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UMYU Scientifica

Variational Quantum-Classical Algorithms: A Review of Theory, Applications, and Opportunities

Philip Adebayo, Frederick Basaky, Edgar Osaghae

Published Dec 30, 2023• 12 citations
Publisher

Abstract

Variational Quantum-Classical Algorithm (VQCA) is a potential tool for machine learning (ML) prediction tasks, but its efficacy, adaptability to big datasets, and optimization for noise reduction on quantum hardware are not clear. We aim to accomplish three study goals in this literature review. We begin by reviewing the justifications for ML practitioners' use of VQCA. Second, we compare the accuracy and effectiveness of VQCA in diverse domains to see whether it has a performance advantage over other ML methods. Finally, we evaluate VQCA's immediate and long-term effects on quantum ML and how well it performs compared to ML techniques for prediction tasks across various applications or domains. Our findings show that VQCA can be significantly more accurate and efficient than conventional algorithms. We also compare traditional ML algorithms with VQCA on various datasets and examine their theoretical guarantees. We equally look into how VQCA might be used practically to address problems in a variety of industries, including banking, healthcare, and energy. In various datasets, we assess the performance and efficacy of VQCA for unsupervised learning tasks. Finally, we go through ways to improve VQCA, particularly for big and complicated problems, to lessen the effect of noise and other sources of error in quantum hardware. Overall, we looked at VQCA’s advantages and disadvantages for ML prediction tasks, including possible directions for future study. Our findings show that VQCA has the potential to completely transform the ML industry, particularly in this emerging era of quantum computing.

