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Chinese Control Conference (CCC)

Robust stabilization of uncertain quantum open systems

Kai Li, Ming Zhang

Published Jul 1, 2017• 0 citations
Publisher

Abstract

We exploit how to overcome phase damping decoherence when the phase damping parameters are uncertain. It is shown that the “relaxed” control goal may be achieved by combing simple open-loop coherent control with periodic projective measurements. Both the sufficient conditions and constructive design procedures are presented. The control design is reduced to selecting the period of projective measurements and fidelity-truncated time based on two lower-bound functions for both probability and fidelity performance. When both probability and fidelity performances are specified, the stabilization time is further maximized by searching the “optimal” period of projective measurements. It is also exemplified that larger uncertainties may lead to shorter stabilization time for the given performance level.

DOI
10.23919/chicc.2017.8028914

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We exploit how to overcome phase damping decoherence when the phase damping parameters are uncertain. It is shown that the “relaxed” control goal may be achieved by combing simple open-loop coherent control with periodic projective measurements. Both the sufficient conditions and constructive design procedures are presented. The control design is reduced to selecting the period of projective measurements and fidelity-truncated time based on two lower-bound functions for both probability and fidelity performance. When both probability and fidelity performances are specified, the stabilization time is further maximized by searching the “optimal” period of projective measurements. It is also exemplified that larger uncertainties may lead to shorter stabilization time for the given performance level.
We propose a scheme to overcome phase damping decoherence by periodically performing open loop tracking control and projective measurement. Although it is impossible to stabilize a qubit subject to Markovian dynamics only by open loop coherent control, one can attain a ``softened'' control goal with the help of periodical projective measurement. The ``softened'' control objective in our scheme is to keep the state of the controlled qubit to stay near a reference pure state with a high probability for a sufficiently long time. Two suboptimal control problems are given in the sense of trace distance and fidelity, respectively, and they are eventually reduced to the design of a period TTT. In our scheme, one can choose the period TTT as long as possible if the ``softened'' control goal is attained. This is in contrast to the observation that quantum Zeno effect takes place only if measurements are performed in a very frequent manner, i.e., the period T\mathit{T}T must be extremely small.
We propose and discuss a novel concept of robust set stabilization by permissible controls; this concept is helpful when dealing with both a priori information of model parameters and different permissible controls including quantum measurements.Both controllability and stabilization can be regarded as the special case of the novel concept.An instance is presented for a kind of uncertain open quantum systems to further justify this generalized concept.It is underlined that a new type of hybrid control based on periodically perturbed projective measurements can be the permissible control of uncertain open quantum systems when perturbed projective measurements are available.The sufficient conditions are given for the robust set stabilization of uncertain quantum open systems by the hybrid control, and the design of the hybrid control is reduced to selecting the period of measurements.
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