Optimal Robust Quantum Control by Inverse Geometric Optimization

Area of Science:

• Quantum mechanics
• Optimal control theory
• Geometric optimization

Background:

• Quantum control aims to steer quantum systems using external fields.
• Designing robust controls against imperfections is a significant challenge.
• Existing methods may lack robustness or exact solvability.

Purpose of the Study:

• To develop a novel inverse geometric optimization technique for quantum control.
• To derive optimal and robust exact solutions for low-dimension quantum control problems.
• To design control fields resilient to pulse inhomogeneities.

Main Methods:

• Utilizing Euler-Lagrange optimization in the dynamical variable space to find optimal trajectories.
• Deriving control fields from robust geodesics and inverted dynamical equations.
• Applying the robust inverse optimization (RIO) method.

Main Results:

• Successfully designed optimal control fields for complete/half population transfer.
• Developed a robust quantum gate design.
• Demonstrated robustness against pulse inhomogeneities.
• RIO method proved versatile for various quantum control applications.

Conclusions:

• The robust inverse optimization (RIO) technique provides optimal and robust solutions for quantum control.
• This method enables precise quantum operations despite external field imperfections.
• RIO is applicable to a wide range of quantum control challenges, including gate design and error suppression.