### Abstract

Optimal control of quantum phenomena involves the introduction of a cost functional J to characterize the degree of achieving a physical objective by a chosen shaped electromagnetic field. The cost functional dependence upon the control forms a control landscape. Two theoretically important canonical cases are the landscapes associated with seeking to achieve either a physical observable or a unitary transformation. Upon satisfaction of particular assumptions, both landscapes are analytically known to be trap-free, yet possess saddle points at precise suboptimal J values. The presence of saddles on the landscapes can influence the effort needed to find an optimal field. As a foundation to future algorithm development and analyzes, we define metrics that identify the 'distance' from a given saddle based on the sufficient and necessary conditions for the existence of the saddles. Algorithms are introduced utilizing the metrics to find a control such that the dynamics arrive at a targeted saddle. The saddle distance metric and saddle-seeking methodology is tested numerically in several model systems.

Original language | English (US) |
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Article number | 465305 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 48 |

Issue number | 46 |

DOIs | |

State | Published - Oct 26 2015 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modeling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

### Keywords

- control landscape
- gradient algorithm
- quantum optimal control
- saddle point

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## Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*48*(46), [465305]. https://doi.org/10.1088/1751-8113/48/46/465305