Riemannian modified Newton optimization on quantum search achieves quadratic convergence and O(√(N/M) log log(1/ε)) complexity when M/N is known.
In this case, the Hes- sian operator is positive along the gradient direc- tion, and the unmodified Newton step would point toward a descent direction
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Achieving double-logarithmic precision dependence in optimization-based quantum unstructured search
Riemannian modified Newton optimization on quantum search achieves quadratic convergence and O(√(N/M) log log(1/ε)) complexity when M/N is known.