Faster quantum ridge regression algorithm for prediction

In this paper, a quantum algorithm based on ridge regression model is proposed. The proposed quantum algorithm consists of two parts. One is the first quantum sub-algorithm to efficiently generate predictive values for new inputs. The non-sparse Hamiltonian simulation technique is applied to simulate the data matrix that is generally non-sparse. Therefore, there is no need to expand the data matrix into a larger sparse Hermitian matrix, and the predictive results can be obtained without projection operation at the end of the first sub-algorithm, which makes it more feasible. The other is to determine a reasonable regularization parameter. To achieve this goal, the second sub-algorithm is proposed. In the second sub-algorithm, the suitable one is selected from some candidates using phase estimation algorithm and the controlled rotation operation. In this way, the whole training dataset can be calculated in parallel, which greatly reduces the time complexity. In addition, it is shown that the proposed quantum ridge regression algorithms can achieve exponential speedup over the classical counterpart when the rank of the data matrix is low.