有关稠密矩阵的量子牛顿法

Optimization algorithm is an important technology for machine learning, which directly affects the convergence speed and accuracy of neural network.Optimization problems are usually solved by iterative method, and gradient descent method is the most commonly used method for unconstrained optimization.The quantum gradient descent method has been used to solve the optimization problems, but it has high requirements for matrix sparsity.This paper introduces an algorithm of quantum gradient descent method based on dense matrix. The combination of Hamiltonian simulation and Fourier approximation of dense matrices is applied to the quantum Newton method, which provides a new idea for the optimization algorithm of dense matrices on quantum computers.