[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86293-en":3,"doc-seo-86293-105":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},86293,13056703020460,"Valentina","https://ap-avatar.wpscdn.com/avatar/be000253dac470eee5d?_k=1778207105932848923",8,"Research & Report","The Time-Space Complexity of Checking Multiple Assertions in Quantum Programs","Runtime assertions enable testing and debugging of quantum programs, but evaluating multiple assertions in a terminal-measurement setting can require extra ancilla space or repeated executions. The naive “learn all outcomes” approach yields a time–space trade-off with linear resource use. The work shows that asymptotically better strategies exist: learning whether any assertion fails, or identifying the first failing assertion, needs only logarithmic complexity. It formalizes the problem and derives lower and upper bounds.","arXiv :2607 . 1 1665v 1 [ cs .PL] 13 Jul 2026  \nThe Time–Space Complexity of Checking Multiple Assertions in Quantum Programs  \nSHENGYUAN YANG and CHARLES YUAN, University of Wisconsin–Madison, USA  \nRuntime assertions are a promising mechanism for testing and debugging quantum programs. But unlike the classical world, checking a quantum program that contains multiple assertions often requires using additional space or running the program additional times. For example, on current quantum hardware where mid-circuit measurement is restricted or costly, an assertion’s pass/fail outcome cannot be revealed immediately. Instead, it is routed into an ancilla qubit during execution and read out by a terminal measurement. For a program with 􀀽 assertions, a naive strategy uses 􀀽 ancillas to learn all 􀀽 outcomes, while an alternative uses one ancilla but repeats program execution over 􀀽 rounds, checking one assertion per round. Both satisfy 􀀨 · 􀀩 = 􀀤 (􀀽) , where 􀀨 is the number of ancillas and 􀀩 the number of executions: a fundamental time–space trade-off.  \nCan one do asymptotically better? We reveal that the answer depends sharply on the information to be learned. Reporting the outcomes of all assertions requires linear complexity, but two partial-information tasks of detecting whether any assertion fails, and of identifying the first failing assertion, require only logarithmic complexity—an asymptotic improvement. Moreover, the checking strategies for these tasks can trade time for space in useful ways. In this work, we formalize the complexity of checking multiple assertions in a quantum program. Using this definition, we establish its landscape of asymptotic lower bounds and constructive upper bounds. We confirm via a case study on Grover’s algorithm that the resource costs of constructed strategies match theoretical predictions, illustrating the practical design space for quantum programmers.  \n1 Introduction  \nQuantum computation offers the promise of asymptotic advantages for problems such as factoring, search, and simulation by manipulating qubits – or quantum bits – whose state is a superposition of zero and one. Recent hardware advances [9, 27] have made increasingly realistic the prospect of running complex quantum programs needed by practical applications. A barrier to the development of complex quantum programs, however, is that they are difficult to test and debug: inspecting an intermediate state of a quantum computation requires performing a measurement, a physical operation that in general can perturb the program’s state and thereby corrupt its output.  \nTo address this challenge, researchers have proposed quantum runtime assertions, schemes to instrument the execution of a quantum program using measurements but minimize any effect on the output. A growing body of work has studied the formal expressiveness of assertion predicates [32, 37, 39], circuit constructions that check individual predicates [37–39], tailoring of predicates to program structure [45], and optimization of checks on hardware [46] . But an essential question remains less explored: how, and how efficiently, can we check multiple assertions in a program?  \nMultiple Assertion Checking. To check a classical program with many assertions, one evaluates each on the instantaneous program state, reads out the pass/fail outcome immediately at negligible cost, and aborts upon failure. But in a quantum program, reading out an assertion outcome requires measurement. Performing it immediately would mean measuring mid-circuit before the program terminates — incurring significant latency, noise, and reset time in hardware [16, 21, 25, 29] .  \nPrior work makes disparate assumptions on this issue. Proq [37] assumes mid-circuit measurement is broadly available, and uses projective measurements at runtime to abort at the earliest failure. Other proposals for quantum assertions [32, 38, 39, 46] target a terminal-measurement model that performs measurement only at the end ","cbCaitKe3MowPiwj","https://ap.wps.com/l/cbCaitKe3MowPiwj","pdf",715704,2,1,36,"English","en",105,"# Introduction\n# Multiple Assertion Checking\n## Running Example","[{\"question\":\"How are the proposed strategies validated in practice?\",\"answer\":\"A case study on Grover’s algorithm compares the constructed strategies’ resource costs against theoretical predictions, demonstrating a practical design space for quantum programmers.\"}]",1784210147,91,{"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},"the-time-space-complexity-of-checking-multiple-assertions-in-quantum-programs","",{"@graph":36,"@context":77},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/the-time-space-complexity-of-checking-multiple-assertions-in-quantum-programs/86293/",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],{"name":72,"@type":73,"acceptedAnswer":74},"How are the proposed strategies validated in practice?","Question",{"text":75,"@type":76},"A case study on Grover’s algorithm compares the constructed strategies’ resource costs against theoretical predictions, demonstrating a practical design space for quantum programmers.","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},[85,89,93,97,102,107,112,115,120,123,127],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":86,"show_sort_weight":87,"slug":88},"Story & Novel",90,"story-novel",{"id":20,"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":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":98,"slug":130},19,"General","general"]