  Transfer learning (TL), a crucial subfield of machine learning, aims to
accomplish a task in the target domain with the acquired knowledge of the
source domain. Specifically, effective domain adaptation (DA) facilitates the
delivery of the TL task where all the data samples of the two domains are
distributed in the same feature space. In this paper, two quantum
implementations of the DA classifier are presented with quantum speedup
compared with the classical DA classifier. One implementation, the quantum
basic linear algebra subroutines (QBLAS)-based classifier, can predict the
labels of the target domain data with logarithmic resources in the number and
dimension of the given data. The other implementation efficiently accomplishes
the DA task through a variational hybrid quantum-classical procedure.
