Quantum Algorithm for Solving Quadratic Nonlinear System of Equations

High-dimensional nonlinear system of equations that appears in all kinds of fields is difficult to be solved on a classical computer, we present an efficient quantum algorithm for solving $n$-dimensional quadratic nonlinear system of equations. Our algorithm embeds the equations into a finite-dimensional system of linear equations with homotopy perturbation method and a linearization technique, then we solve the linear equations with quantum linear system solver and obtain a state which is $\epsilon$-close to the normalized exact solution of the original nonlinear equations with success probability $\Omega(1)$. The complexity of our algorithm is $O(\rm{poly}(\rm{log}(n/\epsilon)))$, which provides an exponential improvement over the optimal classical algorithm in dimension $n$.Comment: 9 pages; Modify the format error of tex source fil