[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83497-en":3,"doc-seo-83497-105":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},83497,687197100911,"Himbo","https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1782698725881665579",8,"Research & Report","Robust Quantum Memory Advantage from Contextuality","Quantum contextuality is recognized as a non-classical resource for quantum technology, but the mechanism yielding unconditional computational advantage remains difficult to pinpoint. This work proves an exponential, noise-resilient memory advantage for quantum finite automata via a graph-theoretic treatment of contextuality. A promise problem is defined on an exclusivity graph G: classical deterministic automata require N=χ(G) states, while a QFA achieves it with memory dimension d≤ξ(G)+1. For Boolean-orthogonality graphs, the separation scales exponentially and preserves an O(1) threshold under depolarizing and coherent noise.","Robust Quantum Memory Advantage from Contextuality  \nShiroman Prakash  \narXiv :2607 .00507v1 [ quant-ph] 1 Jul 2026  \nDepartment of Physics and Computer Science, Dayalbagh Educational Institute, Agra, India  \nAbstract  \nQuantum contextuality is widely recognized as an essential non-classical resource underlying quantum technology, yet illuminating the precise mechanisms through which it translates into unconditional computational advantages remains an ongoing challenge. We demonstrate an exponential, noise-resilient memory advantage for quantum finite automata arising from graph-theoretic approaches to contextuality. We define a promise problem on an exclusivity graph G for which any classical deterministic automaton acts as a non-contextual hidden variable model requiring at least N = χ (G) states, where χ(G) is the graph’s chromatic number. In contrast, by exploiting a structural phenomenon we term representational contextuality, a QFA solves this task using a memory of dimension at most d = ξ (G) + 1, where ξ (G) is the graph’s orthogonal rank. This separation scales exponentially (d = O (n) versus N = 2Ω(n)) for Boolean-orthogonality graphs. Crucially, this memory advantage maintains an O(1) threshold against both depolarizing and coherent noise.  \nContents  \n1 Introduction 2  \n2 Review of finite automata 3  \n3 Representational contextuality and exclusivity graphs 3  \n4 The Kochen-Specker problem 4  \n5 Exponential advantage 6  \n6 Noise robustness 8  \n7 Discussion and outlook 9  \nA Representational contextuality vs. statistical contextuality 14  \nB 60-vertex Kochen-Specker graph 14  \n1 Introduction  \nFinite automata serve as the foundational model for computation under memory constraints [1–3] . Functioning as sequential control protocols, these machines process classical strings one symbol at a time from left to right without the aid of an external tape or the ability to revisit past inputs. While quantum finite automata (QFAs) [4–8] are known to offer significant reductions in memory cost over their classical counterparts, traditional QFA paradigms are notoriously fragile. Standard constructions [5] rely on continuous unitary rotations of arbitrarily small angles, leaving them highly vulnerable to minor coherent perturbations. Other models seek an advantage by processing unbounded input strings, an approach that leads to cumulative operational noise that scales with the length of the input [4,9,6,10,11] . Consequently, the noise thresholds of these traditional automata vanish as the quantum memory advantage grows.  \nHere, we propose a fundamentally different strategy inspired by recent efforts to translate foundational quantum “no-go” theorems into unconditional computational advantages. Inspired by Bravyi, Gosset, and K¨onig [12] who mapped multipartite non-locality to an unconditional separation in circuit depth, we establish a separation in state complexity (memory cost) driven entirely by single-system quantum contextuality [13, 14] . Specifically, we demonstrate that a structural prerequisite of state-independent contextuality – the topological uncolorability of exclusivity graphs [15–18] – gives rise to a language recognition problem for which QFAs possess an unconditional memory advantage over classical automata. Crucially, this advantage arises for a constant input-string length over a scaling alphabet size. The QFA thus maintains a constant O(1) error threshold against both depolarizing noise and systematic coherent errors.  \nTo formalize this, we define the Kochen-Specker Problem (KSP) as a language recognition task, with a promise. We prove an unconditional exponential separation in state complexity: any classical deterministic finite automaton (DFA) requires a memory state space scaling as N = χ (G) to solve the KSP, where χ (G) is the chromatic number of the underlying exclusivity graph G. In this setting, the classical transition function fundamentally acts as anon-contextual hidden variable model. In contra","cbCaimK8lyETviGg","https://ap.wps.com/l/cbCaimK8lyETviGg","pdf",416992,3,1,17,"English","en",105,"# Introduction\n# Review of finite automata\n# Representational contextuality and exclusivity graphs\n# The Kochen-Specker problem\n# Exponential advantage\n# Noise robustness\n# Discussion and outlook\n## Representational contextuality vs. statistical contextuality","[{\"question\":\"What computational task is used to demonstrate the memory advantage?\",\"answer\":\"The document defines the Kochen-Specker Problem (KSP) as a language recognition task with a promise on an exclusivity graph G.\"},{\"question\":\"How do classical deterministic automata and quantum finite automata compare in memory cost?\",\"answer\":\"Any classical deterministic automaton requires N=χ(G) states, where χ(G) is the chromatic number of the exclusivity graph. In contrast, the QFA uses memory dimension d≤ξ(G)+1, where ξ(G) is the orthogonal rank.\"},{\"question\":\"Why is the advantage robust to noise?\",\"answer\":\"The construction maintains an O(1) error threshold against both depolarizing noise and systematic coherent errors.\"}]",1784188439,43,{"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},"robust-quantum-memory-advantage-from-contextuality","",{"@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/robust-quantum-memory-advantage-from-contextuality/83497/",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","2026-07-26","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 computational task is used to demonstrate the memory advantage?","Question",{"text":75,"@type":76},"The document defines the Kochen-Specker Problem (KSP) as a language recognition task with a promise on an exclusivity graph G.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How do classical deterministic automata and quantum finite automata compare in memory cost?",{"text":80,"@type":76},"Any classical deterministic automaton requires N=χ(G) states, where χ(G) is the chromatic number of the exclusivity graph. In contrast, the QFA uses memory dimension d≤ξ(G)+1, where ξ(G) is the orthogonal rank.",{"name":82,"@type":73,"acceptedAnswer":83},"Why is the advantage robust to noise?",{"text":84,"@type":76},"The construction maintains an O(1) error threshold against both depolarizing noise and systematic coherent errors.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":21,"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":52,"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":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},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"]