Texas A&M University’s global prowess in mathematics was on worldwide display this week in two separate locations tied to the same research group and trending topic — Texas A&M mathematician Dr. Eric C. Rowell’s and topological quantum computing.
From the 2017 Microsoft Ignite Conference in Orlando, Fla., to the 5th annual Heidelberg Laureate Forum 2017 in Germany, the Rowell group’s expertise in topological quantum computing was the hot topic de jour – so popular in Heidelberg that Dr. Julia Plavnik, a Rowell group member and postdoctoral researcher in the Department of Mathematics, co-organized a related workshop and gave a 30-minute presentation as one of 200 invited delegates to the elite international gathering.
Topology, or the qualitative study of shapes, took center stage last year when David J. Thouless, F. Duncan M. Haldane and J. Michael Kosterlitz were honored with the 2016 Nobel Prize in Physics for pioneering the subject of topological phases of matter. Rowell, who covered the topic as part of the 2016 Nobel Prizes: The Texas A&M Perspective Symposium co-sponsored by the College of Science, boiled it down to mathematics that is fundamental to physics, complete with applications that include next-generation quantum computers capable of outperforming typical systems using topological particles, known in physics as anyons.
Quantum computers are designed to use what Rowell describes as the “strangeness of quantum mechanical systems” to perform computational tasks more efficiently than ordinary digital computers. While the more standard quantum circuit model stores quantum information in an array of qubits — each of which suffers errors from unwanted interaction with the environment — he says the topological model stores information globally, making it more robust against such errors.
“Imagine a loop of knotted string with the ends fused,” Rowell said. “If you wiggle the string slightly, the string does not become unknotted because the string’s ‘knottiness’ is a global property. The idea of this topological model came from Alexei Kitaev and Michael Freedman around 1997, and relies upon very deep theoretical mathematics and physics, such as quantum topology and topological phases of matter.”
Since 2015, Rowell has been working in tandem with Microsoft on the mathematics of topological quantum computation, which was covered in the keynote address in Orlando in a panel discussion featuring Microsoft Chief Executive Officer Satya Nadella and four Microsoft scientists, including Fields Medalist Michael Freedman. As a consultant with Microsoft Research at Station Q Santa Barbara, Rowell collaborates with Principal Researcher Zhenghan Wang and other Station Q scientists, spending up to four weeks each year in Santa Barbara. Recently, he and Wang co-authored a paper, “Mathematics of Topological Quantum Computing,” that will appear in the Bulletin of the American Mathematical Society. Closer to home, Rowell is set to offer a topics class in the subject at Texas A&M next spring.
“Working with Microsoft scientists on topological quantum computing is very exciting, not only because of the potentially revolutionary advances in computation, but also because theoretical mathematics plays a key role,” Rowell said. “For example, the question of computational power — universality — is translated into an algebraic problem involving braids and knots.”
Plavnik, meanwhile, has been ensconced since Monday in Heidelberg with hundreds of the best mathematical minds in the world, including Sir Michael Francis Atiyah, 1966 Fields Medalist and 2004 Abel Prize recipient, along with two dozen other such luminaries in the discipline. In Plavnik’s case, the invitation to participate was both figurative and literal. Mentored by Atiyah, she and Cambridge University’s Ismael Sierra jointly organized a workshop on topological quantum computing.
“We had 90 minutes to present the topic and do some interactive activities with a broad audience of around 20 young researches and some Laureates,” Plavnik said. “Sir Michael started the session by giving a panoramic introduction to the topic. Then Ismael presented the physical perspective. After them, I introduced the mathematical aspects and tools of topological quantum computing.”
Plavnik used her 30 minutes of world fame to focus on the topological language — braid group representations and their relation to the time-space trajectories of anyons — using the physical motivation to introduce some abstract concepts to help explain the underlying algebra. In addition to defining the respective terms and describing physical models, she provided examples illustrating how mathematicians are able to solve some related questions using topology, once translated into appropriate mathematical language.
Plavnik noted one nice example, in particular — a 2013 paper co-authored by Rowell, Wang and two additional collaborators, proving that there are only finitely many anyonic systems with a given number of distinguishable anyons.
“After presenting all the basic ingredients, we split the participants into groups to discuss the mathematical aspects, the physical aspects, and the informatics aspects of topological quantum computing,” Plavnik said. “We gave them some time to discuss the information, and then each group presented some of this to all of us, the participants of the workshop. We closed the workshop by answering some questions from the previous discussion and commenting about the consequence that a functional quantum computer would have for the world and for our lives.”
From her perspective, Plavnik says it’s been the experience of a lifetime made all the more fulfilling because this year’s chosen theme, quantum computing, happens to be a hot topic near and dear to her professional present and future.
“This is a wonderful environment for young researches to meet Laureates from mathematics and computer science, including Fields Medalists, Abel Prize recipients and Turing Award winners, among others,” Plavnik said. “We had two sessions of three talks each with top level researchers working in the area, showing us their perspective and their approach to this topic. There was also some time for Q&A with the speakers.
“Even during the opening ceremony of the Forum, the Minister of Science of Germany mentioned the importance of studying quantum computing. It feels really good to know that what you are doing matters.”
To learn more about Rowell and his research, including his work with Microsoft, visit http://www.math.tamu.edu/~rowell/.
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