# Hybrid Quantum Neural Network Image Anti-Noise Classification Model Combined with Error Mitigation
## 1 Introduction  
In recent decades, machine learning has rapidly emerged as a foundational technology in the era of big data. Rooted in artificial intelligence and statistics, machine learning explores learning strategies and uncovers latent structures from the available data, enabling predictions and analyses through the derived models [1]. Its applications cover data mining and facial recognition, natural language processing, and identifying biomedical features, such as community detection on social networks [2], affecting all aspects of social life [2; 3; 4]. Quantum machine learning (QML) is an exceptionally promising interdisciplinary research direction, aiming to harness the capabilities of quantum computing alongside machine learning to overcome classical computing limitations. Numerous quantum algorithms have been proposed to enhance various machine learning tasks [5; 6; 7]. Image processing, a pivotal domain within digital image processing, encompasses all aspects of image acquisition, representation, processing, and analysis. With the widespread adoption of digital technology, image processing has found extensive applications, significantly impacting scientific research and playing a crucial role in fields such as medicine, engineering, and entertainment [8; 9; 10; 11]. Image classification, a focal point in computer vision, has been a significant research target, employing techniques such as support vector machines and convolutional neural networks [12; 13]. [PERSON] et al. [14] innovatively incorporated classicaldeep reinforcement learning algorithms, including experience replay and target networks, into variational quantum circuits with reduced weights. Additionally, a classification algorithm combining quantum computing with the decision tree algorithm [15; 16] exists. The latter proposes the quantum representation of a binary classification tree with binary characteristics based on a probability method [16]. With the rapid advancement of quantum machine learning, a pivotal question arises: can quantum machine learning technology be trusted for image classification tasks amidst adversarial noise interference? Label noise, particularly in scenarios like medical image datasets with high-level label noise, can profoundly influence classification outcomes [17]. In autopilot systems, image classification identifies roads, pedestrians, vehicles, etc. Noise introduces inaccuracies in driving decisions, escalating the risk of traffic accidents. Video surveillance relies on image classification for object detection and identification. Noise may lead to false positives or negatives, diminishing the reliability of the monitoring system and compromising the accurate identification of potential threats [18; 19]. Models are prone to overfitting noise labels, causing harm to representation learning and hindering generalization, thereby impacting diagnostic accuracy. Quantum error correction techniques demand substantial quantum bit resources, presenting implementation challenges [20; 21; 22; 23]. To address this, error mitigation strategies, such as the autoencoders proposed by [PERSON] et al. [24], have proven effective for error correction without the need for additional quantum bits. In a different domain, quantum neural networks (QNNs) represent a forefront research area that merges quantum computing with neural networks. Various implementations of quantum neural network models exist, with variational quantum circuits (VQCs) gaining significant attention [25; 26; 27]. In the era of noisy intermediate-scale quantum (NISQ), VQC offers practical feasibility as it can operate within the limitations of the currently available qubits. VQC design not only emphasizes the hardware implementation of quantum computing but also focuses on effective integration with classical computing to overcome the limitations of noise and errors in current quantum computing [28; 29; 30; 31]. Recent research on quantum neural networks includes the work by [PERSON] et al.