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SUMMARY:Symmetry vs Controllability: Spin Chains and Beyond - Xiaoting Wan
 g
DTSTART:20110519T131500Z
DTEND:20110519T141500Z
UID:TALK30629@talks.cam.ac.uk
CONTACT:Ashley Montanaro
DESCRIPTION:Hamiltonian symmetry and controllability are found to be close
 ly related in quantum control theory. For spin chains with XXZ coupling su
 bject to a local control in Z direction on the kth spin\, the total Hilber
 t space is decomposed into series of invariant excitation subspaces under 
 the dynamics. We investigate which locations of the local Z control can in
 duce controllability on the first excitation subspace. It is found that th
 e uncontrollable cases are one-to-one correspondent with the Hamiltonian e
 xternal symmetries. We also use Bethe ansatz to find all such symmetries o
 f XXZ chain. Among different local control strategies\, we concentrate on 
 local end control and derive the subspace controllability. In addition\, w
 e investigate what are the minimal control resources for a fully controlla
 ble XYZ chain\, and find the controllability proof for different control s
 trategies. Some of the results have been included in http://arxiv.org/abs/
 1012.3695 
LOCATION:MR4\, Centre for Mathematical Sciences
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