Probing the Weak-Driving Quantum Speed Limit via Drift-Aware Shooting Methods
Abstract
A central goal of quantum optimal control is to achieve high-fidelity and low-energy control pulses. When quantum optimal control methods optimize every point of a pulse discretized over small time steps independently this can yield high fidelity control but also results in broadband and energy-hungry waveforms. We extend MAGICARP, a shooting method inspired by Pontryagin's maximum principle on energy that generates an entire pulse from a small set of parameters, making it smooth and energy-efficient by construction, from driftless systems to closed systems with the constant drift Hamiltonian of two exchange-coupled spins in an external magnetic field. The optimization proceeds in stages: the dressed states of the drift Hamiltonian structure the target, an initial shooting optimization is performed in the rotating-wave frame, and an exact laboratory-frame refinement follows. Benchmarked against Krotov and GRAPE at matched gate infidelity, MAGICARP consistently achieves the lowest energy and a conserved pulse area, concentrates its spectral weight on the gate-relevant transitions, and is the most robust to fluctuations in the exchange coupling; GRAPE independently converges to essentially the same pulse while black-box Krotov meets the same error at an order-of-magnitude energy premium. This method-independence is what qualifies the bounded solver as a measurement instrument, and the central result follows: a large statistical survey of unselected optimization runs resolves a weak-driving quantum speed limit for two exchange-coupled electron spins: low-amplitude realizations of the two-qubit quantum Fourier transform cease to exist below a critical gate time, and the minimum control energy diverges on approach to this limit. The divergence obeys a simple two-parameter area--pole law, E2law(T)=A/T+B/(T−T*).
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BibTeX
@misc{jankovic2026probing,
title = {{Probing the Weak-Driving Quantum Speed Limit via Drift-Aware Shooting Methods}},
author = {Denis Janković and Saba Taherpour and Paul-Louis Etienney and Paul-Antoine Hervieux and Christoph Wolf},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.22212},
eprint = {2606.22212},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.22212},
}
RIS
TY - UNPB
TI - Probing the Weak-Driving Quantum Speed Limit via Drift-Aware Shooting Methods
AU - Denis Janković
AU - Saba Taherpour
AU - Paul-Louis Etienney
AU - Paul-Antoine Hervieux
AU - Christoph Wolf
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2606.22212
UR - https://arxiv.org/abs/2606.22212
AB - A central goal of quantum optimal control is to achieve high-fidelity and low-energy control pulses. When quantum optimal control methods optimize every point of a pulse discretized over small time steps independently this can yield high fidelity control but also results in broadband and energy-hungry waveforms. We extend MAGICARP, a shooting method inspired by Pontryagin's maximum principle on energy that generates an entire pulse from a small set of parameters, making it smooth and energy-efficient by construction, from driftless systems to closed systems with the constant drift Hamiltonian of two exchange-coupled spins in an external magnetic field. The optimization proceeds in stages: the dressed states of the drift Hamiltonian structure the target, an initial shooting optimization is performed in the rotating-wave frame, and an exact laboratory-frame refinement follows. Benchmarked against Krotov and GRAPE at matched gate infidelity, MAGICARP consistently achieves the lowest energy and a conserved pulse area, concentrates its spectral weight on the gate-relevant transitions, and is the most robust to fluctuations in the exchange coupling; GRAPE independently converges to essentially the same pulse while black-box Krotov meets the same error at an order-of-magnitude energy premium. This method-independence is what qualifies the bounded solver as a measurement instrument, and the central result follows: a large statistical survey of unselected optimization runs resolves a weak-driving quantum speed limit for two exchange-coupled electron spins: low-amplitude realizations of the two-qubit quantum Fourier transform cease to exist below a critical gate time, and the minimum control energy diverges on approach to this limit. The divergence obeys a simple two-parameter area--pole law, E_2^law(T)=A/T+B/(T−T^*).
ER -