[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82989-en":3,"doc-seo-82989-105":30,"detail-sidebar-cat-0-en-105":83},{"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":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},82989,7971461740886,"Theodore","https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2",8,"Research & Report","Low Overhead Error Corrected QCNNs Using Bivariate Bicycle Codes","Quantum convolutional neural networks (QCNNs) merge quantum computing and classical CNNs to accelerate classification, but today’s noisy quantum hardware prevents practical execution. Noise remains too large, and while surface-code fault tolerance achieves error rates below a threshold, its qubit cost is prohibitive. Bivariate bicycle (BB) codes offer a high error threshold, constant encoding rate, and linear code distance. Simulations with realistic noise show a 4-qubit unprotected QCNN fails to converge and learns more slowly. A distance-4 BB QEC method is proposed to improve convergence and move toward practical QCNNs.","Low-Overhead Error-Corrected QCNNs Using  \nBivariate Bicycle Codes  \nAlejandro Rosales and Animesh Yadav  \nSchool of Electrical Engineering and Computer Science  \nOhio University, Athens, OH, USA  \n{ar993823, [yadava](yadava}@ohio.edu)[}](yadava}@ohio.edu)[@ohio.edu](yadava}@ohio.edu)  \narXiv :2607 .05724v 1 [ cs .LG] 7 Jul 2026  \nAbstract—Quantum convolutional neural networks (QCNNs) combine the power of quantum computing and classical CNN for computational speedup in classification tasks. However, noise levels on state-of-the-art quantum devices remain too high for practical QCNN execution. In addition, despite the reliable surface code providing a method for error rates below a threshold value, they have a prohibitively large qubit cost. Recently introduced bivariate bicycle (BB) codes are of particular interest for their high error threshold, constant encoding rate, and linear code distance. Through simulation with realistic hardware noise sources, we demonstrate that a 4-qubit unprotected QCNN fails to converge and exhibits a worse learning rate compared to numerical simulations. Addressing both limitations, we propose a distance-4 BB quantum error-correction (QEC) technique for QCNNs. In doing so, we validate that our low-overhead QEC technique for QCNNS represents a step toward practical QCNNs.  \nIndex Terms—Quantum Convolutional Neural Networks, Bivariate Bicycle Codes, Quantum Error Correction, NISQ  \nI. INTRODUCTION  \nAdvancements in machine learning (ML) have made it a crucial technology across various domains, from signal processing to healthcare, with applications such as speech recognition, computer vision, and drug discovery. However, ML procedures suffer from gradient vanishing in high-dimensional parameter spaces [1], [2] and quadratic sample sizes and training time for certain tasks [3] . On the other hand, quantum computing (QC) shows exponential computational speedups [4]–[6] . The combination of these two technologies, termed quantum machine learning (QML), promises processing of data in exponentially large feature spaces [7], [8] by leveraging quantum effects like superposition and entanglement, and more efficient navigation of high-dimensional optimization landscapes via quantum-enhanced optimization [9] . Although QML holds significant promise, the limited qubit counts of current noisy intermediate-scale quantum (NISQ) devices pose substantial challenges. Furthermore, these devices suffer from high physical error rates introduced by noise sources including stray electromagnetic fields, cosmic rays, and thermal and temporal decoherence of quantum states [10] .  \nQuantum error correction (QEC) is a method for protecting fragile quantum information while controlling qubits to induce a desired computation. For over two decades, the topological toric code has served as the canonical model for topological quantum error correction. [11] . The code encodes two logical qubits into a d × d lattice of physical qubits, with the total  \nqubit count scaling as n = 2d2 , where d is the code distance. With minimum distance d, the code can correct up to 􀀄 ~~d ~~−2~~1~~ 􀀅 arbitrary single-qubit errors. The toric code thus provides reliable protection of quantum information, however it suffers from inefficient encoding rates that makes scaling to hundreds of logical qubits prohibitively resource-intensive. Recent advances in quantum Low-Density Parity-Check (qLDPC), most notably the bivariate bicycle (BB) code [12], have emerged as a promising alternative. The constant encoding rate of BB codes enables fault-tolerant quantum memory with constant space overhead [12], [13], making them an attractive candidate for scalable architectures. However, a key open problem remains for the BB code is that it has yet to support faulttolerant computation, particularly for deep-circuit algorithmsand poses an obstacle to real-world QML use cases.  \nTo this end, we introduce a constant-overhead QEC protocol that integrates with QML, parti","cbCailvGGhiff2IP","https://ap.wps.com/l/cbCailvGGhiff2IP","pdf",669979,3,1,10,"English","en",105,"# Introduction\n## Related Work","[{\"question\":\"What problem is observed for an unprotected 4-qubit QCNN?\",\"answer\":\"With realistic hardware noise sources, a 4-qubit unprotected QCNN fails to converge and exhibits a worse learning rate than numerical simulations.\"}]",1784184486,25,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":78,"head_meta":80,"extra_data":82,"updated_unix":28},"low-overhead-error-corrected-qcnns-using-bivariate-bicycle-codes","",{"@graph":36,"@context":77},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"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":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/low-overhead-error-corrected-qcnns-using-bivariate-bicycle-codes/82989/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-24","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71],{"name":72,"@type":73,"acceptedAnswer":74},"What problem is observed for an unprotected 4-qubit QCNN?","Question",{"text":75,"@type":76},"With realistic hardware noise sources, a 4-qubit unprotected QCNN fails to converge and exhibits a worse learning rate than numerical simulations.","Answer","https://schema.org",{"og:url":51,"og:type":79,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":81,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":84},[85,89,93,97,102,107,112,115,120,123,126],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":86,"show_sort_weight":87,"slug":88},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":90,"show_sort_weight":91,"slug":92},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Exam",70,"exam",{"id":98,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},5,"Comic",60,"comic",{"id":103,"doc_module":4,"doc_module_name":46,"category_name":104,"show_sort_weight":105,"slug":106},6,"Technology",50,"technology",{"id":108,"doc_module":4,"doc_module_name":46,"category_name":109,"show_sort_weight":110,"slug":111},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":113,"slug":114},30,"research-report",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":46,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":22,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":22,"slug":125},"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":98,"slug":129},19,"General","general"]