  We propose a quantum algorithm based on ridge regression model, which get the
optimal fitting parameters w and a regularization hyperparameter {\alpha} by
analysing the training dataset. The algorithm consists of two subalgorithms.
One is generating predictive value for a new input, the way is to apply the
phase estimation algorithm to the initial state |Xi and apply the controlled
rotation to the eigenvalue register. The other is finding an optimal
regularization hyperparameter {\alpha} , the way is to apply the phase
estimation algorithm to the initial state |yi and apply the controlled rotation
to the eigenvalue register. The second subalgorithm can compute the whole
training dataset in parallel that improve the efficiency. Compared with the
classical ridge regression algorithm, our algorithm overcome multicollinearity
and overfitting. Moreover, it have exponentially faster. What's more, our
algorithm can deal with the non-sparse matrices in comparison to some existing
quantum algorithms and have slightly speedup than the existing quantum
counterpart. At present, the quantum algorithm has a wide range of application
and the proposed algorithm can be used as a subroutine of other quantum
algorithms.
