Abstract: Canonical correlation analysis is an important data processing method for dealing with the interdependence of random vectors. However, the complexity of the classical canonical correlation analysis algorithm is polynomial dependent on the data dimension, making this type of algorithm not suitable for analyzing the data whose scale is growing exponentially in the era of big data. Aiming at the defect of classical canonical correlation analysis algorithm, a quantum canonical correlation analysis algorithm was proposed. The algorithm transformes the optimization problems involved in canonical correlation analysis into algebraic problems suitable for quantum computing technology, and uses quantum principal component analysis technology to solve it, thereby reducing the cost of canonical correlation analysis algorithms. Under certain parameter conditions, the proposed algorithm can achieve exponential acceleration in the data dimension, which meets the requirements of this algorithm for today’s actual data processing.

Key words: quantum algorithm, quantum principal component analysis, correlation analysis; exponential acceleration