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Critical Points of the Optimal Quantum Control Landscape: A Propagator Approach

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Abstract

Numerical and experimental realizations of quantum control are closely connected to the properties of the mapping from the control to the unitary propagator (Rabitz et al. in Science 303(5666):1998–2001, 2004). For bilinear quantum control problems, no general results are available to fully determine when this mapping is singular or not. In this paper we give sufficient conditions, in terms of elements of the evolution semigroup, for a trajectory to be non-singular. We identify two lists of “way-points” that, when reached, ensure the non-singularity of the control trajectory. It is found that under appropriate hypotheses one of those lists does not depend on the values of the coupling operator matrix.

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Acknowledgements

GT acknowledges support from the ANR-06-BLAN-0052 program and the MicMac project of INRIA Rocquencourt. TSH and HR were supported by U.S. Department of Energy.

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Authors and Affiliations

  1. Department of Chemistry, Princeton University, Princeton, NJ, 08544, USA

    Tak-San Ho & Herschel Rabitz

  2. CEREMADE, Université Paris Dauphine, Place du Marechal de Lattre de Tassigny, 75016, Paris, France

    Gabriel Turinici

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  1. Tak-San Ho
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  2. Herschel Rabitz
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  3. Gabriel Turinici
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Correspondence to Gabriel Turinici.

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Ho, TS., Rabitz, H. & Turinici, G. Critical Points of the Optimal Quantum Control Landscape: A Propagator Approach. Acta Appl Math 118, 49–56 (2012). https://doi.org/10.1007/s10440-012-9677-3

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  • DOI: https://doi.org/10.1007/s10440-012-9677-3

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