We present a hybrid quantum-classical framework designed to achieve utility-scale performance for Quantum Hadamard Edge Detection (QHED) on Noisy Intermediate-Scale Quantum (NISQ) devices. The framework utilizes a Two-Level Decomposition strategy: (1) Problem-Level Decomposition (PLD), which partitions high-resolution real-world data into buffered sub-images, and (2) Circuit-Level Decomposition (CLD), which employs circuit-cutting to reduce complexity for near-term hardware. This approach, combined with a depth-efficient QHED^M decrement gate, achieves a 62% reduction in circuit depth and 93% fewer two-qubit operations. We demonstrate the framework's domain-agnostic utility by processing real-world data from Medical Image Computing (MIC) and Geospatial Information Systems (GIS). Crucially, we investigate the resilience crossover point by comparing a [[3,1,1]] bit-flip repetition code against passive Quantum Error Mitigation (QEM). Our results indicate that for current coherence times, passive mitigation offers a superior utility advantage by bypassing the gate-overhead penalties inherent in active encoding, recovering nearly 99% of the ideal signal.
We present a hybrid quantum-classical framework designed to achieve utility-scale performance for Quantum Hadamard Edge Detection (QHED) on Noisy Intermediate-Scale Quantum (NISQ) devices. The framework utilizes a Two-Level Decomposition strategy: (1) Problem-Level Decomposition (PLD), which partitions high-resolution real-world data into buffered sub-images, and (2) Circuit-Level Decomposition (CLD), which employs circuit-cutting to reduce complexity for near-term hardware. This approach, combined with a depth-efficient QHED^M decrement gate, achieves a 62% reduction in circuit depth and 93% fewer two-qubit operations. We demonstrate the framework's domain-agnostic utility by processing real-world data from Medical Image Computing (MIC) and Geospatial Information Systems (GIS). Crucially, we investigate the resilience crossover point by comparing a [[3,1,1]] bit-flip repetition code against passive Quantum Error Mitigation (QEM). Our results indicate that for current coherence times, passive mitigation offers a superior utility advantage by bypassing the gate-overhead penalties inherent in active encoding, recovering nearly 99% of the ideal signal.
Quantum computing offers the potential to enhance computational efficiency beyond classical methods, but practical implementation remains challenging due to the limitations of Noisy Intermediate-Scale Quantum (NISQ) hardware, namely, restricted qubit counts, limited connectivity, and the presence of noise and decoherence. This study presents a novel approach to edge detection by leveraging a recently developed Quantum Fuzzy Inference Engine, implemented on a NISQ device. We introduce an optimized quantum circuit for its implementation, reducing qubit requirements and gate depth to improve execution on NISQ hardware. To overcome constraints related to large-scale image processing, a hybrid quantum–classical lookup table approach is employed. Edge detection performance is evaluated on the Berkeley Segmentation Data Set and Benchmarks 500 dataset under different conditions, including classical execution, ideal quantum simulation, noisy quantum simulation, and NISQ hardware calculation. Results demonstrate that the quantum fuzzy logic-based edge detection achieves outcomes comparable to classical methods by using fewer operations, marking a step toward practical quantum-enhanced image processing.
Abstract Quantum image representation constitutes a foundational component of quantum image processing; however, its practical deployment on Noisy Intermediate-Scale Quantum (NISQ) hardware is fundamentally constrained by the cost of quantum state preparation. Existing representations such as the Flexible Representation of Quantum Images (FRQI) and the Novel Enhanced Quantum Representation (NEQR) rely on uniform, full-resolution encoding strategies that incur rapidly increasing gate counts and circuit depths, leading to severe decoherence and error accumulation on near-term devices. These limitations are particularly pronounced for heterogeneous and information-sparse modalities such as medical Magnetic Resonance Imaging (MRI) and Synthetic Aperture Radar (SAR), where uniform pixel-wise encoding introduces substantial redundant state preparation. To address these constraints, we propose Adaptive Hybrid Quantum Image Representation (AHQIR), a saliency-driven selective quantum state-preparation framework designed for efficient encoding of medical and SAR imagery under NISQ limitations. AHQIR departs from global encoding by employing a classical adaptive preprocessing stage to identify diagnostically significant regions in MRI and dominant backscatter structures in SAR images using a statistical thresholding criterion, thereby restricting quantum encoding to a salient pixel subset S. The quantum realization of AHQIR integrates Perception-Aided Encoding (PE) and Coherent-Size Encoding (CE) mechanisms, which condition state preparation on salient pixel coordinates and eliminate the requirement for power-of-two image padding. As a result, circuit depth and multi-qubit gate count scale with the number of salient pixels rather than total image size, enabling physically realizable circuits within current coherence limits. This selective and intentionally lossy design sacrifices global pixel-level fidelity in non-salient regions in order to preserve semantic and structural fidelity within regions of interest. AHQIR is evaluated against multiple state-of-the-art quantum image encoding schemes, including FRQI and NEQR, across Brain Tumor MRI and real-world SAR datasets. Experimental results demonstrate substantial reductions in gate count and improved robustness under realistic noise models, while maintaining reconstruction errors below clinically and analytically relevant thresholds for salient regions. These findings indicate that saliency-aware, selective state preparation offers a practical and scalable pathway for quantum.
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.
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.
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.
The advent of Noisy Intermediate-Scale Quantum (NISQ) machines has brought new opportunities for expanding machine learning abilities with the help of quantum computing. Herein, a complete hybrid quantum-classical learning system is introduced that incorporates classical preprocessing, quantum feature extraction, and classical machine learning in a strategic way to surpass the performance of existing systems for the tasks of complex pattern recognition. We perform large-scale experiments with two popular benchmark datasets: the Iris flower dataset and the Wisconsin Breast Cancer Diagnostic dataset. Our framework shows consistently improving accuracy of2−7%over stark classical methods without sacrificing practicality on state-of-the-art NISQ hardware. With rigorous ablation studies and cross-validation with cutting-edge approaches, we conclude that the best task distribution between traditional and quantum processors is key to near-term quantum advantage. Our introduced framework effectively achieves a quantum circuit depth reduction of 40 % using smart classical preprocessing along with improving classification performance using quantum-augmented feature representation. Our implementation offers both hardware-based execution with Qiskit as well as fast classical simulation modes, so it is available for researchers with limited quantum computing capabilities.