Quantum gradient algorithm for general polynomials

Gradient-based algorithms, popular strategies to optimization problems, are essential for many modern machine-learning techniques. Theoretically, extreme points of certain cost functions can be found iteratively along the directions gradient. The time required calculating gradient $d$-dimensional problems is at a level $\mathcal{O}(poly(d))$, which could boosted by quantum techniques, benefiting high-dimensional data processing, especially engineering with number optimized parameters being in billions. Here, we propose algorithm optimizing general polynomials dressed amplitude encoding, aiming solving fast-convergence within both and memory consumption $\mathcal{O}(poly (\log{d}))$. Furthermore, numerical simulations carried out inspect performance this protocol considering noises or perturbations from initialization, operation truncation. For potential values high-dimension optimizations, supposed facilitate polynomial-optimizations, subroutine future practical computer.