Quantum subspace alignment for domain adaptation
This work addresses domain adaptation for machine learning practitioners by offering quantum algorithms, but it is incremental as it adapts existing classical methods to quantum settings.
The authors tackled domain adaptation by proposing two quantum versions of subspace alignment: QSA for quadratic speedup and VQSA for near-term quantum devices, with VQSA achieving competitive performance in numerical experiments.
Domain adaptation (DA) is used for adaptively obtaining labels of an unprocessed data set with a given related, but different labelled data set. Subspace alignment (SA), a representative DA algorithm, attempts to find a linear transformation to align the subspaces of the two different data sets. The classifier trained on the aligned labelled data set can be transferred to the unlabelled data set to predict the target labels. In this paper, two quantum versions of the SA are proposed to implement the DA procedure on quantum devices. One method, the quantum subspace alignment algorithm (QSA), achieves quadratic speedup in the number and dimension of given samples. The other method, the variational quantum subspace alignment algorithm (VQSA), can be implemented on the near term quantum devices through a variational hybrid quantum-classical procedure. The results of the numerical experiments on different types of datasets demonstrate that the VQSA can achieve competitive performance compared with the corresponding classical algorithm.