Quantum discriminative canonical correlation analysis

TL;DR

This paper introduces a quantum algorithm for discriminative canonical correlation analysis (DCCA) that significantly speeds up computation for large, high-dimensional datasets by leveraging quantum techniques.

Contribution

The paper presents a quantum DCCA algorithm that reduces computational complexity using quantum mean estimation and eigenvalue solving methods.

Findings

Achieves polynomial speedup over classical DCCA

Efficient quantum mean estimation method developed

Uses block-Hamiltonian simulation and quantum phase estimation

Abstract

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.