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.
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.
Quantum computing has emerged as a transformative paradigm capable of addressing computational challenges beyond the reach of classical systems.In the current era of Noisy Intermediate-Scale Quantum (NISQ) devices, practical quantum hardware is characterized by limited qubit counts, short coherence times, gate errors, and the absence of full error correction.Despite these constraints, significant progress has been made in developing quantum machine learning (QML) techniques tailored to operate on near-term quantum processors.This paper presents a comprehensive review of Quantum Machine Learning in the context of NISQ computing.We first outline the fundamental principles of quantum computing, including qubits, superposition, entanglement, and quantum parallelism, followed by a detailed discussion of the NISQ computing model and its hardware limitations.The review then examines hybrid quantum-classical learning frameworks, variational quantum algorithms, quantum data encoding strategies, and noise mitigation techniques that enable practical implementation on existing platforms.Emerging applications across healthcare, finance, cybersecurity, climate modeling, and materials science are also surveyed to highlight the real-world potential of QML.Furthermore, key challenges such as scalability, trainability issues, and algorithmic robustness are analyzed, along with current research efforts aimed at overcoming these barriers.The paper concludes by identifying promising future directions for advancing QML toward quantum advantage.This review aims to provide researchers and practitioners with a structured understanding of the capabilities, limitations, and opportunities of quantum machine learning in the NISQ era .
An interesting approach to using noisy intermediate-scale quantum (NISQ) devices is hybrid classical-quantum machine learning (QML). In these methods, classical processors handle optimisation and large-scale computation, while quantum hardware is devoted to tasks like feature mapping, nonlinear transformations, or kernel evaluation. Practical near-term demonstrations are made possible by this division of labour, which also mitigates existing hardware restrictions. In specialised fields like molecular modelling, materials discovery, and small-sample learning issues, recent advancements in variational quantum circuits, hybrid neural networks, and quantum kernel techniques have produced promising outcomes. However, scalability and wider applicability are still hampered by enduring issues including noise, barren plateaus, and the expense of repeated measurements. Long-term developments will require fault tolerance, logical qubits, and established software infrastructures, whereas near-term success depends on noise-aware algorithm design, repeatable experimental benchmarks, and enhanced error-mitigation strategies. When taken as a whole, these advancements show a viable path to achieving quantum advantage in machine learning. Quanta 2026; 15: 1–12.
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—Quantum Machine Learning (QML) operating on Noisy Intermediate-Scale Quantum (NISQ) hardware represents an emerging computational paradigm to address high-dimensional optimization problems that challenge classical Von Neumann supercomputing architectures. By mapping complex feature vectors into exponentially large 2^N Hilbert state spaces via Parameterized Quantum Circuits (PQCs) and Variational Quantum Algorithms (VQAs), QML targets computational advantages in combinatorial optimization, high-dimensional classification, and quantum-enhanced molecular modeling. However, the theoretical promise of NISQ-era variational computing is severely constrained by three fundamental bottlenecks: (1) Barren Plateaus, characterized by the exponential concentration of measure and vanishing variance of cost function gradients; (2) Hardware Decoherece Noise and readout error rates that corrupt quantum state fidelity; and (3) Classical-to-Quantum State Preparation bottlenecks that can erase theoretical computational speedups. This paper delivers an exhaustive, mathematically formal technical investigation and empirical benchmark of QML architectures for high-dimensional optimization. We formalize the Haar-distributed geometric mechanics of barren plateaus under 2-design unitary assumptions, evaluate barren plateau mitigation through shallow local cost operators and layer-by-layer parameter initialization, and contrast Variational Quantum Eigensolvers (VQE) with Quantum Kernel Support Vector Machines (Q-SVM). Furthermore, we construct an empirical benchmarking testbed executing across both state-vector simulators and superconducting quantum backends (IBM Quantum Heron / Eagle architectures), evaluating 127-qubit Hamiltonian optimization and high-dimensional financial portfolio allocation. Our findings demonstrate that while global cost functions suffer exponential gradient decay Var[grad] ~ O(2^-N) across circuit depth d >= 4, local Hamiltonian decomposition maintains trainable variance, achieving a 98.2% ground-state fidelity under zero-noise extrapolation (ZNE) error mitigation. Finally, we formulate open challenges in quantum error mitigation scaling, non-perturbative barren plateau escapes, and quantum data loading efficiency. Index Terms—Quantum Machine Learning (QML), Parameterized Quantum Circuits (PQCs), Variational Quantum Eigensolver (VQE), Barren Plateaus, Quantum Kernel Methods, NISQ Computing, Error Mitigation, Hilbert Space.
Quantum machine learning sits at the intersection of two paradigm-shifting technologies: quantum computing and deep learning. By exploiting quantum mechanical phenomena – superposition, entanglement, and interference – QML promises exponential or quadratic speedups over classical algorithms for certain learning tasks, as well as the ability to model quantum data natively. However, the path to practical quantum advantage remains contested, constrained by noisy intermediate-scale quantum (NISQ) hardware, limited qubit counts (50–1,000), coherence times (50–500 μs), and high gate error rates (10⁻³–10⁻⁴). This paper provides a rigorous, technically deep survey of QML: mathematical foundations (Hilbert spaces, unitary evolution, measurement, quantum circuits), canonical algorithms (quantum kernel methods, variational quantum circuits (VQCs), quantum neural networks (QNNs), QSVMs, quantum generative adversarial networks (QGANs), encoding strategies (angle, amplitude, basis, and Hamiltonian encoding), optimization landscapes (barren plateaus, parameter shift rules, ansatz design), hardware aware implementation on superconducting (IBM, Google), trapped ion (IonQ), and neutral atom (Pasqal) platforms, empirical benchmarks on near term devices for classification, generative modeling, and quantum chemistry, and pathways to fault tolerant quantum machine learning (FTQML) with error correction (surface codes, logical qubits). Researchers critically assess claims of quantum advantage, identify scenarios where QML may outperform classical ML (small data, high-dimensional feature spaces from quantum systems, kernel estimation), and propose concrete evaluation metrics (quantum-classical cross-validation, resource estimation).
The rapid evolution of Noisy Intermediate-Scale Quantum (NISQ) devices has intensified the need for robust compilation strategies capable of mitigating hardware-induced errors while maximizing computational efficiency. Quantum compilers play a pivotal role in translating high-level quantum algorithms into hardware-executable instructions, yet they face significant challenges related to qubit connectivity constraints, limited coherence times, and stochastic noise. This paper examines error-resilient quantum compiler design for efficient qubit mapping, gate optimization, and noise mitigation in NISQ-era devices, proposing a framework that integrates topology-aware mapping, adaptive gate synthesis, and probabilistic error suppression techniques. By synthesizing advances in quantum circuit optimization, hardware-aware scheduling, and hybrid classical–quantum error correction strategies, the study evaluates how compiler-level innovations can substantially enhance execution fidelity and resource efficiency. The findings suggest that intelligent compiler architectures are critical enablers of practical quantum advantage during the transitional NISQ phase, bridging theoretical algorithm design with real-world hardware constraints.