Practical Hamiltonian learning with unitary dynamics and Gibbs states

Area of Science:

• Quantum Physics
• Quantum Information Science
• Computational Physics

Background:

• Learning Hamiltonian parameters is crucial for understanding quantum many-body systems.
• Existing methods often face scalability challenges with system size and complexity.
• Derivative estimation offers a promising avenue for Hamiltonian learning.

Purpose of the Study:

• To develop a more scalable Hamiltonian learning protocol for quantum many-body systems.
• To improve the scaling dependence on Hamiltonian structural parameters, like locality.
• To provide precise guidelines for optimizing learning protocol hyperparameters.

Main Methods:

• Building upon derivative estimation techniques for Hamiltonian learning.
• Proposing a novel protocol with improved scaling properties.
• Deriving exact performance bounds to determine optimal hyperparameter settings.
• Utilizing numerical simulations on an 80-qubit system to demonstrate practicality.

Main Results:

• The proposed protocol demonstrates improved scaling, especially concerning Hamiltonian locality.
• Exact bounds provide a numerical prescription for optimal hyperparameter tuning (e.g., evolution time, temperature).
• The method shows practical scalability for large quantum systems, validated by simulation.

Conclusions:

• The developed Hamiltonian learning protocol offers significant advantages in scalability and precision.
• This work provides a practical framework for learning complex quantum system parameters.
• The findings pave the way for more efficient characterization of large quantum systems.