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CATEGORIES:CQIF Seminar
SUMMARY:Symmetry vs Controllability: Spin Chains and Beyon
d - Xiaoting Wang
DTSTART;TZID=Europe/London:20110519T141500
DTEND;TZID=Europe/London:20110519T151500
UID:TALK30629AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/30629
DESCRIPTION:Hamiltonian symmetry and controllability are found
to be closely related in quantum control theory.
For spin chains with XXZ coupling subject to a loc
al control in Z direction on the kth spin\, the to
tal Hilbert space is decomposed into series of inv
ariant excitation subspaces under the dynamics. We
investigate which locations of the local Z contro
l can induce controllability on the first excitati
on subspace. It is found that the uncontrollable c
ases are one-to-one correspondent with the Hamilto
nian external symmetries. We also use Bethe ansatz
to find all such symmetries of XXZ chain. Among d
ifferent local control strategies\, we concentrate
on local end control and derive the subspace cont
rollability. In addition\, we investigate what are
the minimal control resources for a fully control
lable XYZ chain\, and find the controllability pro
of for different control strategies. Some of the r
esults have been included in http://arxiv.org/abs/
1012.3695
LOCATION:MR4\, Centre for Mathematical Sciences
CONTACT:Ashley Montanaro
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