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.
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.
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.
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.
Quantum machine learning (QML) has generated significant excitement as a potential game-changer in artificial intelligence. At the heart of any QML model lies a fundamental challenge: how do we translate classical data into the language of quantum mechanics? This encoding process is crucial because the way we represent information in a quantum system can make or break model performance. While researchers have proposed several encoding strategies over the years, most studies focus on idealized conditions, leaving a significant gap in our understanding of how these methods actually behave under the noisy, imperfect conditions of real quantum hardware. In this work, we address this gap through a systematic, simulation-based comparison of three widely used encoding strategies—Angle Encoding, Amplitude Encoding, and the entangling ZZFeatureMap—within a variational quantum classification framework. We evaluate these approaches on standard benchmark datasets under both noiseless and noisy conditions that mimic real quantum devices. To ensure our findings are statistically reliable, each noisy experiment is repeated across 10 independent runs, with results reported using mean accuracy, standard deviation, and 95% confidence intervals. Our results reveal a nuanced but sobering story. While the entangling ZZFeatureMap outperforms simpler methods in ideal noise-free settings, these advantages largely vanish under realistic depolarizing noise. When statistically averaged, all encoding strategies converge to near-random classification accuracy under moderate noise levels. These findings highlight the fragility of quantum advantages on today's noisy intermediate-scale quantum (NISQ) hardware and emphasize the critical need for noise-aware, statistically grounded evaluation protocols when assessing the practical viability of QML models.
Abstract The characterization of quantum noise is fundamental to quantum information processing, quantum control and reliable operation of near-term quantum devices. Conventional descriptions of quantum noise are based on completely positive trace-preserving (CPTP) maps acting on density operators. These models describe effective quantum dynamics after the underlying physical interactions have been represented as a quantum channel. However, in practical cases, imperfections such as calibration errors, control-field fluctuations, finite-resolution waveform generation, and analog hardware noise can act upon the probability amplitudes of a quantum state earlier. The effect of such perturbation in quantum state after normalization has largely been unexplored. In this work, we develop a rigorous mathematical analysis of the normalized additive amplitude noise in a finite-dimensional quantum system. Assuming a zero-mean complex perturbation, we derive a second-order closed form expression for the ensemble-averaged density operator. The analysis leads to state-dependent evolution of the quantum state which cannot be represented by a CPTP map. We further prove that in case of isotropic noise, the ensemble-averaged density operator becomes an effective depolarizing channel. For anisotropic perturbations, we derive the orientation-dependent Bloch-vector contraction which is determined by the covariance geometry of the additive noise. Closed-form expressions are further obtained for measurement probabilities, state fidelity, and ensemble purity, showing that fidelity degradation depends only on the component of the perturbation covariance orthogonal to the input state. Monte Carlo simulations closely match the theoretical analysis, especially for small noise regime. The proposed model establishes a connection between classical additive-noise models and effective quantum dynamics generated by normalized state-space perturbations.
This study presents a noise-aware evaluation framework for hybrid quantum–classical machine learning models applied to medical binary classification. Using three healthcare datasets—Pima Indians Diabetes, Heart Disease, and Breast Cancer Wisconsin—the performance of a Variational Quantum Classifier (VQC) was analyzed under multiple depolarizing noise levels (0.00–0.10). Classical baselines, Logistic Regression (LR) and Support Vector Machine (SVM), were implemented for comparison. The research investigates the impact of noise on predictive accuracy, F1-score, and training time, highlighting the computational overhead of hybrid quantum–classical models. Zero Noise Extrapolation (ZNE), using linear and Richardson methods, was applied to mitigate noise effects, revealing that while ZNE improves performance under certain conditions, extrapolation instability can occur. Transpiler optimization also contributed to improved VQC stability by reducing circuit complexity. Results show that classical models consistently outperformed the VQC in accuracy, stability, and training efficiency. VQC exhibited fluctuating performance under noise, requiring significantly higher training time, and increasing SPSA iterations did not always yield stable accuracy improvements. These findings underscore the challenges of noise robustness, optimization instability, and computational cost in the NISQ era, and suggest directions for future work, including alternative optimizers, adaptive ansatz design, advanced error mitigation, and real hardware benchmarking. This research provides a systematic benchmarking framework for evaluating training time versus noise-level trade-offs, contributing to the development of more reliable quantum machine learning models for medical applications. Keywords: Quantum Machine Learning, Variational Quantum Classifier, Depolarizing Noise, Zero Noise Extrapolation, Medical Classification, Hybrid Quantum–Classical Models, Training Time Analysis
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.