[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83372-en":3,"doc-seo-83372-105":29,"detail-sidebar-cat-0-en-105":90},{"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":11,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},83372,1099514068365,"Aurelia","https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?_k=1776742907772140068",8,"Research & Report","Parallel QEC Decoding Applied to Distributed Quantum Computing","A novel parallel decoding strategy targets quantum error correction (QEC) using Belief Propagation with Ordered Statistics Decoding (BP-OSD). It refines the likelihood ratio (LLR) error vectors produced by BP by performing singular value decomposition (SVD) locally on sub-regions of the lattice. The method is tailored for distributed quantum computers consisting of multiple QPUs linked for entangled-state sharing, and is assessed via complexity, decoding accuracy, and scalability metrics.","Parallel QEC Decoding Applied to Distributed Quantum Computing  \nGabriele Incardona 1 , Davide Ferrari1 , and Michele Amoretti1,*  \n1 Quantum Software Laboratory, Department of Engineering and Architecture, University of Parma, Parma, 43124 Italy  \n([https://www.qslab.unipr.it/](https://www.qslab.unipr.it/))  \n*  \nCorresponding author: Michele Amoretti, [michele.amoretti@unipr.it](michele.amoretti@unipr.it)  \narXiv :2607 .08386v1 [ quant-ph] 9 Jul 2026  \nAbstract  \nA novel parallel approach is proposed for QEC decoding based on Belief Propagation with Ordered Statistics Decoding. The main idea is topre-process the error vectors obtained from Belief Propagation by applying Singular Value Decomposition locally to sub-regions of the lattice. The proposed approach is applied to distributed quantum computers and evaluated in terms of complexity, accuracy, and scalability.  \nIndex terms—Quantum Error Correction, Parallel Decoding, Distributed Quantum Computing  \n1 Introduction  \nEnvironmental decoherence is the process by which quantum systems lose their quantum properties due to interactions with the environment. Quantum Error correction (QEC) utilizes the idea of expanding the Hilbert space beyond what is needed to store a single qubit of information [1, 2] . Logical qubits are formed by encoding quantum information across physical qubits. QEC is cyclically performed on the underlying physical qubits. Errors are detected without measuring the qubits directly; instead, entangled ancilla qubits are measured. Once detected, the errors are corrected.  \nSurface codes, which belong to the family of stabilizer codes, stand as the most promising candidates for building near-term error-corrected qubits because of their two-dimensional architectures, the requirement of only local operations, and high tolerance to quantum noise [3, 4] .  \nIn this work, a novel parallel approach is proposed for QEC decoding based on Belief Propagation with Ordered Statistics Decoding (BP-OSD) [5] . The main idea is to pre-process the error vectors (LLR) obtained from Belief Propagation, applying Singular Value Decomposition (SVD) locally to sub-regions of the lattice. The proposed approach is applied to distributed quantum computers, i.e., systems composed of multiple quantum processing units (QPUs) [6, 7] connected by quantum  \nlinks for sharing entangled states [8] .  \nThe paper is organized as follows. Section 2 introduces stabilizer codes in general and surface codes in particular. Section 3 discusses related works on parallel decoding techniques. Section 4 illustrates the proposed parallel approach to optimizing the BP-OSD decoder. Section 5 shows how to apply the optimized surface code to a distributed quantum computer. Section 6 presentsand discusses simulation results. Finally, Section 7 concludes the paper with an outline for future work.  \n2 Background  \nThe need for long coherence times is one of the most challenging issues that physicists and engineers face in their attempts to build quantum computers. In practice, because of quantum decoherence, qubits can be bit-flipped (|0⟩ ↔ |1⟩) and phase-flipped (|0⟩ ↔ |0⟩,|1⟩ ↔ −|1⟩), not experiencing full flips but rather angular shifts of the qubit state by an angle [9] .  \nCurrent major efforts to build a quantum computer are based on surface codes [10], operated as stabilizer codes [11] . In the following, the minimum background is provided to the reader.  \n2.1 Stabilizer Codes  \nAn [[n, k, d]] stabilizer code encodes k logical qubits into n physical qubits. It is defined by n−k independent stabilizer generators (denoted as checks) forming an abelian subgroup S of the n-fold Pauli Group Gn (i.e. , S ⊂ Gn) . S is denoted as the stabilizer set or stabilizer group. The parameter d is the distance of the code. It signifies the minimum number of physical qubit errors required to cause an undetectable logical error; the higher the number, the better. Formally, d is the minimum weight (number of non-identity P","cbCainPOdvLi4NmN","https://ap.wps.com/l/cbCainPOdvLi4NmN","pdf",650488,4,1,"English","en",105,"# Introduction\n## Background\n### Stabilizer Codes\n### Surface Codes\n# Parallel QEC Decoding Approach\n## Related Works\n# Distributed Quantum Computer Application\n## Simulation Results\n# Conclusion","[{\"question\":\"What is the core idea of the proposed parallel QEC decoder?\",\"answer\":\"The decoder uses BP-OSD and preprocesses the BP-derived error vectors (LLR) by applying SVD locally to sub-regions of the lattice, enabling a parallel decoding workflow.\"},{\"question\":\"Why are surface codes highlighted in the paper?\",\"answer\":\"Surface codes are presented as strong candidates for near-term error-corrected qubits due to their two-dimensional architecture, reliance on local operations, and high tolerance to quantum noise.\"},{\"question\":\"How does the approach relate to distributed quantum computing?\",\"answer\":\"The method is applied to distributed quantum computers made of multiple QPUs connected by quantum links to share entangled states, with evaluation focused on complexity, accuracy, and scalability.\"}]",1784187056,20,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"parallel-qec-decoding-applied-to-distributed-quantum-computing","",{"@graph":35,"@context":84},[36,52,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":20},"https://docshare.wps.com/document/parallel-qec-decoding-applied-to-distributed-quantum-computing/83372/",{"url":51,"name":13,"@type":53,"author":54,"headline":13,"publisher":56,"fileFormat":59,"inLanguage":23,"description":14,"dateModified":60,"datePublished":61,"encodingFormat":59,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":55},"Person",{"url":40,"name":57,"@type":58},"DocShare","Organization","application/pdf","2026-07-25","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":20},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What is the core idea of the proposed parallel QEC decoder?","Question",{"text":74,"@type":75},"The decoder uses BP-OSD and preprocesses the BP-derived error vectors (LLR) by applying SVD locally to sub-regions of the lattice, enabling a parallel decoding workflow.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"Why are surface codes highlighted in the paper?",{"text":79,"@type":75},"Surface codes are presented as strong candidates for near-term error-corrected qubits due to their two-dimensional architecture, reliance on local operations, and high tolerance to quantum noise.",{"name":81,"@type":72,"acceptedAnswer":82},"How does the approach relate to distributed quantum computing?",{"text":83,"@type":75},"The method is applied to distributed quantum computers made of multiple QPUs connected by quantum links to share entangled states, with evaluation focused on complexity, accuracy, and 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