No quantum speedup with Grover-Rudolph state preparation for quantum Monte Carlo integration

We prove that there is no quantum speedup when using quantum Monte Carlo integration to estimate the mean (and other moments) of analytically defined log-concave probability distributions prepared as quantum states using the Grover-Rudolph method.

Automated summary

Research shows that there is no quantum speedup in estimating the mean of analytically defined log-concave probability distributions prepared as quantum states using the Grover-Rudolph method with quantum Monte Carlo integration.