Control Landscapes for Observable Preparation with Open Quantum Systems
arXiv:0708.2119 · doi:10.1063/1.2883738
Abstract
A quantum control landscape is defined as the observable as a function(al) of the system control variables. Such landscapes were introduced to provide a basis to understand the increasing number of successful experiments controlling quantum dynamics phenomena. This paper extends the concept to encompass the broader context of the environment having an influence. For the case that the open system dynamics are fully controllable, it is shown that the control landscape for open systems can be lifted to the analysis of an equivalent auxiliary landscape of a closed composite system that contains the environmental interactions. This inherent connection can be analyzed to provide relevant information about the topology of the original open system landscape. Application to the optimization of an observable expectation value reveals the same landscape simplicity observed in former studies on closed systems. In particular, no false sub-optimal traps exist in the system control landscape when seeking to optimize an observable, even in the presence of complex environments. Moreover, a quantitative study of the control landscape of a system interacting with a thermal environment shows that the enhanced controllability attainable with open dynamics significantly broadens the range of the achievable observable values over the control landscape.
References in corpus (8)
- Dynamical suppression of decoherence in two-state quantum systems
- Experimental Quantum Error Correction
- Feedback control of quantum state reduction
- Teaching the Environment to Control Quantum Systems
- Control landscapes for two-level open quantum systems
- Characterization of the Critical Submanifolds in Quantum Ensemble Control Landscapes
- Cooperating or Fighting with Control Noise in the Optimal Manipulation of Quantum Dynamics
- Controlled Quantum Open Systems
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