{"id":1962,"date":"2021-04-13T11:21:08","date_gmt":"2021-04-13T10:21:08","guid":{"rendered":"http:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/?p=1962"},"modified":"2022-11-11T10:24:55","modified_gmt":"2022-11-11T10:24:55","slug":"holography-and-quantum-error-correction-supervisor-dr-pieter-naaijkens","status":"publish","type":"post","link":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/holography-and-quantum-error-correction-supervisor-dr-pieter-naaijkens\/","title":{"rendered":"Holography and quantum error correction  &#8211; Supervisor: Dr Pieter Naaijkens"},"content":{"rendered":"\n<p><strong>Title of project:<\/strong> Holography and quantum error correction <\/p>\n\n\n\n<p><strong>Code:<\/strong> PN2122B <\/p>\n\n\n\n<p><strong>Supervisor:<\/strong> Dr P. Naaijkens <\/p>\n\n\n\n<p><strong>Project description:<\/strong> Error correction is indispensable in modern computers to ensure a fault-tolerant operation. This is true even more so for quantum computers. Not only are quantum systems more susceptible to noise due to their delicate nature, a single qubit (the quantum analogue of a bit), can undergo a continuum of possible errors. Nevertheless, it is possible to design quantum error correcting codes that tackle this issue. Moreover, if one can make the individual components of a quantum computer (a \u2018quantum gate\u2019) good enough, it is possible to build a fault-tolerant computer that can correct all kinds of errors. An interesting class of examples come from \u2018holography\u2019, where the bulk of a physical system is described completely by what happens on the boundary. An example is the so-called \u2018HaPPY code\u2019, which provide a toy model for the AdS\/CFT correspondence in physics. The key point of the latter is a bulk-boundary correspondence, where the behaviour in the bulk of a system is completely determined by what happens at the boundary. In the HaPPY code, this can be understood as a consequence of error correcting properties. In this project you will look at the main features of such holographic quantum codes and study them in a mathematical setting. A non-technical introduction can be found at https:\/\/www.quantamagazine.org\/how-space-and-timecould-be-a-quantum-error-correcting-code-20190103\/ Knowledge of quantum mechanics is not required for this project, but the student is advised to take MA4016 concurrently with this project. <\/p>\n\n\n\n<p><strong>Project offered as a double module, single module, or both:<\/strong> Double <\/p>\n\n\n\n<p><strong>Prerequisite modules:<\/strong> MA3005 Functional and Fourier Analysis, not necessary, but helpful: MA3007 Coding Theory <\/p>\n\n\n\n<p><strong>Recommended module for concurrent study in year 4<\/strong>: MA4016 Quantum Information <\/p>\n\n\n\n<p><strong>Number of students who could be supervised on this project:<\/strong> 1 <\/p>\n\n\n\n<p><strong>Year:<\/strong> 4 <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Title of project: Holography and quantum error correction Code: PN2122B Supervisor: Dr P. Naaijkens Project description: Error correction is indispensable in modern computers to ensure a fault-tolerant operation. This is true even more so for quantum computers. Not only are quantum systems more susceptible to noise due to their delicate nature, a single qubit (the &hellip; <a href=\"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/holography-and-quantum-error-correction-supervisor-dr-pieter-naaijkens\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Holography and quantum error correction  &#8211; Supervisor: Dr Pieter Naaijkens<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[2,4,8],"tags":[],"class_list":["post-1962","post","type-post","status-publish","format-standard","hentry","category-2021-2022","category-double","category-yr-4-description-2021-2022"],"aioseo_notices":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/posts\/1962","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/comments?post=1962"}],"version-history":[{"count":1,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/posts\/1962\/revisions"}],"predecessor-version":[{"id":1965,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/posts\/1962\/revisions\/1965"}],"wp:attachment":[{"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/media?parent=1962"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/categories?post=1962"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/tags?post=1962"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}