High Fidelity and Fast Population Transfer in a System of Interacting Two-Level Particles via Optimal Control

2018 ◽  
Vol 57 (12) ◽  
pp. 3865-3873 ◽  
Author(s):  
Yu Guo
Author(s):  
Dionisis Stefanatos ◽  
Emmanuel Paspalakis

Abstract We use optimal control theory to show that for a closed Λ-system where the excited intermediate level decays to the lower levels with a common large rate, the optimal scheme for population transfer between the lower levels is actually optical pumping. In order to obtain this result we exploit the large decay rate to eliminate adiabatically the weakly coupled excited state, then perform a transformation to the basis comprised of the dark and bright states, and finally apply optimal control to this transformed system. Subsequently, we confirm the optimality of the optical pumping scheme for the original closed Λ-system using numerical optimal control. We also demonstrate numerically that optical pumping remains optimal when the decay rate to the target state is larger than that to the initial state or the two rates are not very different from each other. The present work is expected to find application in various tasks of quantum information processing, where such systems are encountered


1996 ◽  
Vol 104 (4) ◽  
pp. 1173-1178 ◽  
Author(s):  
Ningjun Wang ◽  
Herschel Rabitz

2002 ◽  
Vol 43 (5) ◽  
pp. 2107 ◽  
Author(s):  
Ugo Boscain ◽  
Grégoire Charlot ◽  
Jean-Paul Gauthier ◽  
Stéphane Guérin ◽  
Hans-Rudolf Jauslin

2004 ◽  
Vol 21 (10) ◽  
pp. 1930-1933 ◽  
Author(s):  
Zhang Xiang-Yun ◽  
Sun Zhen-Rong ◽  
Chen Guo-Liang ◽  
Wang Zu-Geng ◽  
X Zhi-Zhan ◽  
...  

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 84
Author(s):  
Qi Zhang ◽  
Xi Chen ◽  
David Guéry-Odelin

We consider fast high-fidelity quantum control by using a shortcut to adiabaticity (STA) technique and optimal control theory (OCT). Three specific examples, including expansion of cold atoms from the harmonic trap, atomic transport by moving harmonic trap, and spin dynamics in the presence of dissipation, are explicitly detailed. Using OCT as a qualitative guide, we demonstrate how STA protocols designed from inverse engineering method can approach with very high precision optimal solutions built about physical constraints, by a proper choice of the interpolation function and with a very reduced number of adjustable parameters.


2019 ◽  
Author(s):  
Mazen Al Borno ◽  
Saurabh Vyas ◽  
Krishna V. Shenoy ◽  
Scott L. Delp

AbstractThe speed-accuracy tradeoff is a fundamental aspect of goal-directed motor behavior, empirically formalized by Fitts’ law, which relates movement duration to movement distance and target width. Here, we introduce a computational model of three-dimensional upper extremity movements that reproduces well-known features of reaching movements and is more biomechanically realistic than previous models. Critically, these features arise without the need of signal-dependent noise. We analyzed motor cortical neural activity from monkeys reaching to targets of different sizes. We found that the contribution of preparatory neural states to movement duration variability was greater for smaller targets than larger targets, and that movements to smaller targets exhibited less variability in preparatory neural states, but greater movement duration variability. Taken together, these results suggest that Fitts’ law emerges from greater task demands constraining the optimization landscape in a fashion that reduces the number of “good” control solutions (i.e., faster reaches). Thus, the speed-accuracy tradeoff could be a consequence of motor planning variability and optimal control theory, and not exclusively signal-dependent noise, as is currently held.Significance StatementA long-standing challenge in motor neuroscience is to understand the relationship between movement speed and accuracy, known as the speed-accuracy tradeoff. We introduce a computational model of reaching movements based on optimal control theory using a realistic model of musculoskeletal dynamics. The model synthesizes three-dimensional point-to-point reaching movements that reproduce kinematics features reported in motor control studies. Such high-fidelity modeling reveals that the speed-accuracy tradeoff as described by Fitts’ law emerges even without the presence of motor noise, which is commonly believed to underlie the speed-accuracy tradeoff. This suggests an alternative theory based on suboptimal control solutions. The crux of this theory is that some features of human movement are attributable to planning variability rather than execution noise.


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