficiently compute the dot product underlying the logistic function. The use of normalized amplitude coding allows for compact representation of feature vectors and weights, reducing the number of qubits required and potentially speeding up computations for high-dimensional classification problems where classical methods may encounter scalability limitations. The quantum dot product computation is performed using the Hadamard test, which provides a statistical estimate of the probability of measuring an auxiliary qubit. The auxiliary qubit is first put into a superposition state, and after performing controlled unitary operations, amplitude interference is formed, which depends on the scalar product of the feature vector and weight coefficients. The obtained measurement probability is used to estimate the scalar product of the feature vectors and weights. The classical part of the model provides for the execution of operations that are difficult to implement on modern quantum devices, in particular, vector normalization, application of the sigmoid function to estimate the probability of an object belonging to a certain class, calculation of the loss function and iterative update of weight coefficients by the gradient descent method. The purpose of classification is to predict the binary class for an unknown sample based on the training sample. To demonstrate the model, a numerical example is given with a step-by-step calculation of one iteration of logistic regression training. In addition, computer modeling of the hybrid algorithm training process was performed, taking into account the influence of noise on the results of quantum state measurements. A quantum noise model was developed based on the probability of confidence in the measurement result, which is interpreted as an assessment of its reliability in a Bernoulli experiment. Comparison of the obtained results with the classical approach confirms the practical suitability of the hybrid algorithm for binary classification problems. The hybrid model preserves the key properties of classical logistic regression – parameter interpretability and optimization stability, while allowing for the use of quantum advantages for compact data encoding and scalar product computation. This makes the study of hybrid logistic regression relevant for the development of machine learning algorithms on modern quantum platforms.
Logistic regression (LR) is an important machine learning model for classification, with wide applications in text classification, image analysis and medicine diagnosis, etc. However, training LR generally entails an iterative gradient descent method, and is quite time consuming when processing big data sets. To solve this problem, we present a quantum algorithm for LR to implement the key task of the gradient descent method, obtaining the classical gradients in each iteration. It is shown that our algorithm achieves exponential speedup over its classical counterpart in each iteration when the dimension of each data point M grows polylogarithmically with the number of data points N, i.e.,M=O(polylog N). It is worth noting that the optimal model parameters are finally derived by performing simple calculations on the obtained gradients. So once the optimal model parameters are determined, one can use them to classify new data at little cost.
Quantum computing has inspired new ways to represent and process data, offering perspectives that can also benefit classical machine learning. In this work, we investigate how quantum-inspired data representations can be integrated into classical machine learning classifiers such as Logistic Regression, Support Vector Machines, and Naive Bayes for binary classification tasks. The proposed approach utilizes a simple amplitude-based encoding that normalizes feature vectors and incorporates phase-like transformations, assisting classical models to capture complex interactions and patterns in the data similar to quantum information processing. We evaluate this approach on both synthetic and three other benchmark datasets, comparing standard and quantum-inspired data representations. The results highlights that the quantum-inspired data encoding often matches or improves classifier performance in terms of accuracy, F1-Score, and precision. Additionally, the normalized encoding provides a more structured representation of the data, which can help with interpretability and visualization. These results highlight the potential of quantum-inspired transformations as a practical and effective tool for improving classical machine learning pipelines without requirement of quantum hardware.
Feature selection is a pivotal step in machine learning, aimed at reducing feature dimensionality and improving model performance. Conventional feature selection methods, typically framed as NP-hard problems, focus primarily on selecting non-redundant and discriminative features but neglect how these selected features influence downstream machine learning tasks. To bridge this gap, we propose a mixed-integer non-linear programming-based integrated feature selection and logistic regression (IFSLR) model that jointly optimizes feature selection and classifier parameters. To solve the proposed IFSLR model efficiently, we reformulate it into two quantum-computing-compatible quadratic unconstrained binary optimization (QUBO) models via discretization of continuous variables and Taylor expansions, and provide a theoretical approximation guarantee for the proposed QUBO models. To adaptively optimize both the discretization step length optimization sub-problems and the parameterized QUBO sub-problems, we develop a dual-level Q-learning-guided hybrid quantum-classical algorithm that dynamically selects which sub-problem to solve. At the upper level, an adaptive Q learning agent is employed to select appropriate sub-problems during the search process. At the lower level, each iteration addresses either discretization step length optimization sub-problems or parameterized QUBO sub-problems. Experiments on the German credit dataset demonstrate that our method achieves a 10.83% improvement in accuracy and a 4.54-fold enhancement in computational efficiency on average compared with state-of-the-art methods. It also achievesF1 score improvements of 2.86% on the Wisconsin diagnostic breast cancer dataset and 7.65% on the Portuguese bank marketing dataset. The improvements further validate the effectiveness and generalizability of the proposed model and algorithm.
