Abstract Quantum image processing (QIP) promises significant advantages for computer vision, but its realization on Noisy Intermediate-Scale Quantum (NISQ) devices is hampered by a fundamental trade-off between qubit efficiency and measurement robustness. This work introduces a novel hybrid quantum-classical representation that optimizes this trade-off for discrete-variable photonic quantum hardware using path-encoded qubits. Through a dual optimization approach combining simulation-based ablation study and mathematical optimization with bootstrap validation (1000 resamples), we derive an optimal operating point of 𝜶 = 0 . 393 ± 0 . 019 (95% CI: 0.355-0.424). Our architecture requires only 𝑸 = I log 2 ( 𝑵 2 )] + 4 qubits for an 𝑵 × 𝑵 image, achieving logarithmic scaling while maintaining measurement fidelity between 0.92-0.97 on simulated NISQ hardware. We provide complete photonic circuit designs utilizing path encoding, including resource estimates for optical components. Comprehensive performance analysis demonstrates a 38% improvement in error resilience over FRQI and a 27% reduction in qubit requirements over NEQR for typical image operations. Measurement distribution analysis confirms well-separated operational modes with minimal overlap, indicating excellent discrimination capability. This work establishes a practical and scalable framework for implementing QIP on imminent discrete-variable photonic quantum processors.
Abstract Quantum image processing (QIP) promises significant advantages for computer vision, but its realization on Noisy Intermediate-Scale Quantum (NISQ) devices is hampered by a fundamental trade-off between qubit efficiency and measurement robustness. This work introduces a novel hybrid quantum-classical representation that optimizes this trade-off for discrete-variable photonic quantum hardware using path-encoded qubits. Through a dual optimization approach combining simulation-based ablation study and mathematical optimization with bootstrap validation (1000 resamples), we derive an optimal operating point of 𝜶 = 0 . 393 ± 0 . 019 (95% CI: 0.355-0.424). Our architecture requires only 𝑸 = I log 2 ( 𝑵 2 )] + 4 qubits for an 𝑵 × 𝑵 image, achieving logarithmic scaling while maintaining measurement fidelity between 0.92-0.97 on simulated NISQ hardware. We provide complete photonic circuit designs utilizing path encoding, including resource estimates for optical components. Comprehensive performance analysis demonstrates a 38% improvement in error resilience over FRQI and a 27% reduction in qubit requirements over NEQR for typical image operations. Measurement distribution analysis confirms well-separated operational modes with minimal overlap, indicating excellent discrimination capability. This work establishes a practical and scalable framework for implementing QIP on imminent discrete-variable photonic quantum processors.
Abstract The Quantum Image Representation (QIR) remains one of the most significant challenges in Quantum Image Processing (QIP) and Quantum Machine Learning (QML) with the resource constraints required by Noisy Intermediate-Scale Quantum (NISQ) hardware. Currently available pixel representation schemes, such as Flexible Representation of Quantum Images (FRQI) and Novel Enhanced Quantum Representation (NEQR), typically have circuit depth and the number of required qubits that grow with image resolution, rendering them impractical for large-scale images. To alleviate these limitations, we propose the Qubit-Efficient and Resolution-Independent Quantum Image Representation (QRISP), a compact, feature-aware encoding framework that is resource-efficient while preserving discriminative information for classification. The proposed approach divides an image into a user-configurable number of non-overlapping blocks, stores complementary statistical descriptors such as mean intensity, local variance, dominant gradient orientation, and calculates the same descriptors using a series of parameterized rotation gates in a quantum feature register; a position register is used to store block indices, and a lightweight entanglement layer is used to store the feature correlations. One of the major features of QRISP is the resolution-independent quantum circuit structure of quantum resources, which depend on the block configuration rather than the image size, allowing flexible processing and trade-offs between representation fidelity and qubit complexity. Experimental results with the MNIST and Fashion-MNIST datasets for the case of Quantum Support Vector Machine (QSVM) and Quantum Neural Network (QNN) pipelines show significant improvement in the number of gates and depth of the circuits, as well as in the time for computing the kernel, without compromising the classification results from FRQI and NEQR, with respect to which their performance is competitive. This shows their potential for scalable, NISQ-oriented quantum image processing.
