This paper presents a statistical framework for characterizing quantum noise effects in amplitude-encoded images through the analysis of noise-induced amplitude perturbations. Classical grayscale images are encoded as normalized quantum amplitude vectors and subjected to stochastic amplitude damping, phase damping, and depolarizing channels. The resulting perturbations are quantified and modeled using a bounded-domain distribution obtained via a nonlinear transformation of the Ola distribution. A single shape parameter is estimated via maximum-likelihood methods, providing a compact descriptor of perturbation concentration across images, noise channels, and noise levels. Experimental results reveal a consistent decreasing relationship between the estimated parameter and noise level, along with clear channel-dependent statistical signatures. Phase damping, despite producing negligible visual changes in reconstructed images, yields measurable perturbations that are accurately captured by the proposed model. Goodness-of-fit analysis based on Kullback–Leibler divergence, mean absolute error, and likelihood-based criteria demonstrates stable model performance across noise regimes, supported by bootstrap uncertainty analysis. The proposed approach provides a unified and statistically robust representation of quantum noise-induced perturbations in amplitude-encoded images, enabling systematic comparison of noise effects beyond visual inspection. This characterization supports noise-aware quantum image processing by offering a compact, channel-dependent statistical description that can inform algorithm design and evaluation under realistic noise conditions.
This paper presents a statistical framework for characterizing quantum noise effects in amplitude-encoded images through the analysis of noise-induced amplitude perturbations. Classical grayscale images are encoded as normalized quantum amplitude vectors and subjected to stochastic amplitude damping, phase damping, and depolarizing channels. The resulting perturbations are quantified and modeled using a bounded-domain distribution obtained via a nonlinear transformation of the Ola distribution. A single shape parameter is estimated via maximum-likelihood methods, providing a compact descriptor of perturbation concentration across images, noise channels, and noise levels. Experimental results reveal a consistent decreasing relationship between the estimated parameter and noise level, along with clear channel-dependent statistical signatures. Phase damping, despite producing negligible visual changes in reconstructed images, yields measurable perturbations that are accurately captured by the proposed model. Goodness-of-fit analysis based on Kullback–Leibler divergence, mean absolute error, and likelihood-based criteria demonstrates stable model performance across noise regimes, supported by bootstrap uncertainty analysis. The proposed approach provides a unified and statistically robust representation of quantum noise-induced perturbations in amplitude-encoded images, enabling systematic comparison of noise effects beyond visual inspection. This characterization supports noise-aware quantum image processing by offering a compact, channel-dependent statistical description that can inform algorithm design and evaluation under realistic noise conditions.
This paper presents a complexity-aware comparison of bounded-domain statistical models for normalized perturbations induced by quantum noise in amplitude-encoded images. Because these perturbations lie on the unit interval and often exhibit non-Gaussian behavior, bounded-domain modeling provides a natural framework for their statistical characterization. We compare six candidate distributions: the one-parameter Power and Topp–Leone models, the classical two-parameter Beta and Kumaraswamy models, and the two-parameter Modified Kumaraswamy (MK) and Reflected Modified Kumaraswamy (RMK) models. The comparison is conducted under a matched experimental design involving eight benchmark images, three standard completely positive trace-preserving noise channels, and four noise levels. Model performance is evaluated using complementary distributional, likelihood-based, information-criterion, and runtime-based criteria. The results reveal a clear complexity–accuracy trade-off. The one-parameter Power and Topp–Leone models are computationally simple but generally too restrictive to capture the observed perturbation behavior, especially when the empirical distributions broaden. Among the two-parameter models, RMK achieves the strongest overall distributional agreement under the primary Wasserstein distanceW1and the supporting Kullback–Leibler divergence and mean absolute error criteria. Beta remains a consistently competitive and computationally efficient alternative, while Kumaraswamy is useful in selected condition-level regimes. The comparison also shows that likelihood-based improvements do not always translate into stronger global distributional agreement underW1. Mixed-effects and pooled channel-level analyses further show that model performance is strongly channel dependent and varies with noise level. Overall, the findings support bounded-domain statistical modeling as a useful framework for characterizing quantum-noise-induced perturbations and show that additional shape adaptability can be beneficial, although its value depends on the noise channel, noise level, model family, and computational cost.
Abstract Quantum image processing methods that rely on amplitude encoding are sensitive to channel-induced noise, yet reusable benchmarks for evaluating these effects under controlled conditions remain limited. We present QN-AEI, a simulation-based benchmark constructed from 200 images in the BSDS500 training subset. Each image is resized to 64 × 64 pixels and normalized to a 4096-dimensional amplitude vector representing a 12-qubit quantum state, then subjected to three noise channels (amplitude damping, Pauli-Z dephasing, and depolarizing noise) at four levels, η ∈ {0.1, 0.3, 0.5, 0.7}, with 200 stochastic trajectory realizations per image–channel–noise condition. This yields 2,400 conditions, 480,000 noisy realizations, and 1,966,080,000 normalized perturbation samples in total. Each record pairs the clean image and amplitude vector with its noisy statevectors, raw and normalized perturbations, and condition-level metadata; the release also includes source-image provenance, a dataset manifest, validation outputs, summary statistics, documentation, and the MATLAB generation and validation code. QN-AEI supports reproducible benchmarking of quantum-noise characterization, denoising, uncertainty and reliability analysis, and bounded-domain perturbation modeling.
