{"id":6182,"date":"2022-12-02T10:00:00","date_gmt":"2022-12-02T02:00:00","guid":{"rendered":"https:\/\/www.hh-ri.com\/?p=6182"},"modified":"2023-03-22T17:34:16","modified_gmt":"2023-03-22T09:34:16","slug":"quantum-state-tomography-via-non-convex-riemannian-gradient-descent","status":"publish","type":"post","link":"https:\/\/www.hh-ri.com\/2022\/12\/02\/quantum-state-tomography-via-non-convex-riemannian-gradient-descent\/","title":{"rendered":"Quantum state tomography via non-convex Riemannian gradient descent"},"content":{"rendered":"\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Time<\/td><td>Dec 2, 2022, 10:00 am (Taipei Time)<\/td><\/tr><tr><td>Speaker<\/td><td>Ming-Chien Hsu<\/td><\/tr><tr><td>Title<\/td><td>Quantum state tomography via non-convex Riemannian gradient descent<\/td><\/tr><tr><td>Abstract<\/td><td>The recovery of an unknown density matrix of large size requires huge computational resources. The recent Factored Gradient Descent (FGD) algorithm and its variants achieved state-of-the-art performance since they could mitigate the dimensionality barrier by utilizing some of the underlying structures of the density matrix. Despite their theoretical guarantee of a linear convergence rate, the convergence in practical scenarios is still slow because the contracting factor of the FGD algorithms depends on the condition number \u03ba of the ground truth state. Consequently, the total number of iterations can be as large as O(\u221a\u03ba ln(1\/\u03b5)) to achieve the estimation error \u03b5. In this work, we derive a quantum state tomography scheme that improves the dependence on \u03ba to the logarithmic scale; namely, our algorithm could achieve the approximation error \u03b5 in O(ln(1\/\u03ba\u03b5)) steps. The improvement comes from the application of the non-convex Riemannian gradient descent (RGD). The contracting factor in our approach is thus a universal constant that is independent of the given state. Our theoretical results of extremely fast convergence and nearly optimal error bounds are corroborated by numerical results<\/td><\/tr><tr><td>Reference<\/td><td><a href=\"https:\/\/arxiv.org\/abs\/2208.13492\"><\/a><a rel=\"noreferrer noopener\" href=\"https:\/\/arxiv.org\/abs\/2208.13492\" target=\"_blank\">https:\/\/arxiv.org\/abs\/2208.13492<\/a><\/td><\/tr><tr><td>Personal information<\/td><td><\/td><\/tr><tr><td>Video<\/td><td><a href=\"https:\/\/www.youtube.com\/watch?v=TqVAHf0jYhA\">Quantum state tomography via non-convex Riemannian gradient descent &#8211; YouTube<\/a><\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Time Dec 2, 2022, 10:00 am (Taipei Time) Speaker Ming-C [&hellip;]<\/p>\n","protected":false},"author":9,"featured_media":6183,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[7],"tags":[40],"_links":{"self":[{"href":"https:\/\/www.hh-ri.com\/wp-json\/wp\/v2\/posts\/6182"}],"collection":[{"href":"https:\/\/www.hh-ri.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.hh-ri.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.hh-ri.com\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/www.hh-ri.com\/wp-json\/wp\/v2\/comments?post=6182"}],"version-history":[{"count":1,"href":"https:\/\/www.hh-ri.com\/wp-json\/wp\/v2\/posts\/6182\/revisions"}],"predecessor-version":[{"id":6545,"href":"https:\/\/www.hh-ri.com\/wp-json\/wp\/v2\/posts\/6182\/revisions\/6545"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.hh-ri.com\/wp-json\/wp\/v2\/media\/6183"}],"wp:attachment":[{"href":"https:\/\/www.hh-ri.com\/wp-json\/wp\/v2\/media?parent=6182"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.hh-ri.com\/wp-json\/wp\/v2\/categories?post=6182"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.hh-ri.com\/wp-json\/wp\/v2\/tags?post=6182"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}