Quantum subspace alignment for domain adaptation

Domain adaptation (DA) is used for adaptively obtaining labels of an unprocessed data set with given a related, but different labelled data set. Subspace alignment (SA), a representative DA algorithm, attempts to find a linear transformation to align the two different data sets. The classifier trained on the aligned labelled data set can be transferred to the unlabelled data set to classify the target labels. In this paper, a quantum version of the SA algorithm is proposed to implement the domain adaptation procedure on a quantum computer. Compared with the classical SA algorithm, the quantum algorithm presented in our work achieves at least quadratic speedup in the number of given samples and the data dimension. In addition, the kernel method is applied to the quantum SA algorithm to capture the nonlinear characteristics of the data sets.