The fusion of quantum computing with image processing has significantly improved both computational efficiency and fidelity in amplitude-encoded image reconstruction. While prior investigations have delved into advancements in quantum-to-classical data decoding, there remains a dearth of research addressing hybrid quantum-classical architectures and strategies to enhance noise resilience in quantum image processing. This study evaluates the implementation of three quantum transforms: Quantum Fourier Transform (QFT), Quantum Wavelet Transform (QWT), and Quantum Principal Component Analysis (QPCA), focusing on their efficacy in reconstructing images subjected to Gaussian and salt-and-pepper noise. Reconstruction quality is quantified through metrics such as error rates, similarity indices, and uncertainty quantification metrics, supported by a sensitivity analysis to ascertain robustness under varying noise conditions. The results demonstrate that QWT consistently achieves the highest Structural Similarity Index Measure (SSIM), while QFT often yields negative histogram similarity values, indicating significant alterations in color distribution. For instance, when analyzing one image, QWT exhibited a moderate decrease in Peak Signal-to-Noise Ratio (PSNR) from 37.83 to 37.71 with noise introduced, whereas QFT's PSNR experienced a more pronounced decline from 38.70 to 38.48. The study elucidates an inverse relationship between Mean Squared Error (MSE) and PSNR, underscoring the adverse effects of noise on image quality. Notably, QPCA was observed to produce the lowest Euclidean distance, signifying a strong retention of image integrity. These findings underscore the importance of judiciously selecting quantum methodologies tailored to specific application requirements, particularly in critical domains such as medical imaging, where precision and accuracy are paramount.
Quantum Image Processing is based on principles of quantum computing to represent visual information effectively, preparation of a quantum state plays a crucial rule in circuit performance. In Noisy Intermediate-Scale Quantum (NISQ) era, quantum noise and decoherence predominantly affect the fidelity of image-encoded quantum states. This paper deals with a comparative analysis of Four quantum image encoding schemes namely, Flexible Representation of Quantum Images (FRQI), Quantum Probability Image Encoding (QPIE), Order-Encoded Quantum Image Model (OQIM), and Enhanced Flexible Representation of Quantum Images (EFRQI). Noise free and Noisy state preparation simulations are executed using gate-based quantum simulators in the Pennylane environment, incorporating Bit Flip (BF), Phase Flip (PF), Amplitude Damping (AD), Phase Damping (PD), and Depolarizing noise (DN) channels. Image related performance metrics such as, Mean Squared Error (MSE), Peak Signal-to-Noise Ratio (PSNR) in dB, Structural Similarity Index Measure (SSIM), and Intersection over Union (IoU) are used to measure the performance of image encoded quantum states. Our results reveal that distinct noise robustness characteristics’ across various encoding methods reveals the importance of Noise aware encoding selection for NISQ era quantum image processing applications.
Quantum Image Processing is based on principles of quantum computing to represent visual information effectively, preparation of a quantum state plays a crucial rule in circuit performance. In Noisy Intermediate-Scale Quantum (NISQ) era, quantum noise and decoherence predominantly affect the fidelity of image-encoded quantum states. This paper deals with a comparative analysis of Four quantum image encoding schemes namely, Flexible Representation of Quantum Images (FRQI), Quantum Probability Image Encoding (QPIE), Order-Encoded Quantum Image Model (OQIM), and Enhanced Flexible Representation of Quantum Images (EFRQI). Noise free and Noisy state preparation simulations are executed using gate-based quantum simulators in the Pennylane environment, incorporating Bit Flip (BF), Phase Flip (PF), Amplitude Damping (AD), Phase Damping (PD), and Depolarizing noise (DN) channels. Image related performance metrics such as, Mean Squared Error (MSE), Peak Signal-to-Noise Ratio (PSNR) in dB, Structural Similarity Index Measure (SSIM), and Intersection over Union (IoU) are used to measure the performance of image encoded quantum states. Our results reveal that distinct noise robustness characteristics’ across various encoding methods reveals the importance of Noise aware encoding selection for NISQ era quantum image processing applications.
Quantum Amplitude Estimation (QAE) is a fundamental component of many quantum computing algorithms and applications. The practical implementation of QAE workflows on current Noisy Intermediate-Scale Quantum (NISQ) platforms requires accurate probability amplitude representation and reliable measurement recovery. Understanding the behavior of individual computational stages is therefore essential for improving the overall performance of practical quantum estimation procedures. This study presents a component-wise validation of the amplitude encoding process within a controlled quantum simulation environment. The experimental implementation was developed using the Qiskit framework, where classical probability values were encoded into single-qubit quantum states through parameterized rotation operations and subsequently recovered from measurement statistics. A systematic evaluation was performed across the probability interval from 0.1 to 0.9 using 8192 measurement shots for each experiment. The experimental results demonstrate that the recovered measurement probabilities closely match the corresponding target values throughout the investigated domain. Statistical evaluation produced a Mean Absolute Error (MAE) of 0.003521, a Mean Squared Error (MSE) of 1.67 × 10⁻⁵, and a Root Mean Squared Error (RMSE) of 0.004087, indicating high numerical consistency under ideal simulation conditions. The findings suggest that the amplitude encoding stage accurately represents classical probability values and provides a reliable baseline for studying more advanced quantum estimation workflows. The component-wise validation methodology adopted in this work offers a practical framework for investigating individual stages of quantum algorithms and supports future research on hybrid quantum-classical processing strategies for NISQ-era quantum computing.