Topology of the quantum control landscape for observables

Michael Hsieh, Rebing Wu, Herschel Rabitz

Research output: Contribution to journalArticle

29 Scopus citations

Abstract

A broad class of quantum control problems entails optimizing the expectation value of an observable operator through tailored unitary propagation of the system density matrix. Such optimization processes can be viewed as a directed search over a quantum control landscape. The attainment of the global extrema of this landscape is the goal of quantum control. Local optima will generally exist, and their enumeration is shown to scale factorially with the system's effective Hilbert space dimension. A Hessian analysis reveals that these local optima have saddlepoint topology and cannot behave as suboptimal extrema traps. The implications of the landscape topology for practical quantum control efforts are discussed, including in the context of nonideal operating conditions.

Original languageEnglish (US)
Article number104109
JournalJournal of Chemical Physics
Volume130
Issue number10
DOIs
StatePublished - Mar 24 2009

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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