Pontryagin's Principle for Leakage-Immune Adiabatic Quantum State Transfer

The standard stimulated Raman adiabatic passage (STIRAP) protocol enables high-fidelity quantum state transfer in an ideal three-level system via adiabatic following of a dark state evolution. However, in practical systems with more energy levels, control pulses with finite spectral selectivity often couple the three-level subspace to the remaining subspace, introducing leakage that fundamentally limits the transfer performance. Here, we adopt a multilevel chain model for STIRAP that explicitly incorporates this leakage subspace. Using Pontryagin's maximum principle, we formulate a leakage-penalized quantum optimal control problem with the control pulses constrained to experimentally feasible Gaussian pulse families. We derive explicit gradients of the objective functional with respect to the pulse parameters, enabling efficient low-dimensional optimization that suppresses leakage while preserving the counterintuitive STIRAP pulse ordering. Numerical simulations for a superconducting transmon platform demonstrate that the optimized control pulses can significantly enhance the target-state transfer fidelity and provide enhanced robustness to amplitude miscalibration and detuning drifts.