{"id":59,"date":"2024-10-30T10:00:52","date_gmt":"2024-10-30T10:00:52","guid":{"rendered":"https:\/\/blogs.imperial.ac.uk\/imperialquest\/?p=59"},"modified":"2025-01-16T17:05:10","modified_gmt":"2025-01-16T17:05:10","slug":"research-insights-with-dr-rita-ahmadi","status":"publish","type":"post","link":"https:\/\/blogs.imperial.ac.uk\/imperialquest\/2024\/10\/30\/research-insights-with-dr-rita-ahmadi\/","title":{"rendered":"Research Insights with Dr Rita Ahmadi"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" class=\"aligncenter wp-image-82 size-large\" src=\"http:\/\/blogs.imperial.ac.uk\/imperialquest\/files\/2024\/10\/19-1024x576.png\" alt=\"\" \/><\/p>\n<p><strong>Dr Rita Ahmadi <\/strong><strong>is a Research Associate in the Department of Mathematics. In this blog post, she shares more about her research as part of QuEST (Centre for Quantum Engineering, Science and Technology at Imperial College London). Rita investigates quantum algorithms and their real-world applications. She also uses a branch of mathematics called category theory to study the unique behaviours of certain materials.\u00a0<\/strong><\/p>\n<p style=\"font-weight: 400\"><strong>Can you tell us about your research area?<\/strong><\/p>\n<p style=\"font-weight: 400\">I am interested in two primary research themes.<\/p>\n<p><span data-contrast=\"none\">The first theme focuses on quantum algorithms and their applications. We have been investigating the parallels between established quantum subroutines and classical concepts. Our goal is to establish a translation framework between them. The foundational subroutines that lead to quantum advantages are often the same across established algorithms. We are examining these subroutines considering classical practices.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559738&quot;:240,&quot;335559739&quot;:240}\">\u00a0<\/span><\/p>\n<p><span data-contrast=\"none\">The second theme involves applying category theory to physics, particularly in the study of topological phases of matter. Topological phases of matter are special states that go beyond the usual solid, liquid, and gas phases. The complex and exotic behaviours of these materials can be captured using categorical structures. My focus lies on bicategorical structures, which arise <\/span><a href=\"https:\/\/arxiv.org\/abs\/2212.11022\"><span data-contrast=\"none\">in conformal field theories<\/span><\/a><span data-contrast=\"none\">.<\/span><\/p>\n<p style=\"font-weight: 400\"><span class=\"TextRun SCXW15544159 BCX4\" lang=\"EN-US\" xml:lang=\"EN-US\" data-contrast=\"none\"><span class=\"NormalTextRun SCXW15544159 BCX4\">I believe the intersection of mathematics and physics in the late 20th century<\/span><span class=\"NormalTextRun SCXW15544159 BCX4\"> is no accident. New mathematical frameworks have often <\/span><span class=\"NormalTextRun SCXW15544159 BCX4\">emerged<\/span><span class=\"NormalTextRun SCXW15544159 BCX4\"> alongside new physical phenomena, helping our understanding of how these systems work.<\/span><\/span><\/p>\n<p style=\"font-weight: 400\"><span class=\"TextRun SCXW15544159 BCX4\" lang=\"EN-US\" xml:lang=\"EN-US\" data-contrast=\"none\"><span class=\"NormalTextRun SCXW15544159 BCX4\">Category theory was pioneered by <\/span><span class=\"NormalTextRun SCXW15544159 BCX4\">Mac<\/span><\/span> <span class=\"TextRun SCXW15544159 BCX4\" lang=\"EN-US\" xml:lang=\"EN-US\" data-contrast=\"none\"><span class=\"NormalTextRun SCXW15544159 BCX4\">Lane in the mid-20th century and later expanded by <\/span><span class=\"NormalTextRun SCXW15544159 BCX4\">Grothendieck<\/span><span class=\"NormalTextRun SCXW15544159 BCX4\">. The study of topological orders and field theories gained prominence around the same time, with <\/span><\/span><a class=\"Hyperlink SCXW15544159 BCX4\" href=\"http:\/\/www.numdam.org\/item\/PMIHES_1988__68__175_0.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span class=\"FieldRange SCXW15544159 BCX4\"><span class=\"TrackChangeTextInsertion TrackedChange SCXW15544159 BCX4\"><span class=\"TextRun Underlined SCXW15544159 BCX4\" lang=\"EN-US\" xml:lang=\"EN-US\" data-contrast=\"none\"><span class=\"NormalTextRun SCXW15544159 BCX4\" data-ccp-charstyle=\"Hyperlink\">Atiyah applying category theory to topological field theory in 1988<\/span><\/span><\/span><\/span><\/a><span class=\"TextRun SCXW15544159 BCX4\" lang=\"EN-US\" xml:lang=\"EN-US\" data-contrast=\"none\"><span class=\"NormalTextRun SCXW15544159 BCX4\">. Simultaneously, the development of higher categories was partly driven by efforts to <\/span><span class=\"NormalTextRun SCXW15544159 BCX4\">comprehend<\/span><span class=\"NormalTextRun SCXW15544159 BCX4\"> a class of statistical systems known as exactly solvable models. <\/span><span class=\"NormalTextRun SCXW15544159 BCX4\">That is why the field is intriguing to explore<\/span><span class=\"NormalTextRun SCXW15544159 BCX4\">.