Modified Newton-Raphson GRAPE methods for optimal control of spin systems.

Area of Science:

• Quantum Control
• Quantum Computing
• Spectroscopy

Background:

• Quantum optimal control algorithms like GRAPE are crucial for manipulating quantum systems.
• Efficient optimization is key to advancing quantum control applications.

Purpose of the Study:

• To demonstrate quadratic convergence for GRAPE algorithms.
• To present a computationally efficient Newton-Raphson method for GRAPE.

Main Methods:

• Developed a method leveraging the cheap Hessian of the GRAPE fidelity functional.
• Implemented a rational function optimization (RFO) regularized Hessian for Newton-Raphson.
• Utilized techniques like matrix exponential recycling for efficiency.

Main Results:

• Achieved quadratic convergence throughout the active space in GRAPE.
• The Hessian of the GRAPE fidelity functional has the same complexity as the functional itself.
• The RFO Newton-Raphson method requires fewer system trajectory evaluations than other GRAPE algorithms.

Conclusions:

• The proposed RFO Newton-Raphson method offers a significant speedup for GRAPE.
• This advancement enables more efficient quantum control for applications like magnetic resonance spectroscopy.