CONTACTS
 Coordinator
Diego Dalvit

Quantum Lunch Location:
TDivision Conference Room, TA3,
Building 123, Room 121

Quantum Institute: Visitor Schedule
The Quantum Lunch is regularly held on Thursdays in the Theoretical Division Conference Room, TA3, Building 123, Room 121. For more information, contact Diego Dalvit.
November 29, 2007
Thursday, 12:30 PM
John Yard,
TCNLS
Applications of Schur Duality to Quantum Information and Computation
Abstract
Decomposing tensor representations is at the heart of much
of quantum mechanics. For instance, the tensor product of two
spin1/2 representations of SU(2) decomposes as a direct sum of a
singlet and a triplet subspace. More generally, the n'th tensor power
of the standard representation of SU(d) decomposes as a direct sum of
tensor products of irreps of SU(d) and the symmetric group of
permutations on n letters, yielding a dual relationship (known as
Schur duality) between representations of SU(d) and of the symmetric
group. In this talk, I will give applications of Schur duality and
its generalizations to quantum information theory and quantum
computation. For this, I will first show how Schur duality leads to
efficient protocols for processing quantum data. I will then discuss
a deformed version of this duality where the unitary group is replaced
by its corresponding quantum group and the symmetric group by the
braid group on n strands, showing how it leads to definitions of the
Jones and HOMFLY polynomial invariants of knots and links, together
with algorithms for their approximation on a quantum computer. I will
then discussion an analogous decomposition occurring when the unitary
group is replaced by an orthogonal or symplectic group and the
symmetric group by a Brauer algebra. I will then outline how the
quantum group versions of these decompositions lead to definitions of
the Kauffman polynomial link invariant, concluding with a discussion
of how the Kauffman polynomial can be approximated on a quantum
computer.
