A partial least squares regression model based on variational quantum algorithm

Abstract

Partial least squares regression (PLSR) is an essential multivariate correlation analysis method in machine learning field. In this paper, we propose a variational quantum algorithm for partial least regression (VQPLSR). By exploring the relationship between standard basis states and optimization, we design a cost function that can train regression parameters and weight vectors simultaneously. The VQPLS requires only one copy of variables as input, which reduces the complexity of quantum circuit implementation. Compared with PLSR, the VQPLSR achieves an exponential speed-up in the independent variable dimension n and dependent variable dimension w. Simulation results show that regression parameters and weight vectors can be constructed with the error ∼10−5 for 4 × 2 dimensional variable matrix. This algorithm inspires us to explore more quantum applications in machine learning.