Quantum kernel subspace alignment for unsupervised domain adaptation

Domain adaptation (DA), the sub-realm of the transfer learning, attempts to deal with machine learning tasks on an unprocessed data domain with the different, but related labeled source domain. However, the classical DA can not efficiently deal with the cross-domain tasks in quantum mechanical scenarios. In this paper, the quantum kernel subspace alignment algorithm is proposed to achieve the procedure of DA by extracting the non-linear features with the quantum kernel method and aligning the two domains with the unitary evolution. The method presented in our work can be implemented on the universal quantum computer with the quantum basic linear algebra subroutines. Based on the algorithmic complexity analysis, the procedure of the QKSA can be implemented with at least quadratic quantum speedup compared with the classical DA algorithms.