  Discriminative Canonical Correlation Analysis (DCCA) is a powerful supervised
feature extraction technique for two sets of multivariate data, which has wide
applications in pattern recognition. DCCA consists of two parts: (i)
mean-centering that subtracts the sample mean from the sample; (ii) solving the
generalized eigenvalue problem. The cost of DCCA is expensive when dealing with
a large number of high-dimensional samples. To solve this problem, here we
propose a quantum DCCA algorithm. Specifically, we devise an efficient method
to compute the mean of all samples, then use block-Hamiltonian simulation and
quantum phase estimation to solve the generalized eigenvalue problem. Our
algorithm achieves a polynomial speedup in the dimension of samples under
certain conditions over its classical counterpart.