DOI
10.56919/usci.2324.008

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Variational Quantum-Classical Algorithm (VQCA) is a potential tool for machine learning (ML) prediction tasks, but its efficacy, adaptability to big datasets, and optimization for noise reduction on quantum hardware are not clear. We aim to accomplish three study goals in this literature review. We begin by reviewing the justifications for ML practitioners' use of VQCA. Second, we compare the accuracy and effectiveness of VQCA in diverse domains to see whether it has a performance advantage over other ML methods. Finally, we evaluate VQCA's immediate and long-term effects on quantum ML and how well it performs compared to ML techniques for prediction tasks across various applications or domains. Our findings show that VQCA can be significantly more accurate and efficient than conventional algorithms. We also compare traditional ML algorithms with VQCA on various datasets and examine their theoretical guarantees. We equally look into how VQCA might be used practically to address problems in a variety of industries, including banking, healthcare, and energy. In various datasets, we assess the performance and efficacy of VQCA for unsupervised learning tasks. Finally, we go through ways to improve VQCA, particularly for big and complicated problems, to lessen the effect of noise and other sources of error in quantum hardware. Overall, we looked at VQCA’s advantages and disadvantages for ML prediction tasks, including possible directions for future study. Our findings show that VQCA has the potential to completely transform the ML industry, particularly in this emerging era of quantum computing.
Abstract The emergence of noisy intermediate-scale quantum (NISQ) devices has fueled the development of hybrid quantum-classical algorithms for machine learning (ML), promising potential advantages over classical methods. However, the practical efficacy of these algorithms remains uncertain due to challenges like noise susceptibility, trainability issues, and a lack of rigorous benchmarking. This study presents a comprehensive empirical evaluation of two flagship hybrid algorithms the Variational Quantum Eigensolver (VQE) for classification and the Quantum Approximate Optimization Algorithm (QAOA) for combinatorial optimization against state-of-the-art classical baselines under equivalent resource constraints. Through extensive simulations incorporating realistic noise models, we demonstrate that while these quantum approaches achieve competitive performance (e.g., 91.2% accuracy for VQE on a binary classification task), they consistently underperformed optimized classical models like Support Vector Machines (94.8% accuracy) and require orders of magnitude more computational time. Furthermore, we provide empirical validation of critical barriers to scalability, including the barren plateau phenomenon and significant performance degradation under noise, even with advanced error mitigation. Our results indicate that for the tasks studied, current NISQ era algorithms do not yet provide a tangible quantum advantage. This work contributes a rigorous benchmarking framework and a critical, realistic assessment of the field, suggesting that future progress hinges on fundamental algorithmic innovations and hardware improvements rather than incremental refinements of existing paradigms.
The rapid advancement of artificial intelligence has positioned Machine Learning (ML) as a cornerstone technology across scientific and industrial domains. In parallel, the emergence of quantum computing has catalyzed a new interdisciplinary field—Quantum Machine Learning (QML)—which promises to transcend the computational barriers faced by classical algorithms. This review paper systematically examines the evolution of ML from foundational statistical models to contemporary transformer architectures, and provides a structured analysis of QML paradigms including variational quantum circuits (VQCs), quantum kernel methods, and quantum neural networks (QNNs). Drawing from 95+ peer-reviewed publications indexed in Scopus and Science Citation Index (SCI) journals—with particular emphasis on 2025–2026 publications in IEEE Access, Nature Communications, Nature Computational Science, and Physical Review Letters—we analyze performance benchmarks, identify hardware constraints, and outline algorithmic innovations shaping the near-term quantum advantage landscape. Our findings indicate that while classical ML retains superiority in large-scale perception tasks, QML demonstrates significant advantages in combinatorial optimization and quantum chemistry simulation. Recent 2025 advances in error mitigation on superconducting qubits and improved VQC barren-plateau mitigation are narrowing this gap rapidly. The paper concludes with a forward-looking research agenda covering fault-tolerant QML, hybrid architectures, and quantum NLP.
Quantum Machine Learning (QML) is a newly emerging research area at the intersection of classical machine learning (CML) and quantum computing (QC). Data is becoming voluminous rapidly, so it is challenging for classical computers to train Machine Learning (ML) models over massive datasets. The hope is that quantum physics' intrinsic features, such as entanglement, superposition, and interference, could be exploited as resources for training ML models on big datasets that would otherwise be relatively impossible for classical computers. It is theoretically proven that quantum computers have an exponential-time advantage over their classical counterparts in solving several problems, e.g., complex large dimensional matrix multiplication, factorization problem, unstructured database search, etc. QML models attempt to find a quantum advantage over their classical counterparts. Variational Quantum Classifiers (VQC) are hybrid quantum neural networks to perform the task of classification using QML models. VQC models in the present NISQ (Noisy Intermediate Scale Quantum — 50 to 100 qubits) era can produce comparable and even better results than Classical models. In this article, we examined the performance of a VQC while performing a simple binary classification task. In this article, we use a VQC to evaluate this method's performance empirically. We constructed a VQC to predict the label of fresh input for the typical Iris dataset comprising pairings of target outputs and training inputs. Our quantum classifier can reasonably predict species labels using only four qubits. These levels are fairly good compared to the accuracy levels attained by classical classifiers.
Quantum computing has been a source of hype in the past few years—especially in its application to machine learning (ML) use-cases. This paper compares QML algorithms to traditional ML for a variety of classification problems yielding an overview on potential applications that quantum technologies can either complement or provide superior performance. The paper begins by outlining the fundamental principles of quantum computing required for its application in machine learning. This article will highlight key ideas such as quantum parallelism and the use of quantum interference in n-computing efficiency. The conversation turns to Quantum machine learning Algorithms, in comparison with Classical algorithms without any further ado and specific quantum algorithmic extensions which are available for the problem of machines. These quantum algorithms are analyzed in terms of computational speed and accuracy, leveraging qubits to potentially accelerate learning processes and achieve improved results. Both the prospects and challenges of quantum algorithms for practical ML applications, by combining empirical data with insights from theory. The study also investigates how these limitations of quantum computing today such as qubit coherence, error rates and scalability are likely to impact the practical deployment of QML. In the final sections, the paper discusses next steps and future directions for quantum machine learning with a focus on potential milestones that could lift current obstacles to merge more deeply classical and quantum tools of data analysis. The article provides an in-depth data-driven perspective on the emerging intersection of these two fields with a view towards their potential future impact within quantum machine learning.
Quantum computing offers a fundamentally new paradigm for solving complex optimisation and learning tasks by exploiting superposition, entanglement, and other quantum phenomena. Over the past decade, research has increasingly focused on quantum-enhanced approaches to optimisation and machine learning (ML), showing the potential to outperform classical methods in specific settings (Zaman, 2023; Peral-García, 2024). This paper presents a comprehensive review of quantum algorithms for optimisation (e.g., the Quantum Approximate Optimization Algorithm and quantum annealing) and quantum machine learning frameworks (such as quantum support vector machines and quantum neural networks), analysing their theoretical underpinnings, implementation status, and applicability to real-world tasks. Key challenges including hardware noise, limited qubit counts, and algorithmic scalability are examined (Chen, 2024). We also explore hybrid quantum-classical architectures as a near-term route to quantum advantage and propose future research directions aimed at bridging the current gap between quantum algorithm theory and large-scale deployment. Through this synthesis, we aim to provide both academic and practitioner audiences with a clear roadmap for leveraging quantum algorithms in optimisation and ML workflows
Variational Quantum Algorithms are a major method of harnessing Noisy Intermediate-Scale Quantum devices to solve classically intractable problems in physics, chemistry, optimization, and machine learning. The current review offers a critical overview of VQAs, with special emphasis on their theoretical backgrounds, algorithmic structures, and application performance within realistic models of noise. Several key variants, such as the Variational Quantum Eigensolver, Quantum Approximate Optimization Algorithm, and Quantum Neural Networks, are compared in terms of noise robustness, ansatz archi- tecture, and hybrid quantum-classical methods of optimization. Benchmarks in fields such as quantum chemistry, finance modeling, and particles and nuclei physics reveal the poten- tial of VQAs in achieving practical quantum advantage. Fundamentally limiting factors 1such as barren plateaus, optimization overhead, and hardware constraints are considered in addition to mitigation strategies, including adaptive construction of ansatz, informed training in the presence of noise, and quantum error correction using QVECTOR. The paper is concluded with an overview of the scalability and future of VQAs in the direction of transitioning toward fault-tolerant quantum computing.