Quantum Linear Regression With Regularization

The problem we are trying to solve in this article is how to execute linear regression algorithm with regularization based on quantum mechanics system. In the field of machine learning, linear regression is a powerful tool modeling input and output variables using the least squares function of linear equations. And regularization is a technical method to solve the overfitting phenomenon which can be caused when the training data is lack or not universal. The approach we mainly adopt to transform classical linear regression to quantum version is to construct Hamiltonian containing the training data information. And via HHL algorithm and swap test, we can accomplish the training process and also make a prediction with input variable state. Compared with classical analogue, the quantum linear regression algorithm demonstrates quadratic speed up.