  Quantum state transfer is a key operation for quantum information processing.
The original pitch-and-catch protocols rely on flying qubits or single photons
with engineered wavepacket shapes to achieve a deterministic, fast and
high-fidelity transfer. Yet, these protocols overlook two important factors,
namely, the distortion of the wavepacket during the propagation and
non-Markovian effects during the emission and reabsorption processes due to
time-dependent controls. Here we address both difficulties in a general
quantum-optical model and propose a correction strategy to improve quantum
state transfer protocols. Including non-Markovian effects in our theoretical
description, we show how to derive control pulses that imprint phases on the
wavepacket that compensate the distortion caused by propagation. Our
theoretical results are supported by detailed numerical simulations showing
that a suitable correction strategy can improve state transfer fidelities up to
three orders of magnitude.
