Abstract Quantum optimization has become a leading application for near-term quantumcomputing, and yet many publications compare algorithms against idealizedassumptions and small toy benchmarks. This limits the interpretability, reproducibility,and practical relevance of reported performance gains, particularlyin the noisy intermediate-scale quantum (NISQ) era. In this work, we presenta systematic literature review that investigate quantum optimization beyondtoy benchmarks. Following established SLR protocols, we analyze the literaturealong multiple methodological dimensions, including algorithmic approach,benchmark realism, encoding strategies, hybrid quantum-classical workflows,hardware and noise modeling, evaluation metrics, and reporting practices. Weintroduce a unified taxonomy that captures the interaction between problemformulation, encoding overhead, noise-aware execution, and hybrid optimizationloops. In addition, we propose a reproducibility checklist and scoring rubric toassess reporting completeness and experimental rigor across studies. Instead ofdeveloping new quantum optimization algorithms or making theoretical quantumadvantage claims, the main contribution of this work is that it providesa methodological analysis on benchmarking realism and encoding or evaluationpractices as well as reproducibility rigor in NISQ-era quantum optimization studies.Our review uncovers a continued chasm between algorithmic innovation andevaluation maturity, with the number of publications and diversity of methodsgrowing without corresponding growth in standardized benchmarks, strongclassical baselines, noise-consistent evaluation, or reproducibility.
Abstract Quantum optimization has become a leading application for near-term quantumcomputing, and yet many publications compare algorithms against idealizedassumptions and small toy benchmarks. This limits the interpretability, reproducibility,and practical relevance of reported performance gains, particularlyin the noisy intermediate-scale quantum (NISQ) era. In this work, we presenta systematic literature review that investigate quantum optimization beyondtoy benchmarks. Following established SLR protocols, we analyze the literaturealong multiple methodological dimensions, including algorithmic approach,benchmark realism, encoding strategies, hybrid quantum-classical workflows,hardware and noise modeling, evaluation metrics, and reporting practices. Weintroduce a unified taxonomy that captures the interaction between problemformulation, encoding overhead, noise-aware execution, and hybrid optimizationloops. In addition, we propose a reproducibility checklist and scoring rubric toassess reporting completeness and experimental rigor across studies. Instead ofdeveloping new quantum optimization algorithms or making theoretical quantumadvantage claims, the main contribution of this work is that it providesa methodological analysis on benchmarking realism and encoding or evaluationpractices as well as reproducibility rigor in NISQ-era quantum optimization studies.Our review uncovers a continued chasm between algorithmic innovation andevaluation maturity, with the number of publications and diversity of methodsgrowing without corresponding growth in standardized benchmarks, strongclassical baselines, noise-consistent evaluation, or reproducibility.
Abstract The arrival of noisy intermediate-scale quantum (NISQ) devices defines an era in which quantum utility is fundamentally constrained by finite coherence times, limited qubit counts, gate infidelities, restricted connectivity, and measurement noise. Within this regime, hybrid quantum-classical frameworks have emerged as the dominant operational paradigm, particularly for quantum machine learning (QML). This review identifies a fundamental trade-off between expressivity, trainability, and noise resilience that governs the performance and scalability of NISQ-era QML systems. To contextualize these challenges, we introduce the resource-constrained iterative routing framework, a hardware-aware conceptual architecture that integrates topology-aware classical compression and distributed quantum orchestration to maintain circuit depths within device-dependent limits while routing representations toward symmetry-constrained Hilbert subspaces to mitigate noise-induced barren plateaus. Furthermore, we shift the discussion of quantum advantage away from asymptotic fault-tolerant complexity toward the notion of operational NISQ advantage based on finite-resource scaling, trainability preservation, and sampling complexity. We evaluate the practical resource efficiency of variational quantum algorithms, quantum kernel methods, and quantum neural networks across superconducting, trapped-ion, neutral-atom, and photonic platforms. The review also examines reproducibility challenges, emphasizing benchmarking against optimized classical baselines, and discusses strategies for managing the sampling overhead of error mitigation alongside distributed execution and quantum circuit compilation. Ultimately, NISQ in Practice positions hybrid QML as a physically constrained computational paradigm while outlining a pathway from contemporary noisy workflows toward early fault-tolerant quantum architectures.
