MATHEMATICS COLLOQUIUM
Speaker: Nick Bonesteel
Title: Quantum Computing with Braids
Affiliation: Physics, Florida State University
Date: Friday, September 30, 2005.
Place and Time: Room 101 - Love Building, 3:35-4:30 pm.
Refreshments: Room 204 - Love Building, 3:00 pm.
Abstract. A quantum computer is a (so far) hypothetical
device which would exploit the strange properties of quantum
mechanics to perform qualitatively new kinds of
computations -- most notably factoring large integers in polynomial
time. Given the delicate nature of quantum states (one need only
look at them to disturb them!) building a quantum computer will
require some method to protect these states from the environment,
while at the same time allowing for their coherent manipulation.
A particularly elegant proposal for doing this, due to Alexei
Kitaev [1] and Michael Freedman and collaborators [2], is
called "topological quantum computation" (TQC). In TQC quantum
information is stored in exotic states of matter which are
intrinsically protected from decoherence, and quantum operations
are carried out by dragging particle-like excitations (quasiparticles)
around one another in two space dimensions. The resulting
quasiparticle trajectories define world-lines in three dimensional
space-time, and the corresponding quantum operations depend only
on the topology of the braids formed by these world-lines (more
precisely, these operations form a nonabelian representation of
the braid group). In this talk I will review the basic ideas
behind TQC, and then describe recent work [3] showing how to find
braids which can be used to perform arbitrary quantum computations
using a specific kind of quasiparticle that is particularly promising
for experimental realization.
[1] A. Yu. Kitaev, Ann. of Phys. 303, 2 (2003).
[2] M. Freedman, M. Larsen, and Z. Wang, Comm. Math. Phys. 227, 605 (2002).
[3] N.E. Bonesteel, L. Hormozi, G. Zikos, and S.H. Simon, Phys. Rev. Lett,
in press.
www.arxiv.org/quant-ph/0505065.
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