Higher-Order Magnus Corrections to Leakage Elimination Operator-Based Quantum Control Pulse Design in the Low-Frequency Regime
Abstract
Effective quantum control is essential for quantum computing and information processing, yet level leakage remains a bottleneck limiting control fidelity. The leakage elimination operator (LEO) approach is highly effective at suppressing leakage from a target subspace to other subspaces. Analytical control conditions under the high-frequency driving limit have been derived via the Feshbach PQ partitioning technique. However, the driving intensity is subject to fundamental physical bounds, and low-frequency driving is experimentally more feasible. In this work, we reformulate LEO within the Magnus framework and extend it beyond the high-frequency limit. We show that the analytical control conditions obtained from the Feshbach PQ partitioning technique are equivalent to the zeroth-order Magnus expansion. We then analyze the higher-order Magnus corrections. By minimizing the leakage, we obtain a modified pulse condition suitable for the low-frequency regime. As an illustrative example, we study near-perfect state transfer through a one-dimensional spin chain under LEO control. We find that the second-order Magnus correction improves the transmission fidelity at low-frequency driving, while the improvement becomes negligible at high frequencies. Our results provide an effective route for designing control pulses in the low-frequency regime, with potential applications in superconducting qubits, trapped ions, and solid-state spin systems.
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BibTeX
@misc{yu2026higherorder,
title = {{Higher-Order Magnus Corrections to Leakage Elimination Operator-Based Quantum Control Pulse Design in the Low-Frequency Regime}},
author = {Hang Yu and Kai-Yu Yuan and Feng-Hua Ren and Zhao-Ming Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.29854},
eprint = {2606.29854},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.29854},
}
RIS
TY - UNPB
TI - Higher-Order Magnus Corrections to Leakage Elimination Operator-Based Quantum Control Pulse Design in the Low-Frequency Regime
AU - Hang Yu
AU - Kai-Yu Yuan
AU - Feng-Hua Ren
AU - Zhao-Ming Wang
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2606.29854
UR - https://arxiv.org/abs/2606.29854
AB - Effective quantum control is essential for quantum computing and information processing, yet level leakage remains a bottleneck limiting control fidelity. The leakage elimination operator (LEO) approach is highly effective at suppressing leakage from a target subspace to other subspaces. Analytical control conditions under the high-frequency driving limit have been derived via the Feshbach PQ partitioning technique. However, the driving intensity is subject to fundamental physical bounds, and low-frequency driving is experimentally more feasible. In this work, we reformulate LEO within the Magnus framework and extend it beyond the high-frequency limit. We show that the analytical control conditions obtained from the Feshbach PQ partitioning technique are equivalent to the zeroth-order Magnus expansion. We then analyze the higher-order Magnus corrections. By minimizing the leakage, we obtain a modified pulse condition suitable for the low-frequency regime. As an illustrative example, we study near-perfect state transfer through a one-dimensional spin chain under LEO control. We find that the second-order Magnus correction improves the transmission fidelity at low-frequency driving, while the improvement becomes negligible at high frequencies. Our results provide an effective route for designing control pulses in the low-frequency regime, with potential applications in superconducting qubits, trapped ions, and solid-state spin systems.
ER -