[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120510-en":3,"doc-seo-120510-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},120510,1374391974564,"Clementine","https://ap-avatar.wpscdn.com/avatar/14000253aa45c000a9e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779874745381141002",6,"Technology","VeriQR - A Robustness Verification Tool for Quantum Machine Learning Models","Adversarial noise attacks threaten quantum machine learning (QML) models, especially in the NISQ era where noise is unavoidable, making robustness a prerequisite for safe deployment. VeriQR is presented as a first tool for formal verification and robustness improvement of QML models. It models real hardware noise by injecting random noise, provides sound-and-complete local and global verification, and supports efficient under-approximate and tensor-network-based algorithms. It can detect adversarial examples, support adversarial training, and allows customized noise via a graphical interface.","VeriQR: A Robustness Verification Tool for Quantum Machine Learning Models  \nYanling Lin 1 ,2 , Ji Guan2 (B) ⋆ , Wang Fang2 , Mingsheng Ying3 ,  \nZhaofeng Su 1 (B) ⋆⋆   \narXiv :2407 . 13533v1 [ quant-ph] 18 Jul 2024  \n1  \n2  \nUniversity of Science and Technology of China, Hefei 230026, China Key Laboratory of System Software (Chinese Academy of Sciences) and State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing 100190, China  \n3 Centre for Quantum Software and Information, University  \nof Technology Sydney, NSW 2007, Australia  \nAbstract. Adversarial noise attacks present a significant threat to quantum machine learning (QML) models, similar to their classical counterparts. This is especially true in the current Noisy Intermediate-Scale Quantum era, where noise is unavoidable. Therefore, it is essential to ensure the robustness of QML models before their deployment. To address this challenge, we introduce VeriQR, the first tool designed specifically for formally verifying and improving the robustness of QML models, to the best of our knowledge. This tool mimics real-world quantum hardware’s noisy impacts by incorporating random noise to formally validate a QML model’s robustness. VeriQR supports exact (sound and complete) algorithms for both local and global robustness verification. For enhanced efficiency, it implements an under-approximate (complete) algorithm and a tensor network-based algorithm to verify local and global robustness, respectively. As a formal verification tool, VeriQR can detect adversarial examples and utilize them for further analysis and to enhance the local robustness through adversarial training, as demonstrated by experiments on real-world quantum machine learning models. Moreover, it permits users to incorporate customized noise. Based on this feature, we assess VeriQR using various real-world examples, and experimental outcomes confirm that the addition of specific quantum noise can enhance the global robustness of QML models. These processes are made accessible through a user-friendly graphical interface provided by VeriQR, catering to general users without requiring a deep understanding of the counter-intuitive probabilistic nature of quantum computing.  \nThe source code of VeriQR is available at [https://github.com/Veri-Q/](https://github.com/Veri-Q/)[ ](https://github.com/Veri-Q/)VeriQR, while the artifact for reproducing the experiments of this paper is available at [29] .  \nKeywords: Robustness Verification · Quantum Machine Learning · Formal Verification ·Quantum Classifiers · Quantum Noise  \n⋆  \n⋆⋆  \n[guanj@ios.ac.cn](guanj@ios.ac.cn)[ ](guanj@ios.ac.cn)[zfsu@ustc.edu.cn](zfsu@ustc.edu.cn)  \n1 Introduction  \nOver the last decade, machine learning (ML) has driven technological advancements in various fields. The combination of machine learning with quantum computing has given rise to a new field of research known as quantum machine learning (QML) . In classical ML, classification models are vulnerable in adversarial scenarios [8,5] . Specifically, the addition of intentionally crafted noises to the original data can cause classifiers to make incorrect predictions with high confidence. An illustrative example is the misclassification of a panda image asa gibbon with a confidence level exceeding 99% after adding imperceptible noise [37] . Although studies have shown the potential superiority of quantum computers over classical counterparts in certain well-known ML tasks [4], the presence of noise in quantum computation is inevitable due to the limitations of quantum hardware devices in the current Noisy Intermediate-Scale Quantum (NISQ) era [34], which may cause quantum learning systems to suffer from adversarial perturbations from environmental noises. Research on the vulnerability of QML models has garnered widespread attention [31, 15 ,30 ,41 ,23 , 19 ,20] . In particular, formal methods have been employed to verify the robustness of QML models","cbCaiqEREKWoCqw9","https://ap.wps.com/l/cbCaiqEREKWoCqw9","pdf",1648318,1,18,"English","en",105,"# Introduction\n## Background: adversarial noise in QML\n## Related work: classical robustness tools\n## Related work: formal methods for quantum systems\n## Contributions: VeriQR","[{\"question\":\"What problem does VeriQR target in quantum machine learning?\",\"answer\":\"VeriQR targets the formal verification of robustness for QML models under adversarial noise, which can lead to incorrect high-confidence predictions.\"},{\"question\":\"How does VeriQR model the noise effects of real quantum hardware?\",\"answer\":\"It mimics noisy impacts from real-world quantum hardware by incorporating random noise during verification.\"},{\"question\":\"What verification strategies and algorithms does VeriQR provide?\",\"answer\":\"VeriQR offers sound and complete algorithms for both local and global robustness, using an under-approximate (complete) approach for enhanced efficiency and a tensor network-based method for global verification.\"}]","VeriQR - A Robustness Verification Tool for Quantum Machine Learning Models | PDF",1785730426,45,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"veriqr-a-robustness-verification-tool-for-quantum-machine-learning-models","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/technology/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/veriqr-a-robustness-verification-tool-for-quantum-machine-learning-models/120510/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does VeriQR target in quantum machine learning?","Question",{"text":75,"@type":76},"VeriQR targets the formal verification of robustness for QML models under adversarial noise, which can lead to incorrect high-confidence predictions.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does VeriQR model the noise effects of real quantum hardware?",{"text":80,"@type":76},"It mimics noisy impacts from real-world quantum hardware by incorporating random noise during verification.",{"name":82,"@type":73,"acceptedAnswer":83},"What verification strategies and algorithms does VeriQR provide?",{"text":84,"@type":76},"VeriQR offers sound and complete algorithms for both local and global robustness, using an under-approximate (complete) approach for enhanced efficiency and a tensor network-based method for global verification.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,113,118,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":111,"slug":112},50,"technology",{"id":114,"doc_module":4,"doc_module_name":46,"category_name":115,"show_sort_weight":116,"slug":117},7,"Healthcare",40,"healthcare",{"id":119,"doc_module":4,"doc_module_name":46,"category_name":120,"show_sort_weight":121,"slug":122},8,"Research & Report",30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]