{"id":151,"date":"2013-01-03T13:40:15","date_gmt":"2013-01-03T21:40:15","guid":{"rendered":"http:\/\/www.dereviankogroup.com\/?p=151"},"modified":"2013-01-03T14:54:55","modified_gmt":"2013-01-03T22:54:55","slug":"why-is-the-atomic-many-body-problem-so-difficult","status":"publish","type":"post","link":"https:\/\/www.dereviankogroup.com\/dereviankogroup\/rightthere\/why-is-the-atomic-many-body-problem-so-difficult\/","title":{"rendered":"Why is the atomic many-body problem so difficult?"},"content":{"rendered":"

\"illustration<\/a>One could\u00a0rightfully\u00a0state that the atomic-structure problem has been around for a very long time. Yes, this is true - in fact quantum mechanics has been invented to explain atomic properties. Then why do we still struggle to solve it?<\/p>\n

Should we be embarrassed by our inability to solve this basic problem? Sure we can solve it approximately, but solving it\u00a0accurately<\/em>\u00a0is another story.<\/p>\n

So what is holding us back? It is the very same entanglement and complexity of Hilbert space (that is where wave functions live) that makes quantum computing so powerful. To\u00a0illustrate\u00a0this enormous complexity, I'll take my favorite atom, cesium. It has 55 electrons. With 3 degrees of freedom per electron (x, y, and z), the Cs wave function depends on \"55 coordinates. As a result of the calculation I would need to store the wave function. If I \u00a0were to take a very poor grid of 10 points per coordinate, the storage would require $latex\u00a010^{155}$\u00a0memory units.<\/p>\n

$latex\u00a010^{155}$ is of course an astronomically large number - in fact it exceed an estimated number of atoms in the Universe, \"10^{80}\". So even if we were able to compute the Cs wave function, there is no plausible way to store it in usable form.<\/p>\n","protected":false},"excerpt":{"rendered":"

One could\u00a0rightfully\u00a0state that the atomic-structure problem has been around for a very long time. Yes, this is true - in fact quantum mechanics has been invented to explain atomic properties. Then why do we still struggle to solve it? Should we be embarrassed by our inability to solve this basic problem? Sure we can solve […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[6,7,8],"tags":[9,10,23],"class_list":["post-151","post","type-post","status-publish","format-standard","hentry","category-atomic-structure","category-many-body-problem","category-precision","tag-cesium","tag-complexity","tag-quantum-computing"],"yoast_head":"\nWhy is the atomic many-body problem so difficult? - Derevianko Group<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.dereviankogroup.com\/dereviankogroup\/rightthere\/why-is-the-atomic-many-body-problem-so-difficult\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Why is the atomic many-body problem so difficult? - Derevianko Group\" \/>\n<meta property=\"og:description\" content=\"One could\u00a0rightfully\u00a0state that the atomic-structure problem has been around for a very long time. 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