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Researchers explored quantum system Hamiltonians using experimental data. Simulations confirmed a convex domain exists around the true Hamiltonian, even with noise, aiding Hamiltonian inversion.

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Area of Science:

  • Quantum mechanics
  • Computational physics

Background:

  • Identifying quantum system Hamiltonians from experimental data is crucial.
  • Hamiltonian inversion involves finding parameters that best reproduce experimental measurements.

Purpose of the Study:

  • To investigate the local convexity of the Hamiltonian inversion landscape.
  • To determine if a convex domain exists around the true Hamiltonian using simulations.

Main Methods:

  • Developed a gradient-based Hamiltonian search algorithm.
  • Incorporated the algorithm into an inversion routine.
  • Performed simulations with both noise-free and noisy experimental data.

Main Results:

  • Simulations demonstrated a sizable convex domain around the true Hamiltonian.
  • Convexity was observed even with limited experimental data.
  • The presence of noise did not eliminate the convex domain.

Conclusions:

  • The findings support the theoretical prediction of local convexity in Hamiltonian inversion.
  • The identified convex domain facilitates Hamiltonian identification.
  • The method is robust to noise and data limitations.