[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-123797-en":3,"doc-seo-123797-105":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":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},123797,3848291630094,"Emma Wilson","https://eur-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45",8,"Research & Report","Localization of quantum walk with classical randomness - Comparison between manual methods and supervised machine learning","A transition in quantum-walk dynamics induced by classical randomness reshapes the walker’s probability distribution from a two-peak form to a single-peak form once the random parameter surpasses a critical value. The work establishes the generality by demonstrating localization for random rotation or translation. The transition point is located manually using probability-distribution inspection together with moment of inertia and inverse participation ratio. Supervised learning methods—SVM, MLP, and CNN—identify the transition and yield comparable localization exponents, except for random translation where neural methods underestimate due to complex probability distributions.","Localization of quantum walk with classical randomness: Comparison between manual  \nmethods and supervised machine learning  \narXiv :2304 . 14348v2 [ quant-ph] 2 Aug 2023  \nChristopher Mastandrea 1 and Chih-Chun Chien 1, ∗  \n1 Department of Physics, University of California, Merced, CA 95343, USA  \nA transition of quantum walk induced by classical randomness changes the probability distribution of the walker from a two-peak structure to a single-peak one when the random parameter exceedsa critical value. We first establish the generality of the localization by showing its emergence in the presence of random rotation or translation. The transition point can be located manually by examining the probability distribution, momentum of inertia, and inverse participation ratio. As a comparison, we implement three supervised machine learning methods, the support vector machine, multi-layer perceptron neural network, and convolutional neural network with the same data and show that they can identify the transition and produce comparable exponents of the localization except for the case with random translation, where the two neural-network methods tend to underestimate the exponent due to the complicated probability distributions in the transition regime. Our work illustrates potentials and challenges facing machine learning of physical systems with mixed quantum and classical probabilities.  \nI. INTRODUCTION  \nWhile classical random walk finds broad applications in physics, chemistry, biology, finance, and many other places [1–3], the simplest quantum analogue, the quantum walk (QW), exhibits interesting probabilistic behavior due to the underlying wavefunction even if all the operations are deterministic [4] . Recently, there is a trend in studying various quantum walks with classical randomness [5–9], in the sense that the parameter set or geometry of QW is drawn from a classical probability distribution. The resulting probability distribution thus has contributions from both classical and quantum randomness. As the classical randomness increases, a transition from delocalization to localization emerges, which has stimulated lasting research interest.  \nThere have been experimental demonstrations of discrete-time quantum walk with classical randomness in the quantum operators of the evolution and exhibitions of the transition from quantum dynamics with multipeak probability distributions in real or momentum space to classical-like dynamics with Gaussian-like probability distributions. For example, phase-disordered photons [7, 10], trapped ions with randomized phases [11], superconducting qubits with random frequencies [12], and neutral atoms with random microwave pulses [13] have been implemented to demonstrate the transition induced by classical randomness.  \nPrevious theoretical investigations [9, 14–16] have suggested possible resemblance between the localization transition in quantum walk with classical randomness and the Anderson localization [17], a paradigmatic phenomenon in condensed matter physics. The Anderson localization was first developed in electronic transport,  \n∗ [cchien5@ucmerced.edu](cchien5@ucmerced.edu)  \nwhere electrons in a solid encounter a localization transition as the parameters from the underlying materials are drawn from a classical probability distribution. Ref. [18] proposed a scaling theory applicable to higher dimensions and showed that in one and two dimensions, any amount of disorder will lead to electron localization in the thermodynamic limit. Nevertheless, in a finite system, the Anderson localization only occurs when the system size exceeds the localization length. For example, Ref. [14] evaluates the localization length inferred from the inverse participation ratio. Although the Anderson localization typically has spatial randomness while QW usually has temporal randomness, the finite localization length hints why quantum walk is experimentally realizable in finitesize systems even if imperfec","cbCaivPDYLiL3MEJ","https://ap.wps.com/l/cbCaivPDYLiL3MEJ","pdf",1875643,1,12,"English","en",105,"# Introduction\n## Classical random walk and quantum walk\n## Experimental and theoretical background\n## Connection to Anderson localization\n## Role of machine learning in identifying transitions","[{\"question\":\"What change does classical randomness induce in the quantum-walk probability distribution?\",\"answer\":\"When the random parameter exceeds a critical value, the distribution transitions from a two-peak structure to a single-peak one.\"},{\"question\":\"How can the localization transition point be determined manually?\",\"answer\":\"By examining the probability distribution patterns and using quantities such as moment of inertia and the inverse participation ratio.\"},{\"question\":\"Which supervised machine learning methods are compared, and what is their performance?\",\"answer\":\"The comparison includes SVM, MLP, and CNN. They can identify the transition and produce comparable localization exponents, but neural networks tend to underestimate the exponent for random translation because the transition-regime distributions are complex.\"}]","Localization of quantum walk with classical randomness - Comparison between manual methods and supervised machine learning | PDF",1785818615,30,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"localization-of-quantum-walk-with-classical-randomness-comparison-between-manual-methods-and-supervised-machine-learning","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"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":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/localization-of-quantum-walk-with-classical-randomness-comparison-between-manual-methods-and-supervised-machine-learning/123797/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-04",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What change does classical randomness induce in the quantum-walk probability distribution?","Question",{"text":75,"@type":76},"When the random parameter exceeds a critical value, the distribution transitions from a two-peak structure to a single-peak one.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How can the localization transition point be determined manually?",{"text":80,"@type":76},"By examining the probability distribution patterns and using quantities such as moment of inertia and the inverse participation ratio.",{"name":82,"@type":73,"acceptedAnswer":83},"Which supervised machine learning methods are compared, and what is their performance?",{"text":84,"@type":76},"The comparison includes SVM, MLP, and CNN. They can identify the transition and produce comparable localization exponents, but neural networks tend to underestimate the exponent for random translation because the transition-regime distributions are complex.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,122,127,130,134],{"id":20,"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":53,"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":29,"slug":121},"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]