

International youth conference "Geometry & Control"
April 15, 2014 17:00, Poster session, Moscow, Steklov Mathematical Institute of RAS






Optimal Quantum Control of the Landau–Zener System by Measurements
Alexander Pechen^{}, Anton Trushechkin^{} ^{} Steklov Mathematical Institute of Russian Academy of
Sciences, Moscow, Russia

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Abstract:
In the recent works by A. Pechen et al. and F. Shuang et al. a problem of
optimal control of a twolevel quantum system by nonselective measurements
was considered. In these works, the time instants of measurements are
fixed; the maximization of a transition probability is performed over
various observables. Note that, in case of twolevel system, quantum
dynamics without measurements is a unitary evolution in the twodimensional
complex vector space; a von Neumann observable is specified by a unit
vector of the space.
\looseness=1
In the present work, we consider a special (but important) case of
twolevel quantum system, namely, the Landau–Zener system (spin1/2
charged particle in timedependent magnetic field). We consider a problem
of maximization of a transition probability when an observable is fixed,
but instants of measurements are variable. We obtain full exact solution of
the maximization problem in the large coupling constant limit for an
arbitrary number of measurements. Also we establish a duality between two
different problem statements: maximization over various observables under
fixed time instants of measurements and maximization over various time
instants under a fixed observable.
Language: English

