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Journal of Discrete Mathematical Sciences and Cryptography

Quantum machine learning : Developing hybrid quantum-classical algorithms for enhanced computational power

Rina Suresh Patil, Alpana Prashant Adsul, Sonam Singh Bhati, Vivek Deshpande, Payala Krishnanjaneyulu, Edupuganti Mounika

Published Jan 1, 2026• 0 citations
Publisher

Abstract

The increasing need for machine learning to run with less computer resources is causing quantum computing to be considered as a viable substitute for conventional computing. This paper presents a hybrid quantum-classical system that improves learning by means of a classical optimisation loop combined with parameterised quantum circuits. While conventional procedures handle parameter updates and convergence, the proposed approach stores and processes high-dimensional data using quantum variational circuits. Qiskit is used by us to construct this architecture and run it on conventional datasets like Iris, MNIST (binary), CIFAR-100 (subset), HIGGS, and GTEx (gene expression). Particularly for jobs with complex, nonlinear patterns, the findings indicate that the mixed approach is as accurate as or more accurate than classical baselines. Real quantum hardware also works well with the system; noise has no impact on its precision. This work demonstrates how combined quantum-classical learning models might circumvent hardware constraints and provide genuine quantum benefits for applications requiring large data processing.

DOI
10.47974/jdmsc-2543

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The increasing need for machine learning to run with less computer resources is causing quantum computing to be considered as a viable substitute for conventional computing. This paper presents a hybrid quantum-classical system that improves learning by means of a classical optimisation loop combined with parameterised quantum circuits. While conventional procedures handle parameter updates and convergence, the proposed approach stores and processes high-dimensional data using quantum variational circuits. Qiskit is used by us to construct this architecture and run it on conventional datasets like Iris, MNIST (binary), CIFAR-100 (subset), HIGGS, and GTEx (gene expression). Particularly for jobs with complex, nonlinear patterns, the findings indicate that the mixed approach is as accurate as or more accurate than classical baselines. Real quantum hardware also works well with the system; noise has no impact on its precision. This work demonstrates how combined quantum-classical learning models might circumvent hardware constraints and provide genuine quantum benefits for applications requiring large data processing.
This paper investigates optimization strategies for hybrid algorithms that integrate Quantum Machine Learning (QML) with classical machine learning to enhance computational performance and accuracy. Recognizing the limitations of classical algorithms in processing high-dimensional and complex data, and the practical constraints of current quantum computing, such as noise, decoherence, and limited qubit counts, we explore how a synergistic combination can overcome these challenges. We examine key hybrid models, including Quantum Support Vector Machines and Quantum Neural Networks, which leverage quantum principles like superposition and entanglement within classical frameworks. We address challenges posed by quantum noise and hardware limitations, discussing error mitigation techniques and strategies for efficient quantum-classical integration. By focusing on task allocation that takes benefit from the strengths of both quantum and classical processors, optimizing quantum circuit design, and effective resource management, we demonstrate that optimized hybrid algorithms can significantly improve computational efficiency and accuracy. Our findings suggest that continued advancements in quantum hardware and integration methods are essential to fully realize the potential of hybrid computational tools in applications like machine learning, data analysis, and optimization.
Quantum computers acting as ML accelerators have attracted considerable interest as a promising avenue for addressing the limitations of classical computing confronted with solving complex, high-dimensional problems and handling large data sets. The most exciting aspect of quantum computing lies in its quantum advantage via techniques such as quantum parallelism, superposition, and entanglement which allows not only for rapid data processing, but also a means to resolve complex optimization problems beyond the capacity of classical algorithms. Nevertheless, the usage of quantum computing in machine learning is still a fledgling domain, with challenges concerning quantum noise, hardware restrictions, and algorithmic development. In particular, this research is concerned with the development of and study on hybrid quantum-classical algorithms that target to improve ML models in terms of computational capabilities by making use of the best of both worlds. To address this, researchers are developing hybrid algorithms that leverage the strengths of quantum computing for specific tasks, like optimization and pattern recognition, while still relying on classical computing for more flexible and larger-scale processing, ultimately achieving more efficient machine learning systems that can handle large datasets and complex problem-solving more effectively. It includes potential hybrid approaches like quantum-enhanced optimization algorithms, quantum neural networks, and quantum support vector machines, and examines how such algorithms can be used for practical ML problems including data classification, regression and clustering. Furthermore, the paper proposes that hybrid quantum algorithms offer several advantages over their classical counterparts, such as faster convergence rates, higher accuracy in high-dimensional spaces, and improved handling of non-linear and complex problem landscapes. Key advancements in the area of data processing speed and efficiency in problem-solving with and without quantum in the machine learning workflow are also highlighted in the research through comparative analysis and simulation studies. Lastly, the paper concludes by outlining the obstacles yet to be surmounted and the opportunities that lie ahead for hybrid quantum-classical algorithms, such as further improvement of quantum hardware and error mitigation methods, as well as the design of new algorithmic paradigms that seamlessly integrates the classical and quantum computing spaces.
