Journal
JOURNAL OF COMPUTATIONAL AND THEORETICAL NANOSCIENCE
Volume 6, Issue 8, Pages 1837-1863Publisher
AMER SCIENTIFIC PUBLISHERS
DOI: 10.1166/jctn.2009.1246
Keywords
Quantum Information; Optimal Control Theory; Open Quantum Systems; Qubit; Quantum Gate; Decoherence; Josephson Junction; Quantum Dot
Categories
Funding
- FWF [P18829]
- Austrian Science Fund (FWF) [P18829] Funding Source: Austrian Science Fund (FWF)
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This article provides a review of recent developments in the formulation and execution of optimal control strategies for the dynamics of quantum systems. A brief introduction to the concept of optimal control, the dynamics of of open quantum systems, and quantum information processing is followed by a presentation of recent developments regarding the two main tasks in this context: state-specific and state-independent optimal control. For the former, we present an extension of conventional theory (Pontryagin's principle) to quantum systems which undergo a non-Markovian time-evolution. Owing to its importance for the realization of quantum information processing, the main body of the review, however, is devoted to state-independent optimal control. Here, we address three different approaches: an approach which treats dissipative effects from the environment in lowest-order perturbation theory, a general method based on the time-evolution superoperator concept, as well as one based on the Kraus representation of the time-evolution superoperator. Applications which illustrate these new methods focus on single and double qubits (quantum gates) whereby the environment is modeled either within the Lindblad equation or a bath of bosons (spin-boson model). While these approaches are widely applicable, we shall focus our attention to solid-state based physical realizations, such as semiconductor-and superconductor-based systems. While an attempt is made to reference relevant and representative work throughout the community, the exposition will focus mainly on work which has emerged from our own group.
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