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A benchmark dataset for quantum noise effects in amplitude-encoded images

Ola Al-Ta’ani

Published Oct 16, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.21203/rs.3.rs-11381515/v1

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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.
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.
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.
Near-term quantum machine learning (QML) models operate in environments wherein noise is unavoidable, arising from both imperfect classical data acquisition and the limitations of noisy intermediate-scale quantum (NISQ) hardware. Although most existing studies have focused primarily on quantum circuit noise in isolation, the combined influence of corrupted classical inputs and quantum hardware noise has received comparatively little attention. In this work, we present a systematic experimental study of the robustness of a variational quantum classifier under realistic multi-level noise conditions. Using the Titanic dataset as a benchmark, a range of dataset-level noise models-including speckle noise, impulse noise, quantization noise, and feature dropout are applied to classical features prior to quantum encoding using a ZZ feature map. In parallel, hardware-inspired quantum noise channels such as depolarizing noise, amplitude damping, phase damping, Pauli errors, and readout errors are incorporated at the circuit level using the Qiskit Aer simulator. The experimental results indicate that noise in classical input data can significantly intensify the effects of quantum decoherence, resulting in less stable training and noticeably lower classification accuracy. Together, these observations emphasize the importance of designing and evaluating quantum machine learning pipelines with noise in mind, and highlight the need to consider classical and quantum noise simultaneously when assessing QML performance in the NISQ era
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 (QIP) is a field that aims to utilize the benefits of quantum computing for manipulating and analyzing images. However, QIP faces two challenges: the limitation of qubits and the presence of noise in a quantum machine. In this research we propose a novel approach to address the issue of noise in QIP. By training and employing a machine learning model that identifies and corrects the noise in quantum processed images, we can compensate for the noisiness caused by the machine and retrieve a processing result similar to that performed by a classical computer with higher efficiency. The model is trained by learning a dataset consisting of both existing processed images and quantum processed images from open access datasets. This model will be capable of providing us with the confidence level for each pixel and its potential original value. To assess the model's accuracy in compensating for loss and decoherence in QIP, we evaluate it using three metrics: Peak Signal to Noise Ratio (PSNR), Structural Similarity Index (SSIM), and Mean Opinion Score (MOS). Additionally, we discuss the applicability of our model across domains well as its cost effectiveness compared to alternative methods.