Colloquium on July 15, 2009

Michael Freedman
Microsoft Corporation, Station Q, Santa Barbara, USA

Topology, Physics, and Complexity: The Birthing of the Quantum Computer

Computers have wrought huge changes in what we do and how we live. But the underlying logic of our computers is of the 19th century. Computers might, instead, be designed to ?-Y´think¡ in a quantum mechanical way. The tidal wave that brought us quantum mechanics is set to wash over us again 100 years later. We cannot know in which ways the quantum computer will change our world, but there is reason to believe that quantum computing is the ultimate mode of information processing consistent with physics. So the short answer to, ´What will quantum computers do?¡ is, ´Everything possible.¡ Topology is geometry after you have forgotten local details; it deals with discrete structures. In physics local detail is usually of paramount importance, however there are rare low temperature systems whose most important properties are topological in nature. The discrete nature of topology may allow us to control quantum mechanical evolutions in these systems with amazing precision. This is just what quantum computation requires.