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 “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.
Michael H. Freedman is a mathematician at Microsoft. In
1986, he was awarded a Fields Medal for his work on the
Poincaré conjecture, one of the most famous problems of the 20th century.
Freedman was awarded a doctorate by Princeton University in 1973. After
graduating, he was appointed a lecturer in the Department of Mathematics
at the University of California, Berkeley. In 1976 he was appointed
professor in the Department of Mathematics at the University of
California, San Diego (UCSD). He was appointed the Charles Lee Powell
chair of mathematics at UCSD in 1985. He has received numerous other
awards and honors including Sloan and Guggenheim Fellowships, a
MacArthur Fellowship, the National Medal of Science and the AMS Veblen
Prize. He is an elected member of the National Academy of Sciences, and
the American Academy of Arts and Sciences. He currently works at
University of California, Santa Barbara (at the Microsoft funded Station
Q) where his team is involved in the development of the quantum
computer.
Introduction by David Gross.
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