Scalable combinatorial optimization under resource-constrained quantum hardware remains a fundamental challenge in the Noisy Intermediate-Scale Quantum (NISQ) era, due to the mismatch between exponentially growing solution spaces and limited quantum computational capacity. In this work, we propose a NISQ-aware hybrid quantum-classical optimization framework that reformulates large-scale combinatorial optimization as a resource-bounded distribution evolution process. Instead of directly optimizing individual solutions, the proposed framework operates on a probabilistic representation of the solution space, enabling efficient exploration under hardware constraints. Specifically, large problem instances are decomposed into qubit-compatible subproblems via clustering-based decomposition, ensuring resource-bounded optimization. Within each subproblem, a quantum genetic algorithm evolves the solution distribution, while periodically embedded amplitude amplification acts as a controlled quantum enhancement mechanism that accelerates convergence without increasing circuit depth. A classical refinement stage ensures global solution consistency. Extensive experiments on benchmark and synthetic datasets demonstrate that the proposed framework consistently outperforms classical and quantum-inspired baselines, with performance gains that become more pronounced as problem scale increases. This scale-dependent behavior indicates that scalability is achieved through structured decomposition rather than increased quantum complexity. Noise simulations further confirm robustness under realistic NISQ conditions, and ablation studies validate that both quantum evolutionary search and amplitude amplification contribute significantly to performance improvements.
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.
In quantum image processing, a fundamental step is encoding classical image data into quantum states. This can be achieved using methods such as Flexible Representation of Quantum Images (FRQI), Quantum Probability Image Encoding (QPIE), and Novel Enhanced Quantum Representation (NEQR). However, on real quantum hardware, these encodings can quickly lead to circuits with many gates, large circuit depth, and high qubit usage, which is a problem for Noisy Intermediate-Scale Quantum (NISQ) devices. In this work, we investigate whether low-rank state approximation, formulated via Schmidt decomposition, can help reduce this complexity. The method keeps only the most significant parts of a quantum state's entanglement structure, making state preparation more efficient while preserving most of the image information. We compare the three encoding techniques in their original form and with low-rank approximation, evaluating metrics such as circuit depth, CNOT count, MSE, and visual quality of reconstructed images. The results reveal meaningful trade-offs between accuracy and resource efficiency, with the FRQI model achieving a 97 percent reduction in circuit depth while maintaining a near-perfect reconstruction (MSE of about 0.27). This demonstrates the potential of low-rank techniques for advancing practical quantum image processing on near-term hardware.
Abstract Quantum Image Representation (QIR) is a fundamental concept in quantum image processing. It describes how classical images are converted into quantum states for processing on quantum computers. Researchers proposed several QIR models, with FRQI and NEQR being the most popular ones. These models show the possibilities of the quantum image encoding. Nevertheless, they are also limited in some way. Mostly, pixel intensity accuracy, the required number of qubits, and circuit complexity have trade-offs. Their application to Noisy Intermediate-Scale Quantum (NISQ) devices becomes challenging, the quantum resources being small in such devices, due to this. In the following paper, we introduce our own approach, which is the Intensity-Preserving Quantum image Representation (IP-QIR). The key aim of IP-QIR is to maintain the information about the grayscale intensities and decrease the amount of quantum resources. IP-QIR quantifies pixel intensities by a controlled rotation scheme. The measurement statistics of a single qubit hold the intensity information and the position qubits represent the spatial information. The strategy uses small patches of images rather than complete images to make it easy to implement. This will decrease the depth of circuit design and makes the approach less advanced to the near-term quantum hardware. IBM Qiskit simulations are used in assessing the performance of IP-QIR. The three types of grayscale images of which experiments are run are the synthetic image patches, SAR images and medical TB chest X-ray images. It is revealed that IP-QIR maintains the intensity information compared to the FRQI and NEQR. SAR and medical data can reach values of fidelity of 84.12\%. The other notable point is that the size of a 4 x 4 image patch only needs five qubits which are much lower than in NEQR. Meanwhile, good reconstruction accuracy is achieved. These findings demonstrate the fact that IP-QIR is an effective and realistic approach to quantum image representation on the NISQ-era quantum devices.
Abstract In image processing, the amount of data to be processed grows rapidly, in particular when dealing with images of more than two dimensions or time series of images. Thus, efficient processing is a challenge, as data sizes may push even supercomputers to their limits. Quantum image processing promises to encode images with logarithmically less qubits than classical pixels in the image. In theory, this is a huge progress, but so far not many experiments have been conducted in practice, in particular on real backends. Often, the precise conversion of classical data to quantum states, the exact implementation, and the interpretation of the measurements in the classical context are challenging. We investigate these practical questions in this paper. In particular, we study the feasibility of the flexible representation of quantum images (FRQI). Furthermore, we check experimentally the limit in the current noisy intermediate-scale quantum era, i.e., up to which image size an image can be encoded, both on simulators and on real backends. Finally, we propose a method for simplifying the circuits needed for the FRQI. With our alteration, the number of gates can be reduced, especially the one of the error-prone controlled-NOT gates. As a consequence, the size of manageable images increases.