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Quantum optimally controlled transition landscapes.

Herschel A Rabitz1, Michael M Hsieh, Carey M Rosenthal

  • 1Department of Chemistry, Princeton University, Princeton, NJ 08544, USA. hrabitz@princeton.edu

Science (New York, N.Y.)
|March 27, 2004
PubMed
Summary
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Finding optimal quantum control is simplified: the landscape has only perfect or no control extrema, avoiding local traps. This applies universally to controllable quantum systems, even with noise.

Area of Science:

  • Quantum Control
  • Quantum Information Science
  • Theoretical Physics

Background:

  • Experimental and simulation studies suggest high-quality quantum control is achievable.
  • Understanding the structure of quantum control landscapes is crucial for efficient optimization.

Purpose of the Study:

  • To theoretically prove the structure of quantum control landscapes for unconstrained controllable quantum systems.
  • To determine if suboptimal local extrema exist in these landscapes.
  • To investigate the universality and robustness of the landscape structure.

Main Methods:

  • Mathematical proof analyzing the extrema of the transition probability landscape.
  • Consideration of unconstrained control fields for quantum systems.
  • Analysis of the impact of weak control field noise and environmental decoherence.

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Main Results:

  • The quantum control landscape for unconstrained systems exhibits only two types of extrema: perfect control or no control.
  • No suboptimal local extrema exist, eliminating traps in the search for optimal quantum control.
  • The landscape structure is universal for quantum systems of the same dimension, independent of the specific Hamiltonian.
  • Weak noise and decoherence preserve the general landscape structure, albeit with reduced resolution.

Conclusions:

  • The inherent structure of quantum control landscapes simplifies the search for optimal control strategies.
  • The absence of local extrema provides a robust theoretical foundation for achieving high-fidelity quantum control.
  • These findings have broad implications for various quantum technologies relying on precise control.