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Topological Phase Transitions in a Constrained Two-Qubit Quantum Control Landscape.

Nicolò Beato1, Pranay Patil2,3, Marin Bukov1

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This summary is machine-generated.

Researchers discovered new topological control landscape phase transitions (CLPTs) in quantum control. These transitions, linked to topology changes, can be detected in current experiments.

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Area of Science:

  • Quantum Information Science
  • Quantum Control Theory
  • Topological Data Analysis

Background:

  • Optimal quantum control aims to find control protocols that steer quantum systems efficiently.
  • Control landscape phase transitions (CLPTs) signify abrupt alterations in optimal control protocols as parameters change.
  • Existing research primarily focuses on CLPTs related to the geometry of the optimal control set.

Purpose of the Study:

  • To introduce and characterize a new class of CLPTs based on topological properties.
  • To investigate these topological CLPTs in the context of a two-qubit state-preparation problem.
  • To establish methods for detecting these topological transitions in experimental settings.

Main Methods:

  • Utilized stochastic homotopic dynamics to sample control protocols.
  • Analyzed the distance distribution of sampled protocols.
  • Investigated changes in the topological features, specifically the number of connected components, of the optimal level set.

Main Results:

  • Demonstrated the existence of topological CLPTs in a two-qubit state-preparation scenario.
  • Observed discontinuous changes in the topology (number of connected components) of the optimal level set.
  • Showed that these topological changes are dependent on the protocol duration.

Conclusions:

  • Topological properties offer a new perspective for understanding CLPTs in optimal quantum control.
  • The identified topological CLPTs can be detected using current experimental techniques.
  • This work expands the understanding of control landscapes and provides new avenues for experimental control design.