{"id":192501,"date":"2015-07-21T00:00:00","date_gmt":"2015-07-21T12:07:27","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/advances-in-quantum-algorithms-devices-quantum-monte-carlo-versus-quantum-adiabatic-optimization\/"},"modified":"2016-07-15T15:25:01","modified_gmt":"2016-07-15T22:25:01","slug":"advances-in-quantum-algorithms-devices-quantum-monte-carlo-versus-quantum-adiabatic-optimization","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/advances-in-quantum-algorithms-devices-quantum-monte-carlo-versus-quantum-adiabatic-optimization\/","title":{"rendered":"Advances in Quantum Algorithms & Devices: Quantum Monte Carlo versus Quantum Adiabatic Optimization"},"content":{"rendered":"<div class=\"asset-content\">\n<p>How many queries are needed to determine a polynomial F(X)? We look at this question when F(X) is defined over a finite field GF(q) and has degree d, such that d+1 queries are obviously sufficient. Shamir&#8217;s Secret Sharing protocol is based on the result that d+1 classical queries are also needed as no interpolation is possible based on only d values of F. Here we look at how many quantum queries are sufficient to perform the same task. Earlier work by [Kane & Kutin 2009] and [Meyer & Pommersheim 2010] proved that at least d\/2+1\/2 quantum queries are needed, while [Boneh and Zhandry 2012] showed that d quantum queries are sufficient. In this talk we will describe a quantum algorithm that uses only d\/2+1\/2 queries and that has a constant success probability. Our algorithm relies on the analysis of the classical Moment Problem defined over finite fields.  (Joint work with Andrew Childs)<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>How many queries are needed to determine a polynomial F(X)? We look at this question when F(X) is defined over a finite field GF(q) and has degree d, such that d+1 queries are obviously sufficient. Shamir&#8217;s Secret Sharing protocol is based on the result that d+1 classical queries are also needed as no interpolation is [&hellip;]<\/p>\n","protected":false},"featured_media":199142,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr_hide_image_in_river":0,"footnotes":""},"research-area":[],"msr-video-type":[],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-192501","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/YSyDHDN7zKs","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/192501","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/192501\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/199142"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=192501"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=192501"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=192501"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=192501"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=192501"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=192501"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=192501"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=192501"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=192501"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=192501"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}