{"id":192511,"date":"2015-07-21T00:00:00","date_gmt":"2015-07-21T13:07:50","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/advances-in-quantum-algorithms-devices-exact-synthesis-for-qubit-unitaries\/"},"modified":"2016-07-15T15:25:06","modified_gmt":"2016-07-15T22:25:06","slug":"advances-in-quantum-algorithms-devices-exact-synthesis-for-qubit-unitaries","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/advances-in-quantum-algorithms-devices-exact-synthesis-for-qubit-unitaries\/","title":{"rendered":"Advances in Quantum Algorithms & Devices: Exact synthesis for qubit unitaries"},"content":{"rendered":"<div class=\"asset-content\">\n<p>The Solovay-Kitaev Theorem shows that any finite subset of SU(2) generating a dense subgroup can be used to epsilon-approximate an arbitrary qubit unitary using a quantum circuit of length O(polylog(1\/epsilon)).   Recent advances in quantum compiling achieved dramatically improved approximations to arbitrary unitaries with O(log(1\/epsilon))-length circuits over special qubit gate sets.  A necessary component of such compiling tasks involves solving the \u201cexact synthesis problem\u201d for the given gate set: Given a unitary that can be expressed as a circuit over the elementary gates, the exact synthesis problem is to find the shortest circuit implementing that unitary.   In this talk, I will present joint work with Vadym Kliuchnikov, showing how sophisticated mathematical tools from the theory of quaternion orders can be put to work to solve this problem for a very broad class of gate sets including Clifford+T, V-basis and braiding of nonabelian anyons in SU(2) Chern-Simons theory at finite level.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Solovay-Kitaev Theorem shows that any finite subset of SU(2) generating a dense subgroup can be used to epsilon-approximate an arbitrary qubit unitary using a quantum circuit of length O(polylog(1\/epsilon)). Recent advances in quantum compiling achieved dramatically improved approximations to arbitrary unitaries with O(log(1\/epsilon))-length circuits over special qubit gate sets. A necessary component of such [&hellip;]<\/p>\n","protected":false},"featured_media":199147,"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-192511","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/d_428En3an8","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/192511","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\/192511\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/199147"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=192511"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=192511"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=192511"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=192511"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=192511"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=192511"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=192511"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=192511"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=192511"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=192511"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}