Physics – Quantum Physics
Scientific paper
2010-06-18
Phys. Rev. A 84, 012109 (2011)
Physics
Quantum Physics
10 figures
Scientific paper
Quantum optimal control experiments and simulations have successfully manipulated the dynamics of systems ranging from atoms to biomolecules. Surprisingly, these collective works indicate that the effort (i.e., the number of algorithmic iterations) required to find an optimal control field appears to be essentially invariant to the complexity of the system. The present work explores this matter in a series of systematic optimizations of the state-to-state transition probability on model quantum systems with the number of states $N$ ranging from 5 through 100. The optimizations occur over a landscape defined by the transition probability as a function of the control field. Previous theoretical studies on the topology of quantum control landscapes established that they should be free of sub-optimal traps under reasonable physical conditions. The simulations in this work include nearly 5000 individual optimization test cases, all of which confirm this prediction by fully achieving optimal population transfer of at least 99.9% upon careful attention to numerical procedures to ensure that the controls are free of constraints. Collectively, the simulation results additionally show invariance of required search effort to system dimension $N$. This behavior is rationalized in terms of the structural features of the underlying control landscape. The very attractive observed scaling with system complexity may be understood by considering the distance traveled on the control landscape during a search and the magnitude of the control landscape slope. Exceptions to this favorable scaling behavior can arise when the initial control field fluence is too large or when the target final state recedes from the initial state as $N$ increases.
Moore Katharine W.
Rabitz Herschel
No associations
LandOfFree
Exploring Quantum Control Landscapes: Topology, Features, and Optimization Scaling does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Exploring Quantum Control Landscapes: Topology, Features, and Optimization Scaling, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exploring Quantum Control Landscapes: Topology, Features, and Optimization Scaling will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-260813