  Correlation alignment (CORAL), a representative domain adaptation (DA)
algorithm, decorrelates and aligns a labelled source domain dataset to an
unlabelled target domain dataset to minimize the domain shift such that a
classifier can be applied to predict the target domain labels. In this paper,
we implement the CORAL on quantum devices by two different methods. One method
utilizes quantum basic linear algebra subroutines (QBLAS) to implement the
CORAL with exponential speedup in the number and dimension of the given data
samples. The other method is achieved through a variational hybrid
quantum-classical procedure. In addition, the numerical experiments of the
CORAL with three different types of data sets, namely the synthetic data, the
synthetic-Iris data, the handwritten digit data, are presented to evaluate the
performance of our work. The simulation results prove that the variational
quantum correlation alignment algorithm (VQCORAL) can achieve competitive
performance compared with the classical CORAL.
