The Problem with Grover-Rudolph State Preparation for Quantum Monte-Carlo
Steven Herbert
TL;DR
This paper demonstrates that the Grover-Rudolph method does not provide a quantum speed-up for Monte-Carlo estimation of moments of certain probability distributions.
Contribution
It proves the fundamental limitation of the Grover-Rudolph state preparation method in quantum Monte-Carlo applications for log-concave distributions.
Findings
No quantum speed-up for estimating moments using Grover-Rudolph.
Limitations apply to analytically-defined log-concave distributions.
Quantum advantage is not achievable with this method in the studied context.
Abstract
We prove that there is no quantum speed-up when using quantum Monte-Carlo to estimate the mean (and other moments) of analytically-defined log-concave probability distributions prepared as quantum states using the Grover-Rudolph method.
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