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Abstract :
[en] We solve the problem of steering a three-level
quantum system from one eigen-state to another in minimum
time and study its possible extension to the time-optimal control
problem for a general n-level quantum system. For the threelevel
system we find all optimal controls by finding two types of
symmetry in the problem: Z2 × S3 discrete symmetry and S1
continuous symmetry, and exploiting them to solve the problem
through discrete reduction and symplectic reduction. We then
study the geometry, in the same framework, which occurs in
the time-optimal control of a general n-level quantum system.
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