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Finite elements and moving asymptotes accelerate quantum optimal control-FEMMA
Mengjia He1, Yongbo Deng1, Burkhard Luy2,3
1Institute of Microstructure Technology, Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen, Germany.
The Journal of Chemical Physics
|February 11, 2026
Summary
This study accelerates quantum optimal control for spin manipulation by integrating the finite element method and method of moving asymptotes. This approach efficiently solves for spin trajectories and control gradients, achieving rapid convergence for high-fidelity pulses.
Area of Science:
- Quantum physics
- Quantum information science
- Quantum computing
Background:
- Quantum optimal control is crucial for designing precise spin manipulation pulses.
- Gradient-based pulse optimization faces challenges in gradient evaluation speed and convergence rate.
Purpose of the Study:
- To accelerate single-spin optimal control by developing a novel computational approach.
- To enhance the efficiency and convergence of gradient-based pulse optimization methods.
Main Methods:
- Combined the finite element method (FEM) with the method of moving asymptotes (MMA).
- Reformulated the Liouville-von Neumann equation as a linear system by treating discretized time as spatial coordinates.
- Utilized ensemble fidelities and gradients within the MMA framework.
Main Results:
- Achieved an accelerated solution for both spin trajectory and control gradient.
- Demonstrated efficient computation by solving the reformulated Liouville-von Neumann equation.
- Attained rapid convergence for a target fidelity of 0.995.
Conclusions:
- The integrated FEM-MMA approach significantly accelerates single-spin optimal control.
- This method provides an efficient pathway for designing high-fidelity quantum control pulses.
- The technique shows promise for advancing quantum technologies reliant on precise spin manipulation.
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