The entwining of quantum computing with classical machine learning has proven to be one of the most promising frontiers of artificial intelligence, as it possesses the potential to speed up intricate computations in ways that classical systems will never be able to achieve. This study delves into the theoretical and practical implications of hybrid quantum-classical approaches in machine learning, while also examining their advantages, limitations, and applicability in different domains. Utilizing quantum entanglement and parallelism, hybrid solutions also have the potential to process high-dimensional data, optimize complex functions, and facilitate pattern recognition tasks more efficiently. However, noise, decoherence, and limited qubit connectivity on current hardware pose considerable barriers to practical implementations. The authors discuss hybrid architectures like quantum-enhanced optimizers and variational quantum circuits which include classical pre- and post-processing to alleviate quantum limitations. Moreover, a comparative study is performed to show the effectiveness of hybrid models comparing with classical machine learning state-of-the-art in natural language processing, computer vision and financial modeling. Results indicate that although hybrid quantum–classical approaches provide significant gains in optimization and computational efficiency; these benefits remain limited by hardware limitations and the scalability of quantum algorithms. With these considerations in mind, the paper offers guidance for targeting future research directions in quantum machine learning, including advances in quantum error correction, quantum hardware scalability, and new algorithmic approaches. Additional advancements needed and notably, the study focused on a smaller representation of data Since quantum computing is relatively new and researchers are still exploring its application, it is still early days in terms of machine learning models that are solely, intrinsically quantum.
With the advancement of quantum computing in the Noisy Intermediate-Scale Quantum (NISQ) era, hybrid quantum-classical algorithms have emerged as promising approaches for addressing certain machine learning tasks. This study investigates the Variational Quantum Classifier (VQC), a hybrid model that integrates parameterized quantum circuits with classical optimization routines, implemented via IBM’s Qiskit framework. We provide a detailed account of the VQC architecture, including feature encoding, ansatz construction, and optimization methodology. To assess its performance, we conduct a comparative analysis between VQC and classical Support Vector Classifiers (SVC) across synthetic and real-world datasets, including Iris and a binary-filtered version of MNIST. Experimental results reveal that classical models consistently achieve higher accuracy and faster training times. However, the VQC demonstrates functional viability, particularly under noise-free conditions and reduced-dimensionality settings. These findings underscore the current limitations of quantum models while highlighting the potential of VQC as a proof-of-concept for quantum-enhanced learning as quantum hardware matures.
Quantum computing has emerged as one of the most influential paradigms capable of transforming computational processes that struggle under classical limitations. In recent years, hybrid quantum–classical algorithms have gained significant attention for their ability to leverage the strengths of both architectures, especially within the Noisy Intermediate-Scale Quantum (NISQ) era. This research paper explores a quantum-enhanced optimization framework designed to improve machine learning model performance through parameterized quantum circuits (PQCs). The goal of this study is to provide a practical, scalable approach that can be integrated into existing machine learning workflows without requiring fully developed fault-tolerant quantum hardware. The proposed framework uses classical preprocessing to encode data into quantum states, followed by quantum transformations that explore richer feature spaces due to quantum superposition and entanglement. A classical optimizer then updates the quantum circuit parameters based on measurement results, forming an end-to-end feedback loop. This hybrid model aims to demonstrate improved optimization efficiency, reduction in loss-function plateaus, and better generalization for specific ML tasks involving small to medium-sized datasets. This paper provides a comprehensive investigation of methodology, literature background, and experimental reasoning with statistical analysis, along with conceptual diagrams illustrating system architecture and circuit layouts. The outcomes further strengthen the viability of hybrid quantum–classical computation as a promising direction for advanced machine learning systems.
Quantum machine learning has emerged as a promising approach to enhance computational efficiency by leveraging the principles of quantum computing. However, the limitations of current Noisy Intermediate-Scale Quantum (NISQ) devices, such as noise, limited qubit availability, and circuit depth constraints, restrict the implementation of fully quantum models. To address these challenges, this study focuses on the design, implementation, and performance evaluation of hybrid quantum-classical machine learning (HQML) models. The proposed approach integrates parameterized quantum circuits with classical optimization techniques to enable efficient learning within NISQ environments. The study employs standard benchmark datasets, including Iris, Breast Cancer, and MNIST, to evaluate the performance of the hybrid model. The results indicate that the HQML model achieves competitive accuracy on small and medium-sized datasets while maintaining balanced precision, recall, and F1-score. However, performance declines for complex datasets due to hardware limitations and noise effects. Additionally, the hybrid model demonstrates a lower number of parameters compared to classical deep learning models but requires higher training time due to iterative quantum-classical optimization. The findings highlight that hybrid quantum-classical models provide a practical and scalable approach for utilizing quantum computing in the current technological landscape. Although challenges related to noise, scalability, and computational overhead persist, advancements in quantum hardware and algorithm design are expected to improve performance. This study contributes to the growing field of quantum machine learning by providing a systematic framework for evaluating hybrid models on NISQ devices and identifying key areas for future research.