基于量子奇异值估计的岭回归算法

Ridge regression algorithm based on quantum singular value estimation

作为一种有监督学习算法,岭回归算法有着十分广泛的使用。本工作将量子奇异值估计与经典岭回归算法相结合,提出了一种量子岭回归算法。该算法利用量子计算的并行特性,实现了对岭回归拟合参数的求解以及预测值的获取。复杂度分析表明,所提算法有效解决了数据矩阵为非厄米矩阵时需要进行矩阵拓展或者矩阵运算的问题,与经典算法相比在运行时间上具有指数级加速。此外,本工作还给出了所提算法的量子电路图并对其关键步骤进行了仿真实验,实验结果验证了所提算法的有效性和可行性。

As a kind of supervised learning algorithm,ridge regression algorithm has a wide range of applications.A quantum ridge regression algorithm is proposed by combining quantum singular value estimation with classical ridge regression algorithm.In the proposed algorithm,the parallel property of quantum computation is utilized to solve the fitting parameters of ridge regression and obtain the predicted values.Complexity analysis shows that the proposed algorithm effectively solves the problem of matrix expansion or matrix operation when the data matrix is non-Hermitian matrix,and has exponential acceleration in running time compared with the classical algorithms.In addition,the quantum circuit diagram of the proposed algorithm is also provided and the key steps of the algorithm are simulated.The simulation results confirm its effectiveness and feasibility.