[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-140263-105":59,"doc-detail-140263-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","random-natural-gradient","Random Natural Gradient","","Random Natural Gradient introduces resource-efficient alternatives to Quantum Natural Gradient for hybrid quantum-classical variational algorithms. Classical optimization is identified as a key bottleneck due to multiple local minima and barren plateaux, while Quantum Natural Gradient needs substantial quantum state preparations to compute the quantum natural gradient. The work proposes Random Natural Gradient using random measurements and the classical Fisher information, reducing quantum resources to linear complexity in the number of parameters and preserving accuracy in simulations. It also develops a stochastic-coordinate approximation that updates only a sampled fraction of parameters per iteration, achieving strong benchmark performance with fewer resources.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/random-natural-gradient/140263/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/random-natural-gradient/140263.png","ImageObject",300,407,{"name":92,"@type":93},"Theodore","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-09-17","2026-08-24",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What main problem does the paper target in hybrid quantum-classical optimization?","Question",{"text":112,"@type":113},"It targets the classical optimization loop, which suffers from multiple local minima and barren plateaux, reducing the appeal of standard hybrid approaches.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does Random Natural Gradient reduce quantum resource requirements compared with Quantum Natural Gradient?",{"text":117,"@type":113},"It replaces the quantum Fisher information used in QNG with random measurements and the classical Fisher information matrix, reducing required quantum state preparations from quadratic to linear in the number of circuit parameters.",{"name":119,"@type":110,"acceptedAnswer":120},"What is the stochastic-coordinate Quantum Natural Gradient approach proposed in the work?",{"text":121,"@type":113},"It draws inspiration from stochastic-coordinate methods and approximates QNG by optimizing only a randomly sampled small fraction of the total parameters at each iteration, while maintaining good benchmark performance with fewer resources.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},140263,1787572493,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":29,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144},7971461740886,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","Random Natural Gradient  \nIoannis Kolotouros and Petros Wallden  \nUniversity of Edinburgh, School of Informatics, EH8 9AB Edinburgh, United Kingdom  \narXiv :2311 .04135v3 [ quant-ph] 10 Oct 2024  \nHybrid quantum-classical algorithms appear to be the most promising approach for near-term quantum applications. An important bottleneck is the classical optimization loop, where the multiple local minima and the emergence of barren plateaux make these approaches less appealing. To improve the optimization, the Quantum Natural Gradient (QNG) method [Quantum 4, 269 (2020)] was introduced – a method that uses information about the local geometry of the quantum state-space. While the QNGbased optimization is promising, in each step it requires more quantum resources, since to compute the QNG one requires O (m2 ) quantum state preparations, where m is the number of parameters in the parameterized circuit. In this work we propose two methods that reduce theresources/state preparations required for QNG, while keeping the advantages and performance of the QNG-based optimization. Specifically, we first introduce the Random Natural Gradient (RNG) that uses random measurements and the classical Fisher information matrix (as opposed to the quantum Fisher information used in QNG) . The essential quantum resources reduce to linear O (m) and thus offer a quadratic “speed-up”, while in our numerical simulations it matches QNG in terms of accuracy. We give some theoretical arguments for RNG and then benchmark the method with the QNG on both classical and quantum problems. Secondly, inspired by stochastic-coordinate methods, we propose a novel approximation to the QNG which we call Stochastic-Coordinate Quantum Natural Gradient that optimizes only a small (randomly sampled) fraction of the  \nIoannis Kolotouros: [i.kolotouros@sms.ed.ac.uk](i.kolotouros@sms.ed.ac.uk)  \nPetros Wallden: [petros.wallden@ed.ac.uk](petros.wallden@ed.ac.uk)  \ntotal parameters at each iteration. This method also performs well in our benchmarks, while it uses fewer resources than the QNG.  \n1 Introduction  \nWe are approaching the era where quantum computers of ≈ 1000 qubits will become widely available. Despite the increase in scale, these quantum devices still inherit imperfect operations and short coherence times making them unsuitable for certain quantum algorithms. To address these issues, people employed classical computers to work in conjunction with these imperfect devices and developed variational quantum algorithms (VQAs) [1 , 2] . However, the question of whether these hybrid quantum-classical architectures will allow for a practical advantage is still open.  \nIn these approaches, the computational task of interest is transformed into the ground state of an interacting qubit Hamiltonian. The user then selects a properly suited parameterized quantum circuit, either problem-specific such as QAOA [3] or problem agnostic suited for the available quantum hardware [4], and iteratively prepares and measures quantum states. Additionally, the classical computer post-processes the quantum measurements to calculate an objective function (or its higher-order derivatives) in order to update the parameters of the quantum circuit towards a descent direction. When the optimization terminates, the quantum computer returns a quantum state which is a solution (or an approximation) for the computational task considered.  \nIn order to make such a framework practical, certain conditions must be met. In the NISQ regime, we need to distinguish the classical from the quantum resources required to solve a problem. For the number of parameters used and their corresponding matrices (e.g. the Hessian) of size m × m, the classical computers are powerful enough to perform standard linear algebra calcu-  \nAccepted in  2024-10-09, click title to verify. Published under CC-BY 4 .0. 1  \nlations with perfect accuracy while the quantum computers are still imperfect, with slow compilation times. For this","cbCaigAtjKLgFxED","https://ap.wps.com/l/cbCaigAtjKLgFxED","pdf",1321442,27,"English","# Introduction\n## Variational quantum algorithms and hybrid optimization\n## Optimization bottlenecks in NISQ\n## Information-theoretic optimization: natural gradient methods\n## Goals of the paper: RNG and stochastic-coordinate QNG","[{\"question\":\"What main problem does the paper target in hybrid quantum-classical optimization?\",\"answer\":\"It targets the classical optimization loop, which suffers from multiple local minima and barren plateaux, reducing the appeal of standard hybrid approaches.\"},{\"question\":\"How does Random Natural Gradient reduce quantum resource requirements compared with Quantum Natural Gradient?\",\"answer\":\"It replaces the quantum Fisher information used in QNG with random measurements and the classical Fisher information matrix, reducing required quantum state preparations from quadratic to linear in the number of circuit parameters.\"},{\"question\":\"What is the stochastic-coordinate Quantum Natural Gradient approach proposed in the work?\",\"answer\":\"It draws inspiration from stochastic-coordinate methods and approximates QNG by optimizing only a randomly sampled small fraction of the total parameters at each iteration, while maintaining good benchmark performance with fewer resources.\"}]","Random Natural Gradient | PDF",68]