[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84383-en":3,"doc-seo-84383-105":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":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},84383,13056703020460,"Valentina","https://ap-avatar.wpscdn.com/avatar/be000253dac470eee5d?_k=1778207105932848923",8,"Research & Report","An Effective Quantum Hoare Logic for Hybrid Quantum Programs with Unbounded Loops","Hybrid quantum-classical programs with complex control structures, including unbounded loops, create new obstacles for analyzing quantum software under limited hardware resources. Existing quantum Hoare logics typically lack both expressiveness for such hybridization and efficient equational reasoning needed for semi-automated tooling. This work presents the first semi-automated static analysis combining effective functional verification with resource estimation (termination or cost) for hybrid quantum programs with unbounded loops. Integer hybrid path-sums extend path-sums to while loops, using loop invariants to derive termination and expected resource consumption, implemented in Haskell.","arXiv :2607 .08548v1 [ quant-ph] 9 Jul 2026  \nAn Effective Quantum Hoare Logic for Hybrid Quantum Programs with Unbounded Loops  \nJAD ISSA, CEA LIST/LSL, Qbricks Team, France and Université de Lorraine, CNRS, Inria, LORIA, MOCQUA team, France  \nCHRISTOPHE CHARETON, CEA LIST/LSL, Qbricks Team, France  \nROMAIN PÉCHOUX, Université de Lorraine, CNRS, Inria, LORIA, MOCQUA team, France  \nWhile quantum hardware remains limited, hybrid quantum-classical algorithms with complex control structures, including unbounded loops, are emerging, posing new challenges for quantum program analysis, including the accurate estimation of the resource consumption of a given program. Meanwhile, precise analysis techniques such as symbolic execution have largely left out hybridization and unbounded recursion. On the other hand, current quantum Hoare logics that generally support them are lacking in expressiveness and miss out on efficient computational equational reasoning that could be implemented in a semi-automated tool. This leaves a gap awaiting to be filled. In this work, we answer this challenge with the first semi-automated static analysis solution combining effective functional verification and resource (termination or cost) estimation for hybrid quantum programs with unbounded loops. Towards that end, we introduce integer hybrid path-sums (IHPS), extending path-sums to handle unbounded while loops, as a representation of possible executions of a program. A generic strategy for determining termination and expected resource consumption via loop invariants is also proposed and illustrated on several examples. Finally, the solution is implemented as a semi-automatic Haskell program. This work is the first step toward the design of a complete static resource analysis tool for hybrid quantum programs, essential for the development of real-world quantum computing.  \n1 Introduction  \n1.1 Context and Motivations  \nIn the quest for higher computational power, quantum computing has been under research since its introduction by Feynman and Benioff in the early 1980s [13] . For much ofits history, research in quantum computing has focused on proving the advantage of quantum computers over classical computers, be it theoretically (e.g., Shor’s algorithm for factoring in polynomial time [49]) or experimentally (e.g., the demonstration of the so-called quantum advantage by Google in 2024 [32]) .  \nHowever, a major challenge for integrated and scalable quantum computing is the integration of purely quantum (also called unitary) sequences of computation in a wider environment that includes classical operations and classical control structures [25, 54] . As such, today’s quantum applications often require hybrid programming languages offering hybrid unbounded recursion asa core component of the computation. This requirement is, for instance, notably observed in all variants of repeat-until-success (RUS), where a given block of unitary computations is run until an identifiable success condition is met. Such patterns appear, for instance, in the post-selection [63] model of computation, where a computation is simply discarded if the measurement does not result in a desired outcome, as well as in the synthesis of unitaries [15, 39, 47] . RUS has also been used to apply eventually deterministic 2-qubit gates in linear optical quantum computing [31, 38, 39], and it often appears in error correction, for, e.g., the fault-tolerant preparation of logical states by repeatedly preparing a faulty state and measuring whether it is correct [55] . Finally, most quantum algorithms (including Grover, Phase Estimation, Shor, etc.) do not succeed with probability 1 in a single run and tend to benefit from being repeated until success.  \nAuthors’ Contact Information: Jad Issa, [jad.issa@{cea.fr](jad.issa@{cea.fr), [univ-lorraine.fr}](univ-lorraine.fr}), CEA LIST/LSL, Qbricks Team, Nancy, France and  \nUniversité de Lorraine, CNRS, Inria, LORIA, MOCQUA team, Paris, France; Christo","cbCaimhZ50rrvyMk","https://ap.wps.com/l/cbCaimhZ50rrvyMk","pdf",927046,3,1,46,"English","en",105,"# Introduction\n## Context and Motivations\n# Verification Needs for Hybrid Programs","[{\"question\":\"What problem does the document address for hybrid quantum programs with unbounded loops?\",\"answer\":\"It addresses the lack of accurate static methods to verify functional correctness and estimate resources such as termination or execution cost when quantum programs include unbounded loops and hybrid control.\"},{\"question\":\"What is integer hybrid path-sums (IHPS)?\",\"answer\":\"IHPS extends path-sums to represent possible program executions in the presence of unbounded while loops, enabling analysis of loop behavior in hybrid quantum programs.\"},{\"question\":\"How does the proposed approach determine termination and expected resource consumption?\",\"answer\":\"It uses loop invariants within a generic strategy to infer termination and expected resource consumption, and it demonstrates the method through multiple examples.\"}]",1784195213,116,{"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":86,"head_meta":88,"extra_data":90,"updated_unix":28},"an-effective-quantum-hoare-logic-for-hybrid-quantum-programs-with-unbounded-loops","",{"@graph":36,"@context":85},[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/an-effective-quantum-hoare-logic-for-hybrid-quantum-programs-with-unbounded-loops/84383/",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","2026-07-25","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the document address for hybrid quantum programs with unbounded loops?","Question",{"text":75,"@type":76},"It addresses the lack of accurate static methods to verify functional correctness and estimate resources such as termination or execution cost when quantum programs include unbounded loops and hybrid control.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is integer hybrid path-sums (IHPS)?",{"text":80,"@type":76},"IHPS extends path-sums to represent possible program executions in the presence of unbounded while loops, enabling analysis of loop behavior in hybrid quantum programs.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the proposed approach determine termination and expected resource consumption?",{"text":84,"@type":76},"It uses loop invariants within a generic strategy to infer termination and expected resource consumption, and it demonstrates the method through multiple 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