\u00a0<\/span><\/span><\/p>\n<p style=\"font-weight: 400\"><strong>What led you to study this area?<\/strong><\/p>\n<p style=\"font-weight: 400\"><span class=\"TextRun SCXW229851467 BCX4\" lang=\"EN-US\" xml:lang=\"EN-US\" data-contrast=\"none\"><span class=\"NormalTextRun SCXW229851467 BCX4\">I<\/span><span class=\"NormalTextRun SCXW229851467 BCX4\">t <\/span><span class=\"NormalTextRun SCXW229851467 BCX4\">was a combination of coursework and a dopamine rush<\/span><span class=\"NormalTextRun SCXW229851467 BCX4\">.<\/span><span class=\"NormalTextRun SCXW229851467 BCX4\">\u00a0I would say m<\/span><span class=\"NormalTextRun SCXW229851467 BCX4\">y <\/span><span class=\"NormalTextRun SCXW229851467 BCX4\">entry into quantum computing was the <\/span><\/span><a class=\"Hyperlink SCXW229851467 BCX4\" href=\"https:\/\/journals.aps.org\/pr\/abstract\/10.1103\/PhysRev.47.777\" target=\"_blank\" rel=\"noreferrer noopener\"><span class=\"FieldRange SCXW229851467 BCX4\"><span class=\"TrackChangeTextInsertion TrackedChange SCXW229851467 BCX4\"><span class=\"TextRun Underlined SCXW229851467 BCX4\" lang=\"EN-US\" xml:lang=\"EN-US\" data-contrast=\"none\"><span class=\"NormalTextRun SCXW229851467 BCX4\" data-ccp-charstyle=\"Hyperlink\">EPR paper (Einstein-Podolsky-Rosen)<\/span><\/span><\/span><\/span><\/a><span class=\"TextRun SCXW229851467 BCX4\" lang=\"EN-US\" xml:lang=\"EN-US\" data-contrast=\"none\"><span class=\"NormalTextRun SCXW229851467 BCX4\">. My interest in topological phases of matter was sparked by <\/span><\/span><a class=\"Hyperlink SCXW229851467 BCX4\" href=\"https:\/\/link.springer.com\/chapter\/10.1007\/978-1-4615-5923-8_19\" target=\"_blank\" rel=\"noreferrer noopener\"><span class=\"FieldRange SCXW229851467 BCX4\"><span class=\"TrackChangeTextInsertion TrackedChange TrackChangeHoverSelectColorRed SCXW229851467 BCX4\"><span class=\"TextRun SCXW229851467 BCX4\" lang=\"EN-US\" xml:lang=\"EN-US\" data-contrast=\"none\"><span class=\"NormalTextRun TrackChangeHoverSelectHighlightRed SCXW229851467 BCX4\">Kitaev\u2019s<\/span><\/span><\/span><span class=\"TrackChangeTextInsertion TrackedChange TrackChangeHoverSelectColorRed SCXW229851467 BCX4\"><span class=\"TextRun Underlined SCXW229851467 BCX4\" lang=\"EN-US\" xml:lang=\"EN-US\" data-contrast=\"none\"><span class=\"NormalTextRun TrackChangeHoverSelectHighlightRed SCXW229851467 BCX4\" data-ccp-charstyle=\"Hyperlink\"> 1997 paper<\/span><\/span><\/span><\/span><\/a><span class=\"TextRun SCXW229851467 BCX4\" lang=\"EN-US\" xml:lang=\"EN-US\" data-contrast=\"none\"><span class=\"NormalTextRun SCXW229851467 BCX4\">, where a complex set of physical phenomena is elegantly disguised within a simple toy model known as the Toric code, which is also one of the most efficient error-correcting codes.<\/span><\/span><\/p>\n<p style=\"font-weight: 400\"><strong>What are the main aims of your current research?<\/strong><\/p>\n<p style=\"font-weight: 400\"><span class=\"TextRun SCXW130107298 BCX4\" lang=\"EN-US\" xml:lang=\"EN-US\" data-contrast=\"none\"><span class=\"NormalTextRun SCXW130107298 BCX4\">My main goal<\/span><span class=\"NormalTextRun SCXW130107298 BCX4\"> is to<\/span><span class=\"NormalTextRun SCXW130107298 BCX4\"> understand how quantum algorithms work, focusing on specific applications in the real world and <\/span><span class=\"NormalTextRun SCXW130107298 BCX4\">classical practices<\/span><span class=\"NormalTextRun SCXW130107298 BCX4\">.\u00a0<\/span><\/span><span class=\"EOP SCXW130107298 BCX4\" data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559738&quot;:240,&quot;335559739&quot;:240}\">\u00a0<\/span><\/p>\n<p style=\"font-weight: 400\"><strong>How could this research potentially benefit society?<\/strong><\/p>\n<p><span data-contrast=\"none\">Many researchers, some from Imperial College London, have published a roadmap to highlight how quantum computing will benefit society on multiple levels. As an early career researcher, I want to broaden my understanding<\/span>\u00a0and emphasise the value of curiosity-driven research.