*Chetan Nayak (l) and Michael Freedman Photo by Nell Campbell.*

In the spring of 1997, former graduate students at the University of California at San Diego invited Michael Freedman, a topologist who was awarded the Fields Medal in 1986 for his work on the Poincaré conjecture, to give a talk at Microsoft Research in Redmond, Wash. At the conclusion of that talk, an employee then there, physicist Nathan Myrvold, offered Freedman a job to work, more or less, on whatever he wanted.

Freedman’s talk must have indicated to Myrvold that what Freedman wanted to work on was an idea he had in the late 1980s for possible applications of topology to computation.

Freedman accepted the job offer and assembled a small group of mathematicians and physicists to pursue the idea. That Microsoft group has taken up temporary residence at the KITP until its permanent offices are ready in the building, now under construction, that will house the California NanoSystems Institute (CNSI), located next to the side of Kohn Hall with the KITP’s former main entrance.

Why locate his topnotch research group in Santa Barbara? Said Freedman,

“The KITP is the center of the world for theoretical physics, I think. I wanted our group either to be in KITP or an easy stone’s throw away. And that’s the way it’s working out. Here at Santa Barbara, I am in this new growing place plus there is this physics institute, which is cycling through programs that bring everyone I would ever want to talk to right to me.”

“The people I wanted to recruit to work with me (I know them all; every single person has been a collaborator) were all coming from universities. I thought it would be very difficult to assemble this group because, obviously, the people you want for a project like this are people who have a lot of options in their lives. I am not the only person who realizes their brilliance. The people I wanted to bring on board would look at this opportunity and say, ‘This is going to be the most vibrant place to do my work and also culturally easy, on a university campus.’”

Employees of the Microsoft group hold UCSB adjunct positions in the departments of Mathematics and Physics, “as is most appropriate depending on our training,” said Freedman. “We all expect to be close participants in the university life so we will advise graduate students, for example, and in fact we will probably support graduate students as well. We’ve already given a two-quarter course in the Mathematics Department that had 16 to 18 people in attendance at any given meeting. Many physicists came; Matthew Fisher and Andreas Ludwig [both UCSB faculty and theorists] and all their condensed matter students trekked over to South Hall,” where the Mathematics Department resides.

### The Witten Effect

The impetus for Freedman’s idea to use topological phases for quantum computing came from his engagement with the ideas for which theoretical physicist Edward Witten (a student at Princeton in the mid-1970s of KITP Director David Gross) was to win the Fields Medal in 1990.

Freedman, on leave from UC San Diego in 1988, attended a seminar in the Harvard Mathematics Department. Said Freedman, “We went through Witten’s paper” on quantum field theory and the Jones polynomial. “I had the idea then that the technology of Witten’s paper could potentially be used to make a new kind of computer.”

Some British mathematicians showed in 1988 that evaluating the Jones polynomial was computationally difficult. At about the same time, Freedman said, “I was working very hard in this seminar to understand Witten’s paper, where he was saying, in a sense, that if you do the right kind of physical experiment, you do the Jones polynomial. So a light flashed on in my head, which said, it looks stupid to calculate the Jones polynomial on an ordinary computer if there is some laboratory physics you could do to get the answer. And that must mean that there is a new kind of computer that hasn’t been thought of yet.”

Freedman got very excited. “I talked to everyone I knew or could find at Harvard to ask if we could build a quantum computer this way. I wanted to know what would we need to make this physics that Witten is talking about. In a sense I was asking the question two years too early. Everyone was very negative. One source said, ‘What Witten thinks of as physics is not what you learned in high school’; that, in effect, there is no material system in the world that acts the way his equations dictate.”

But there is — the fractional quantum Hall effect (FQHE). Though discovered in 1982, the FQHE systems known to physicists at the time of Freedman’s quest in 1988 exhibited fractional but ordinary abelian statistics, and not the non-abelian statistics of the mathematical structures discovered by theoretical physicists Greg Moore and Nathan Seiborg in 1987, which were integral to Witten’s work on the Jones polynomial and which Freedman’s idea for a quantum computer required. (“Non-abelian” roughly pertains in group theory to a pair that is noncommutative, such that “ab” is not equivalent to “ba.”)

Moore, a string theorist (now at Rutgers University in New Jersey), joined his Yale colleague, condensed matter physicist Nicholas Read, in the early 1990s to search for FQHE states with non-abelian statistics. They found several.

Freedman found out about FQHE in a popular article written by UCLA physicist Steve Kivelson and published in Scientific American in 1996. “Then,” said Freedman, “I really got interested. I knew that there were physical systems that were governed by a Chern-Simons term that actually would be producing observations potentially that would be exactly what Witten had talked about.”

Afire with that realization, Freedman shortly thereafter accepted his former students’ invitation to talk at Microsoft Research. Of course, his subject was the topological phases approach to quantum computing, whose exploration has now become the main mission of the Microsoft project.

“The possibility was out there,” said Freedman, “as a very abstract mathematical idea in Witten’s paper, but Witten proposed no connection to the real world.”

In brief, it is an ironic tale of the interplay between two remarkable minds: the physicist who had the great abstract mathematical insights (via sidetracking from string theory), and the pure mathematician who intuited the relevance of those insights to condensed matter physics and the “real world” of potentially transformative technology.