Populated by programmers worrying about fixes for the latest operating systems and rollouts of new applications, a software company might seem an odd place for rethinking the very foundations of computation. But at Microsoft Research, Michael Freedman is doing just that. One of the world’s most heralded mathematicians and a 1986 winner of the Fields Medal-math’s equivalent of a Nobel Prize-Freedman is spending his days pondering one of the toughest puzzles in physics: how to transform quantum computing from an abstract dream into a feasible technology. And he believes he may have found a solution.

For decades, physicists have speculated that quantum computers would define the ultimate limits for speed, size, and power in computers. The peculiar laws of quantum mechanics dictate that a “quantum bit” has almost magical computing potential. While the digital bits stored in a desktop computer correspond to either ones or zeroes, quantum bits-sometimes represented in the spin of nuclei or ions-can be both ones and zeroes simultaneously. Even odder, quantum bits are linked by a phenomenon called “entanglement.” Together, these properties mean that a computational operation on one quantum bit affects others, implying potentially awesome computing power. In theory at least, quantum computers will need only microseconds to crack even the most sophisticated encryption codes and will be able to search petabyte databases in a flash.

“The idea is to store a bit of information on each atom,” says MIT quantum computer researcher Seth Lloyd. “It’s the logical endpoint of Moore’s Law.”

At this nanoscopic scale, however, the world is anything but logical. For those hoping to build a quantum computer, that is both good and bad, and it’s where Freedman’s work comes in. Specifically, he’s trying to solve a problem that has bedeviled quantum computing researchers seeking a way to store information in the spin of nuclei or ions: even the slightest disturbance scrambles the quantum bits and destroys their entanglement. Topology, Freedman’s brand of abstract math, might provide the answer. Topologists worry about the qualities of geometric shapes rather than quantities such as size: the way strands of a knot are entwined is more important than how big the knot is. And Freedman believes that if quantum bits were based on topology, they would be far more robust.