Highly Adiabatic Time-Optimal Quantum Driving at Low Energy Cost

Area of Science:

• Quantum Control Theory
• Quantum Technologies

Background:

• Environmental interactions rapidly degrade quantum states, necessitating time-efficient control.
• Traditional quantum control methods often face complex boundary-value problems.

Purpose of the Study:

• To develop a time-optimal control scheme that circumvents the quantum brachistochrone equation's boundary-value problem.
• To enable faster manipulation of quantum systems while minimizing energy costs.

Main Methods:

• Formulated a novel approach to time-optimal control by relaxing the control Hamiltonian's form.
• Developed a coupled system of equations for the control Hamiltonian and protocol duration.
• Employed an ansatz-free approach to quantum control theory.
• Utilized a Landau-Zener type Hamiltonian for driven systems.

Main Results:

• Successfully circumvented the boundary-value problem inherent in the quantum brachistochrone equation.
• Demonstrated an efficient method for maneuvering driven quantum systems.
• Achieved accelerated state transformations with high adiabaticity and low energy cost.

Conclusions:

• The proposed method offers a practical and efficient solution for time-optimal quantum control.
• This approach is valuable for quantum technologies sensitive to environmental decoherence.
• The ansatz-free, coupled-equation system simplifies quantum control strategy development.