Utah State University mathematicians Nathan Geer and Matthew Young, along with their students and collaborators throughout the world, revel in exploring the exquisite and puzzling intricacies of mathematical theory. Some 14 years ago, Geer and colleagues developed non-semisimple topological quantum field theories (TQFTs), a mathematical framework to study a wide range of physical theories, which have blossomed into continuing research.<\/p>\n
\u201cWe did this purely from a mathematical perspective \u2014 simply guided by the internal logic and beauty of the subject, following where the ideas led us and adding new collaborators along the way,\u201d says Geer, professor in USU\u2019s Department of Mathematics and Statistics<\/a>. \u201cYet this abstract work has become directly relevant to quantum physics, connecting with mathematical physics and opening new doors for discovery.\u201d<\/p>\n Remarkably, he says, it turns out non-semisimple theories are more powerful than the traditional semisimple ones and possess novel properties.<\/p>\n \u201cThe exciting part of this discovery is these new properties allow researchers to predict the existence of entirely new kinds of quantum particles \u2014 illustrating the beauty of mathematics,\u201d Geer says. \u201cWhat we\u2019re finding could help to unlock some vexing obstacles to the widespread implementation of quantum computing.\u201d<\/p>\n Geer and his team\u2019s TQFT research is cited in recent articles in PhysicsWorld<\/a> and Scientific American<\/a>, which detail findings published in the journal Nature Communications<\/a> by Geer and Young\u2019s longtime peer and frequent collaborator, Aaron Lauda, professor and dean at the University of Southern California. Lauda and his team use Geer\u2019s TQFTs to suggest a breakthrough path through current quantum computer barriers.<\/p>\n And what are those barriers? Thinking back to the beginnings of personal computer use helps to explain challenges posed by quantum computing.<\/p>\n People of a certain age will remember when the 1982 sci-fi movie TRON pioneered computer-generated imagery to illustrate binary digits \u2014 \u201cbits\u201d \u2014 as cranky, beleaguered polyhedral-shaped objects chirping \u201cyes\u201d and \u201cno\u201d as they sped, collided and bounced through cyberspace. The visual representation helped fledging users comprehend the inner workings of an emerging explosion of accessible, mass-market personal computers.<\/p>\n As mystifying as it was when introduced to the ordinary user, digital or \u201cclassical\u201d computing, with its either black or white discrete states, is much simpler than leveraging quantum phenomena to crunch data.<\/p>\n In contrast, quantum computing, which promises exponentially faster and more accurate computational power and problem-solving uses quantum bits, or \u201cqubits,\u201d which can be \u201cyes\u201d and \u201cno\u201d simultaneously and linked with other qubits. Yet these fundamental units of quantum information \u2014 the building blocks of this new technology \u2014 are very fragile.<\/p>\n \u201cQuantum computing relies on the ability to very accurately manipulate quantum systems \u2013 for example, moving a small particle to a specified point in space and keeping it there,\u201d says Young, assistant professor in the Department of Mathematics and Statistics. \u201cA challenge with this technology is preventing errors from entering the system, causing particles to, using the building block analogy, shift and topple out of place.\u201d<\/p>\n And that\u2019s where the TQFTs he, Geer, their students and collaborators are studying may offer a path forward.<\/p>\n \u201cIn theory, TQFTs provide a sturdier option, which spreads the information out over a stronger, more stable area, making qubits less vulnerable to environmental noise,\u201d Geer says.<\/p>\n The different properties of non-semisimple TQFTs would, in theory, lead to better qubits, though they\u2019re not yet physically realized, he says. \u201cBut this approach gives engineers and physicists a mathematical foundation to look for them.\u201d<\/p>\n Following this idea, Lauda and his collaborators\u2019 recent paper outlines a concrete proposal to use non-semisimple TQFTs to realize new qubits, which they call \u201cneglectons.\u201d<\/p>\n \u201cThe name neglecton was chosen because these quasi-particles are neglected in more traditional semisimple approaches,\u201d Geer says.<\/p>\n Geer and Young, both National Science Foundation CAREER research award recipients, along with their students, continue to actively pursue non-semisimple TQFT and its mathematical physics applications, including its implications for the future of quantum computing.<\/p>\n \u201cIf neglectons truly exist, it would be a dream come true to see the theoretical mathematics we\u2019ve worked on lead to a real-world discovery,\u201d Geer says.<\/p>\n","protected":false},"excerpt":{"rendered":"Utah State University mathematicians Nathan Geer and Matthew Young, along with their students and collaborators throughout the world,…\n","protected":false},"author":2,"featured_media":169195,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[46],"tags":[191,10815,3,1026,16992,13546,74,7349,3324,57973],"class_list":{"0":"post-169194","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-computing","8":"tag-computing","9":"tag-media","10":"tag-news","11":"tag-press-releases","12":"tag-stories","13":"tag-story","14":"tag-technology","15":"tag-today","16":"tag-utah","17":"tag-utah-state-university"},"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts\/169194","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/comments?post=169194"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts\/169194\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/media\/169195"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/media?parent=169194"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/categories?post=169194"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/tags?post=169194"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}