{"id":5837,"date":"2021-09-14T23:09:31","date_gmt":"2021-09-15T04:09:31","guid":{"rendered":"https:\/\/scottaaronson.blog\/?p=5837"},"modified":"2021-09-15T08:00:42","modified_gmt":"2021-09-15T13:00:42","slug":"open-problems-related-to-quantum-query-complexity","status":"publish","type":"post","link":"https:\/\/scottaaronson.blog\/?p=5837","title":{"rendered":"Open Problems Related to Quantum Query Complexity"},"content":{"rendered":"\n

Way back in 2005, I posed Ten Semi-Grand Challenges for Quantum Computing Theory<\/a>, on at least half of which I’d say there’s been dramatic progress in the 16 years since (most of the challenges were open-ended, so that it’s unclear when to count them as “solved”). I posed more open quantum complexity problems<\/a> in 2010, and some classical complexity problems<\/a> in 2011. In the latter cases, I’d say there’s been dramatic progress on about a third of the problems. I won’t go through the problems one by one, but feel free to ask in the comments about any that interest you.<\/p>\n\n\n\n

Shall I push my luck as a problem-poser? Shall or shall not, I have.<\/p>\n\n\n\n

My impetus, this time around, was a kind invitation by Travis Humble, the editor-in-chief of the new ACM Transactions on Quantum Computing<\/a><\/em>, to contribute a perspective piece to that journal on the occasion of my ACM Prize<\/a>. I agreed—but only on the condition that, rather than ponderously pontificate about the direction of the field, I could simply discuss a bunch of open problems that I wanted to see solved. The result is below. It’s coming soon to an arXiv near you, but Shtetl-Optimized<\/em> readers get it first.<\/p>\n\n\n\n

Open Problems Related to Quantum Query Complexity<\/a><\/strong> (11 pages, PDF)<\/p>

by Scott Aaronson<\/p>

Abstract:<\/em> I offer a case that quantum query complexity still has loads of enticing and fundamental open problems—from relativized QMA versus QCMA and BQP versus IP, to time\/space tradeoffs for collision and element distinctness, to polynomial degree versus quantum query complexity for partial functions, to the Unitary Synthesis Problem and more.<\/p><\/blockquote>\n\n\n\n

Some of the problems on my new hit-list are ones that I and others have flogged for years or even decades, but others, as far as I know, appear here for the first time. If your favorite quantum query complexity open problem, or a problem I’ve discussed in the past, is missing, that doesn’t mean that it’s been solved or is no longer interesting—it might mean I simply ran out of time or energy before I got to it.<\/p>\n\n\n\n

Enjoy! And tell me what I missed or got wrong or has a trivial solution that I overlooked.<\/p>\n","protected":false},"excerpt":{"rendered":"

Way back in 2005, I posed Ten Semi-Grand Challenges for Quantum Computing Theory, on at least half of which I’d say there’s been dramatic progress in the 16 years since (most of the challenges were open-ended, so that it’s unclear when to count them as “solved”). I posed more open quantum complexity problems in 2010, […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"jetpack_seo_schema_type":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"{title}\n\n{excerpt}\n\n{url}","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,"jetpack_post_was_ever_published":false},"categories":[5,4],"tags":[],"class_list":["post-5837","post","type-post","status-publish","format-standard","hentry","category-complexity","category-quantum"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/5837","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\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5837"}],"version-history":[{"count":3,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/5837\/revisions"}],"predecessor-version":[{"id":5840,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/5837\/revisions\/5840"}],"wp:attachment":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5837"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5837"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5837"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}