High-Order Hermite Optimization: Fast and Exact Gradient Computation in Open-Loop Quantum Optimal Control using a Discrete Adjoint Approach
Abstract
This work introduces the High-Order Hermite Optimization (HOHO) method, an open-loop discrete adjoint method for quantum optimal control. Our method is the first of its kind to efficiently compute exact (discrete) gradients when using continuous, parameterized control pulses while solving the forward equations (e.g. Schrodinger's equation or the Linblad master equation) with an arbitrarily high-order Hermite Runge-Kutta method. The HOHO method is implemented in QuantumGateDesignjl (https://github.com/leespen1/QuantumGateDesign.jl), an open-source software package for the Julia programming language, which we use to perform numerical experiments comparing the method to Juqboxjl (https://github.com/LLNL/Juqbox.jl). For realistic model problems we observe speedups up to 775x.
Keywords
Cite
@article{arxiv.2505.09857,
title = {High-Order Hermite Optimization: Fast and Exact Gradient Computation in Open-Loop Quantum Optimal Control using a Discrete Adjoint Approach},
author = {Spencer Lee and Daniel Appelo},
journal= {arXiv preprint arXiv:2505.09857},
year = {2026}
}
Comments
Accepted for publication in Journal of Computational Physics. 30 pages, 6 figures, 4 algorithms, 7 tables. Compared to the original submission, this version contains an additional figure, revised explanations and conclusions, as well as numerous typo fixes