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The Surprising Ease of Finding Optimal Solutions for Controlling Nonlinear Phenomena in Quantum and Classical Complex
Herschel Rabitz1, Benjamin Russell1, Tak-San Ho1
1Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States.
The Journal of Physical Chemistry. A
|May 4, 2023
Summary
Complex systems in quantum and classical physics are surprisingly easy to control. This ease stems from analyzing the "control landscape" and its underlying assumptions, simplifying optimization searches.
Area of Science:
- Covers nonlinear phenomena in both quantum and classical complex systems.
- Encompasses diverse fields from atomic manipulation to natural selection and directed evolution.
Background:
- Optimal control of complex systems is often surprisingly easy to achieve across various scientific domains.
- This ease is observed despite the inherent complexity of these systems.
Purpose of the Study:
- To explain the observed ease of achieving optimal control in diverse complex systems.
- To introduce the concept of the "control landscape" as a unifying framework.
Main Methods:
- Defines the "control landscape" as the optimization objective versus control variables.
- Proposes three underlying assumptions for readily finding good outcomes: existence of an optimum, local movement, and sufficient resources.
- Discusses the use of gradient-like and stochastic algorithms based on landscape smoothness.
Main Results:
- Suggests that control landscapes provide a unified explanation for the ease of optimization.
- Highlights that successful searches are often short, despite high-dimensional control spaces.
- Algorithm choice (gradient-like vs. stochastic) depends on landscape properties (smooth vs. rough).
Conclusions:
- The systematic ease of achieving good control in complex systems can be understood through control landscape analysis.
- The validity of the three core assumptions (optimum existence, local movement, resource availability) is crucial for each specific scenario.
- Efficient optimization is achievable even in high-dimensional control spaces.
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