---------- Forwarded message ----------
From: Xiao-Gang Wen <wen(a)dao.mit.edu>
Date: 2011/4/3
Subject: Fw: upcoming Applied Math Colloquium on topological order and
quantum computing
To: aaronson(a)csail.mit.edu
Hi
Zhenghan Wang from Microsoft (
http://stationq.cnsi.ucsb.edu/~wang/) is
giving the applied mathematics colloquium this Monday (April 4) at
4:30pm in 2-105 on topological phases and quantum computing, which may
be of interest to you and your students.
Feel free to forward the info about the talk to anyone who might be
interested.
Xiao-Gang
Begin forwarded message:
Applied Mathematics Colloquium, April 4 2011, 4:30pm, Room 2-105
Title: Topological phases of matter: modeling and application to
quantum computing
Speaker: Zhenghan Wang, Microsoft Research
ABSTRACT:
Topological phases of matter are exotic quantum states of matter
that possess an elusive order, dubbed topological order by X.-G.
Wen. Elementary excitations in topological phases of matter are
quasi-particles, named anyons by F. Wilczek, which obey neither
bosonic nor fermionic statistics. Modeling of two dimensional
topological phases of matter utilizes a diverse variety of
mathematics: (2+1)-topological quantum field theory as effective
theory, conformal field theory as edge theory, and modular tensor
category as an algebraic theory of anyons. A topological phase of
matter that harbors non-abelian anyons is essentially a topological
quantum computer immune to local errors and thus provides a
realization of fault-tolerant quantum computation.
In this survey talk, we will start with the only currently known
examples of topological phases of matter---fractional quantum Hall
liquids--and explain their theoretical models.
The effective theories of fractional quantum Hall liquids are the
quantum Witten-Chern-Simons theories, and the major components of
the modeling ground state wave functions of quantum Hall liquids are
translation-invariant symmetric polynomials with an arbitrary number
of variables (most such polynomials occur as conformal blocks of the
conformal field theories which describe the edges). Next, we will
discuss how quantum computing is carried out by braiding non-abelian
anyons. We will address when braiding alone can lead to universal
quantum gates and hence Shoræ¯ factoring algorithm can be
implemented by a topological quantum computer. Finally, we
conjecture that the failure of the universality of braiding gates is
related to a form of explicit locality in topological quantum field
theory involving the Yang-Baxter equation.
------- End of Forwarded Message
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-----------------------------------------
Xiao-Gang Wen
Cecil and Ida Green Professor of Physics
Department of Physics, 6C-317 Phone 617-253-5016
Massachusetts Institute of Technology Fax 617-253-2562
77 Massachusetts Avenue
Cambridge, MA 02139
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