  Domain adaptation, a crucial sub-field of transfer learning, aims to utilize
known knowledge of one data set to accomplish tasks on another data set. In
this paper, we perform one of the most representative domain adaptation
algorithms, transfer component analysis (TCA), on quantum devices. Two
different quantum implementations of this transfer learning algorithm; namely,
the linear-algebra-based quantum TCA algorithm and the variational quantum TCA
algorithm, are presented. The algorithmic complexity of the
linear-algebra-based quantum TCA algorithm is $O(\mathrm{poly}(\log (n_{s} +
n_{t})))$, where $n_{s}$ and $n_{t}$ are input sample size. Compared with the
corresponding classical algorithm, the linear-algebra-based quantum TCA can be
performed on a universal quantum computer with exponential speedup in the
number of given samples. Finally, the variational quantum TCA algorithm based
on a quantum-classical hybrid procedure, that can be implemented on the near
term quantum devices, is proposed.