This paper presents a qualitative analysis of hybrid quantum-classical computing approaches aimed at solving complex optimization problems using near-term quantum processors. Hybrid algorithms leverage the strengths of quantum and classical computing to tackle computationally intensive tasks often constrained by current quantum hardware limitations. Through an extensive literature review and synthesis of recent empirical studies, we benchmark various hybrid algorithms, such as the Quantum Approximate Optimization Algorithm (QAOA) and Variational Quantum Eigensolver (VQE), focusing on their performance, scalability, and practical applicability on noisy intermediate-scale quantum (NISQ) devices. The study highlights the advantages, challenges, and future prospects of integrating hybrid quantum-classical computation in optimization domains, providing a comprehensive framework and qualitative insights into benchmarking methodologies and critical performance metrics.
The Noisy Intermediate-Scale Quantum (NISQ) era, defined by qubit counts in the hundreds and gate error rates that preclude long coherence times, imposes severe constraints on purely quantum computation. The central problem is that achieving practical quantum advantage for real-world tasks must overcome these hardware limitations, yet fault-tolerant quantum computers with full error correction remain years away. To address this, we present a systematic survey of hybrid classical-quantum computing models, in which classical high-performance resources orchestrate the workflow, perform iterative optimization, and apply error mitigation to noisy quantum processing units. Our review encompasses variational quantum algorithms, such as the variational quantum eigensolver and quantum approximate optimization algorithm; classical optimizers tailored for noisy quantum landscapes; error mitigation techniques including zero-noise extrapolation and probabilistic error cancellation; and circuit knitting that partitions large circuits across small QPUs. We find that these hybrid architectures have already demonstrated domain-specific utility in quantum chemistry for molecular ground-state estimation, in logistics and finance for combinatorial optimization, and in machine learning for generative and recommendation models. Notably, they often surpass purely classical or purely quantum approaches on carefully chosen benchmarks. The evidence indicates that hybrid classical-quantum systems are not a temporary stopgap but a durable paradigm. Their role will persist into the early fault-tolerant era, where small, logical qubits will similarly require classical coordination. Consequently, the field urgently demands the establishment of standardized hybrid performance benchmarks, the maturation of robust quantum-classical middleware capable of efficient transpiration and execution management, and holistic co-design frameworks that seamlessly integrate hardware constraints, software stack layers, and application-specific requirements from the outset.
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.
Quantum optimisation is emerging as a promising approach alongside classical heuristics and specialised hardware, yet its performance is often difficult to assess fairly. Traditional benchmarking methods, rooted in digital complexity theory, do not directly capture the continuous dynamics, probabilistic outcomes, and workflow overheads of quantum and hybrid systems. This paper proposes principles and protocols for fair benchmarking of quantum optimisation, emphasising end-to-end workflows, transparency in tuning and reporting, problem diversity, and avoidance of speculative claims. By extending lessons from classical benchmarking and incorporating application-driven and energy-aware metrics, we outline a framework that enables practitioners to evaluate quantum methods responsibly, ensuring reproducibility, comparability, and trust in reported results.
The current stage of quantum computing development is defined by Noisy Intermediate-Scale Quantum (NISQ) devices, which operate with a moderate number of qubits that are inherently susceptible to noise and decoherence. Despite the absence of full error correction, NISQ systems have demonstrated the ability to perform computational tasks that challenge classical simulation under certain conditions. This paper explores the concept of quantum advantage in the NISQ era by analysing prominent algorithmic approaches, benchmarking methodologies, and the practical constraints imposed by contemporary hardware. Hybrid quantum–classical algorithms, sampling-based experiments, and performance metrics are examined to assess the extent to which near-term quantum devices can outperform classical systems. The study finds that while progress toward quantum advantage is evident, significant technical and algorithmic limitations prevent its widespread realization. The paper concludes by identifying key research directions required to bridge the gap between experimental demonstrations and practical quantum computing applications.