  We analyze the efficiency of protocols for adiabatic quantum state transfer
assisted by an engineered reservoir. The target dynamics is a quantum
trajectory in the Hilbert space and is a fixed point of a time-dependent master
equation in the limit of adiabatic dynamics. We specialize to quantum state
transfer in a qubit and determine the optimal schedule for a class of
time-dependent Lindblad equations. The speed limit on state transfer is
extracted from a physical model of a qubit coupled to a reservoir, from which
the Lindblad equation is derived in the Born-Markov limit. Our analysis shows
that the resulting efficiency is comparable to the efficiency of the optimal
unitary dynamics. Numerical studies indicate that reservoir-engineered
protocols could outperform unitary protocols outside the regime of the
Born-Markov master equation, namely, when correlations between the qubit and
reservoir become relevant. Our study contributes to the theory of shortcuts to
adiabaticity for open quantum systems and to the toolbox of protocols of the
NISQ era.
