  Multi-view Feature Extraction (MvFE) has wide applications in machine
learning, image processing and other fields. When dealing with massive
high-dimensional data, the performance of classical computer faces severe
challenges due to MvFE involves expensive matrix calculation. To address this
challenge, a quantum-accelerated cross-regression algorithm for MvFE is
proposed. The main contributions are as follows:(1) a quantum version algorithm
for MvFE is proposed for the first time, filling the gap of quantum computing
in the field of MvFE;(2) a quantum algorithm is designed to construct the
block-encoding of the target data matrix, so that the optimal Hamiltonian
simulation technology based on the block-encoding framework can be used to
efficiently realize the quantum simulation of the target data matrix. This
approach reduces the dependence of the algorithm's on simulation errors to
enhance algorithm performance;(3) compared with the classical counterpart
algorithm, the proposed quantum algorithm has a polynomial acceleration in the
number of data points, the dimension of data points and the number of view
data.
