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This is a Quantitative Study study.

October 10, 2025Open Access

Finite elements and moving asymptotes accelerate quantum optimal control - FEMMA

Key Points

This method achieves significant speedup in quantum optimal control optimization, reducing computation time dramatically.
The approach yields gradients that are over an order of magnitude faster than GRAPE, with minimal accuracy loss.
Using finite elements, the Liouville-von Neumann equation is reformulated for efficient optimization, enhancing convergence.
Moving asymptotes improve efficiency further, outperforming traditional methods like L-BFGS and nearing Newton-level performance.

Abstract

Quantum optimal control is central to designing spin manipulation pulses. While GRAPE efficiently computes gradients, realistic ensemble models make optimization time-consuming. In this work, we accelerated single-spin optimal control by combining the finite element method with the method of moving asymptotes. By treating discretized time as spatial coordinates, the Liouville-von Neumann equation was reformulated as a linear system, yielding gradients solving over an order of magnitude faster than GRAPE with less than one percent relative-accuracy loss. The moving asymptotes further improves convergence, outperforming L-BFGS and approaching Newton-level efficiency.

Finite elements and moving asymptotes accelerate quantum optimal control - FEMMA

Key Points

Abstract

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