Brain tumor image classification is an essential pre-processing task for tumor diagnosis and treatment planning. In medical imaging, quantum computing analyse medical imaging data, offering potential speedups and new representations compared to classical methods. The brain images are transformed through resizing and normalization to a uniform 32 × 32 × 3 resolution. Subsequently, these processed images are converted into vectors to enable encoding into quantum states. The feature set is reduced using Principal Component Analysis (PCA) to ensure compatibility with the restricted qubit count in the quantum circuits. Through amplitude encoding, these vectors are mapped to quantum states, allowing for a compact and efficient data representation within the quantum domain. A parameterized Variational Quantum Circuit(VQC), consisting of entangling gates and trainable rotations, processes the encoded quantum states to learn features that can effectively discriminate between classes. The loss is calculated from the measured expectation values of Pauli-Z observables and optimized using classical gradient descent, where the objective function is the mean squared error. The trained quantum model is designed for multi-class classification, specifically distinguishing between meningioma, glioma tumors, pituitary tumors, and the absence of a tumor. The outcome of this proposed work demonstrates the VQC’s advantage over classical baselines, including Random Forest, and Support Vector Machine (SVM) and Multi-Layer Perceptron (MLP). The VQC achieved the highest accuracy of 95% and the best robustness (Specificity 0.983). Crucially, the VQC accomplished this using only 24 trainable parameters, showcasing a significant increase in parameter efficiency compared to the classical models. The novelty of this work is the quantitative demonstration that a custom-designed, resource-efficient quantum model can outperform established classical deep learning methods in both performance and efficiency for complex medical image classification. The VQC provides a 3.5-fold gain in parameter efficiency, achieving the highest accuracy of 95% using only 24 trainable parameters. This efficiency is enabled by the novel application of amplitude encoding to the medical images, which compresses 16 features into just 4 qubits. The VQC demonstrates robustness vital for medical diagnostics, achieving a Specificity of 0.983. Its shallow architecture is also NISQ-friendly and remains stable by avoiding the Barren Plateau issue (Gradient Norm: 0.11), validating the path toward quantum advantage in diagnostic tools. The results of this approach highlight the potential amplitude encoding in quantum machine learning, as a feasible and effective method for classifying real-world medical images. This work also opens avenues for future hybrid quantum-classical diagnostic systems that could utilize richer quantum state encodings for significant gains in computational efficiency and accuracy.
This research explores the integration of quantum computing with classical machine learning to enhance data classification tasks using Quantum Neural Networks (QNN) and Parameterized Quantum Circuits (PQC). The hybrid approach leverages the advantages of both quantum and classical systems to improve the efficiency and accuracy of data processing. In this model, data is encoded into qubits using amplitude encoding, representing input vectors as amplitudes of quantum states. The QNN is initialized by placing the qubits in superposition using Hadamard gates, followed by data encoding with parameterized rotational gates that map classical data to quantum states using rotation angles. PQC plays a central role by applying layers of parameterized quantum operations to process data in the quantum space. These parameters are optimized during the training process, where a quadratic loss function minimizes the error between the predicted quantum states and the true class labels using gradient descent. Experiments conducted on the MNIST dataset show that the hybrid the hybrid quantum-classical neural network (QCNN) with PQC achieves a classification accuracy of over 95%, highlighting its potential in machine learning applications. The results demonstrate that integrating quantum computing with classical machine learning enhances performance in complex data analysis tasks due to the exponential growth of quantum state space and the parallelism of quantum systems, making hybrid models promising for computer vision and classification tasks.
This study presents a noise-aware evaluation framework for hybrid quantum–classical machine learning models applied to medical binary classification. Using three healthcare datasets—Pima Indians Diabetes, Heart Disease, and Breast Cancer Wisconsin—the performance of a Variational Quantum Classifier (VQC) was analyzed under multiple depolarizing noise levels (0.00–0.10). Classical baselines, Logistic Regression (LR) and Support Vector Machine (SVM), were implemented for comparison. The research investigates the impact of noise on predictive accuracy, F1-score, and training time, highlighting the computational overhead of hybrid quantum–classical models. Zero Noise Extrapolation (ZNE), using linear and Richardson methods, was applied to mitigate noise effects, revealing that while ZNE improves performance under certain conditions, extrapolation instability can occur. Transpiler optimization also contributed to improved VQC stability by reducing circuit complexity. Results show that classical models consistently outperformed the VQC in accuracy, stability, and training efficiency. VQC exhibited fluctuating performance under noise, requiring significantly higher training time, and increasing SPSA iterations did not always yield stable accuracy improvements. These findings underscore the challenges of noise robustness, optimization instability, and computational cost in the NISQ era, and suggest directions for future work, including alternative optimizers, adaptive ansatz design, advanced error mitigation, and real hardware benchmarking. This research provides a systematic benchmarking framework for evaluating training time versus noise-level trade-offs, contributing to the development of more reliable quantum machine learning models for medical applications. Keywords: Quantum Machine Learning, Variational Quantum Classifier, Depolarizing Noise, Zero Noise Extrapolation, Medical Classification, Hybrid Quantum–Classical Models, Training Time Analysis