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This research presents the High-Order Hermite Optimization (HOHO) method, a novel discrete adjoint approach that enables exact gradient computation for continuous control pulses in quantum optimal control. By integrating high-order Hermite Runge-Kutta solvers with open-loop optimization, the technique achieves significant speedups—up to 775x—in solving forward equations like Schrödinger's or Lindblad master equations compared to existing tools such as Juqbox.jl. The method is implemented in an open-source Julia package and represents a substantial advancement in the efficiency of quantum gate design algorithms.
High-Order Hermite Optimization: Fast and Exact Gradient Computation in Open-Loop Quantum Optimal Control using a Discrete Adjoint Approach
arXiv:2505.09857v5 Announce Type: replace-cross 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 QuantumGateDesign$.$jl (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 Juqbox$.$jl (https://github.com/LLNL/Juqbox.jl). For realistic model problems we observe speedups up to 775x.
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 QuantumGateDesign$.$jl (this https URL), an open-source software package for the Julia programming language, which we use to perform numerical experiments comparing the method to Juqbox$.$jl (this https URL). For realistic model problems we observe speedups up to 775x.
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
Numerical Analysis (math.NA); Quantum Physics (quant-ph)
G.1.7; G.1.6; G.4; J.2
arXiv:2505.09857 [math.NA]
(or arXiv:2505.09857v5 [math.NA] for this version)
https://doi.org/10.1016/j.jcp.2026.114697 DOI(s) linking to related resources
Full text under the publisher's open licence · 163 words
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