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Coarse-Grained Effective Hamiltonian via the Magnus Expansion for a Three-Level System.

Nicola Macrì1,2, Luigi Giannelli1,3, Elisabetta Paladino1,2,3

  • 1Dipartimento di Fisica e Astronomia "Ettore Majorana", Università di Catania, 95123 Catania, Italy.

Entropy (Basel, Switzerland)
|February 25, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces the Magnus expansion for deriving accurate effective Hamiltonians in quantum technologies. This method overcomes ambiguities in adiabatic elimination, enabling systematic improvements for complex quantum systems.

Keywords:
adiabatic eliminationleakagelow-energy Hamiltonian

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Area of Science:

  • Quantum physics
  • Quantum information science
  • Quantum computing

Background:

  • Quantum state processing is crucial for quantum technologies.
  • Real quantum systems often exhibit complex dynamics and non-ideal control.
  • Existing approximation schemes like adiabatic elimination can be ambiguous and difficult to improve systematically.

Purpose of the Study:

  • To develop a systematic and ambiguity-free method for deriving effective Hamiltonians.
  • To improve the accuracy of approximations in quantum state processing.
  • To enable better control and understanding of complex quantum systems.

Main Methods:

  • Utilizing the Magnus expansion as a systematic tool.
  • Deriving effective Hamiltonians in low-dimensional Hilbert subspaces.
  • Analyzing the role of coarse-graining in time for approximation validity.

Main Results:

  • The Magnus expansion provides ambiguity-free effective Hamiltonians.
  • Approximation validity depends on proper time coarse-graining of the exact dynamics.
  • Effective Hamiltonians were validated using quantum operation fidelities.

Conclusions:

  • The Magnus expansion offers a robust approach for effective Hamiltonian derivation in quantum systems.
  • This method facilitates systematic improvement and accuracy in quantum state processing.
  • The findings contribute to the advancement of reliable quantum technologies.