We study the numerical integration problem of functions from the generalized Hölder class Formula: see text, which is determined by a generalized modulus of smoothness Formula: see text, in the quantum model of computation. We obtain the exact order of complexity of this problem. The results show that quantum algorithms have faster convergence rates than those of deterministic and randomized ones. Quantitatively, the improvement amounts to the factors Formula: see text for the deterministic case and Formula: see text for the randomized case, where Formula: see text is the number of function evaluations involved in the computational process. Furthermore, we apply our general results to the case Formula: see text with Formula: see text and Formula: see text and obtain the corresponding complexity.
Wan et al. (Fri,) studied this question.