<\/p>\n<p><span data-contrast=\"none\">Throughout history, many of humanity\u2019s most fundamental discoveries and inventions have emerged not from immediate practical concerns but from a simple yet profound desire \u201c<\/span>to understand<span data-contrast=\"none\">.\u201d Researchers have a passion for uncovering the mysteries of nature and often their contributions have frequently had lasting and transformative impacts.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559738&quot;:240,&quot;335559739&quot;:240}\">\u00a0<\/span><\/p>\n<p><span data-contrast=\"none\">A clear example is Geoffrey Hinton, a <\/span><a href=\"https:\/\/www.nobelprize.org\/prizes\/physics\/2024\/hinton\/facts\/\"><span data-contrast=\"none\">recent Nobel Prize recipient<\/span><span data-contrast=\"none\"> (Physics, 2024)<\/span><\/a><span data-contrast=\"none\"> who continued to work on neural networks and deep learning at a time when the field was nearly dormant and out of favour. By purely utilitarian standards, he might have been expected to abandon the field; however, his curiosity drove him to persist\u2014and today, AI is revolutionising our world.\u00a0<\/span><\/p>\n<p style=\"font-weight: 400\"><strong>What are the next steps in your research? Are there any challenges ahead?<\/strong><\/p>\n<p style=\"font-weight: 400\"><span class=\"TextRun SCXW153453578 BCX4\" lang=\"EN-US\" xml:lang=\"EN-US\" data-contrast=\"none\"><span class=\"NormalTextRun SCXW153453578 BCX4\">I have been exploring examples where bicategorical structures fit well, yet <\/span><span class=\"NormalTextRun SCXW153453578 BCX4\">certain<\/span> <span class=\"NormalTextRun SCXW153453578 BCX4\">structures<\/span><span class=\"NormalTextRun SCXW153453578 BCX4\"> are absent in the literature. The next step is to <\/span><span class=\"NormalTextRun SCXW153453578 BCX4\">establish<\/span><span class=\"NormalTextRun SCXW153453578 BCX4\"> these missing links. Additionally, I am reassessing the computational complexity of certain quantum algorithms known for their speed-up over classical methods. <\/span><\/span><\/p>\n<p style=\"font-weight: 400\"><span class=\"TextRun SCXW153453578 BCX4\" lang=\"EN-US\" xml:lang=\"EN-US\" data-contrast=\"none\"><span class=\"NormalTextRun SCXW153453578 BCX4\">While the quantum advantage is <\/span><span class=\"NormalTextRun SCXW153453578 BCX4\">evident<\/span><span class=\"NormalTextRun SCXW153453578 BCX4\">, I believe the total computational cost has not been fully accounted for. By <\/span><span class=\"NormalTextRun SCXW153453578 BCX4\">leveraging<\/span><span class=\"NormalTextRun SCXW153453578 BCX4\"> classical results, the next step is to refine these bounds and provide a clearer picture of quantum versus classical efficiency for these algorithms.<\/span><\/span><span class=\"EOP SCXW153453578 BCX4\" data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559738&quot;:240,&quot;335559739&quot;:240}\">\u00a0<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Dr Rita Ahmadi is a Research Associate in the Department of Mathematics. In this blog post, she shares more about her research as part of QuEST (Centre for Quantum Engineering, Science and Technology at Imperial College London). Rita investigates quantum algorithms and their real-world applications. She also uses a branch of mathematics called category theory [&hellip;]<\/p>\n","protected":false},"author":1481,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-59","post","type-post","status-publish","format-standard","hentry","category-uncategorised"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Research Insights with Dr Rita Ahmadi - Centre for Quantum Engineering, Science and Technology<\/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:\/\/blogs.imperial.ac.uk\/imperialquest\/2024\/10\/30\/research-insights-with-dr-rita-ahmadi\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Research Insights with Dr Rita Ahmadi - Centre for Quantum Engineering, Science and Technology\" \/>\n<meta property=\"og:description\" content=\"Dr Rita Ahmadi is a Research Associate in the Department of Mathematics. In this blog post, she shares more about her research as part of QuEST (Centre for Quantum Engineering, Science and Technology at Imperial College London). Rita investigates quantum algorithms and their real-world applications. 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