Searching for an optimal control in the presence of saddles on the quantum-mechanical observable landscape
Abstract
The broad success of theoretical and experimental quantum optimal control is intimately connected to the topology of the underlying control landscape. For several common quantum control goals, including the maximization of an observable expectation value, the landscape has been shown to lack local optima if three assumptions are satisfied: (i) the quantum system is controllable, (ii) the Jacobian of the map from the control field to the evolution operator is full rank, and (iii) the control field is not constrained. In the case of the observable objective, this favorable analysis shows that the associated landscape also contains saddles, i.e., critical points that are not local suboptimal extrema. In this paper, we investigate whether the presence of these saddles affects the trajectories of gradient-based searches for an optimal control. We show through simulations that both the detailed topology of the control landscape and the parameters of the system Hamiltonian influence whether the searches are attracted to a saddle. For some circumstances with a special initial state and target observable, optimizations may approach a saddle very closely, reducing the efficiency of the gradient algorithm. Encounters with such attractive saddles are found to be quite rare. Neither the presence of a large numbermore »
- Authors:
-
- Princeton Univ., NJ (United States)
- Tsinghua Univ., Beijing (China)
- Publication Date:
- Research Org.:
- Princeton Univ., NJ (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC); National Natural Science Foundation of China (NSFC); US Army Research Office (ARO); National Science Foundation (NSF)
- OSTI Identifier:
- 1535745
- Alternate Identifier(s):
- OSTI ID: 1365603
- Grant/Contract Number:
- FG02-02ER15344; W911NF-16-1-0014; CHE-1464569
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review A
- Additional Journal Information:
- Journal Volume: 95; Journal Issue: 6; Journal ID: ISSN 2469-9926
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; optics; physics; coherent control; quantum control; semiclassical physics
Citation Formats
Riviello, Gregory, Wu, Re-Bing, Sun, Qiuyang, and Rabitz, Herschel. Searching for an optimal control in the presence of saddles on the quantum-mechanical observable landscape. United States: N. p., 2017.
Web. doi:10.1103/physreva.95.063418.
Riviello, Gregory, Wu, Re-Bing, Sun, Qiuyang, & Rabitz, Herschel. Searching for an optimal control in the presence of saddles on the quantum-mechanical observable landscape. United States. https://doi.org/10.1103/physreva.95.063418
Riviello, Gregory, Wu, Re-Bing, Sun, Qiuyang, and Rabitz, Herschel. Thu .
"Searching for an optimal control in the presence of saddles on the quantum-mechanical observable landscape". United States. https://doi.org/10.1103/physreva.95.063418. https://www.osti.gov/servlets/purl/1535745.
@article{osti_1535745,
title = {Searching for an optimal control in the presence of saddles on the quantum-mechanical observable landscape},
author = {Riviello, Gregory and Wu, Re-Bing and Sun, Qiuyang and Rabitz, Herschel},
abstractNote = {The broad success of theoretical and experimental quantum optimal control is intimately connected to the topology of the underlying control landscape. For several common quantum control goals, including the maximization of an observable expectation value, the landscape has been shown to lack local optima if three assumptions are satisfied: (i) the quantum system is controllable, (ii) the Jacobian of the map from the control field to the evolution operator is full rank, and (iii) the control field is not constrained. In the case of the observable objective, this favorable analysis shows that the associated landscape also contains saddles, i.e., critical points that are not local suboptimal extrema. In this paper, we investigate whether the presence of these saddles affects the trajectories of gradient-based searches for an optimal control. We show through simulations that both the detailed topology of the control landscape and the parameters of the system Hamiltonian influence whether the searches are attracted to a saddle. For some circumstances with a special initial state and target observable, optimizations may approach a saddle very closely, reducing the efficiency of the gradient algorithm. Encounters with such attractive saddles are found to be quite rare. Neither the presence of a large number of saddles on the control landscape nor a large number of system states increases the likelihood that a search will closely approach a saddle. Finally, even for applications that encounter a saddle, well-designed gradient searches with carefully chosen algorithmic parameters will readily locate optimal controls.},
doi = {10.1103/physreva.95.063418},
journal = {Physical Review A},
number = 6,
volume = 95,
place = {United States},
year = {Thu Jun 22 00:00:00 EDT 2017},
month = {Thu Jun 22 00:00:00 EDT 2017}
}
Web of Science
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- arXiv
Works referencing / citing this record:
Optimal and robust control of quantum state transfer by shaping the spectral phase of ultrafast laser pulses
journal, January 2018
- Guo, Yu; Dong, Daoyi; Shu, Chuan-Cun
- Physical Chemistry Chemical Physics, Vol. 20, Issue 14