{"id":132,"date":"2006-09-21T17:54:00","date_gmt":"2006-09-21T17:54:00","guid":{"rendered":"https:\/\/scottaaronson.blog\/?p=132"},"modified":"2006-09-21T17:54:00","modified_gmt":"2006-09-21T17:54:00","slug":"only-eight-annoying-questions-to-go","status":"publish","type":"post","link":"https:\/\/scottaaronson.blog\/?p=132","title":{"rendered":"Only eight annoying questions to go"},"content":{"rendered":"<p>A month ago, I posed the following as the <a href=\"https:\/\/scottaaronson.blog\/?p=112\">10<sup>th<\/sup> most annoying question in quantum computing<\/a>:<\/p>\n<blockquote><p>Given an n-qubit pure state, is there always a way to apply Hadamard gates to some subset of the qubits, so as to make all 2<sup>n<\/sup> computational basis states have nonzero amplitudes?<\/p><\/blockquote>\n<p>Today Ashley Montanaro and Dan Shepherd of the University of Bristol sent me the answer, in a <a href=\"http:\/\/www.scottaaronson.com\/hadamard.pdf\">beautiful 4-page writeup<\/a> that they were kind enough to let me post here.  (The answer, as I expected, is yes.)<\/p>\n<p>This is a clear advance in humankind&#8217;s scientific knowledge, which is directly traceable to this blog.  I am in a good mood today.<\/p>\n<p>The obvious next question is to find an \u03b1&gt;0 such that, for any n-qubit pure state, there&#8217;s some way to apply Hadamards to a subset of the qubits so as to make all 2<sup>n<\/sup> basis states have |amplitude| at least \u03b1. Clearly we can&#8217;t do better than \u03b1=sin<sup>n<\/sup>(\u03c0\/8).  Montanaro and Shepherd conjecture that this is tight.<\/p>\n<p>What&#8217;s the motivation?  If you have to ask&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A month ago, I posed the following as the 10th most annoying question in quantum computing: Given an n-qubit pure state, is there always a way to apply Hadamard gates to some subset of the qubits, so as to make all 2n computational basis states have nonzero amplitudes? Today Ashley Montanaro and Dan Shepherd of [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"_wpas_customize_per_network":false},"categories":[4],"tags":[],"class_list":["post-132","post","type-post","status-publish","format-standard","hentry","category-quantum"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/132","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=132"}],"version-history":[{"count":0,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/132\/revisions"}],"wp:attachment":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=132"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=132"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=132"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}