The paper introduces a quantum algorithm framework for estimating properties of discrete probability distributions, with a focus on estimating Rényi entropies. The key highlights and insights are:
The authors propose quantum algorithms that can estimate the α-Rényi entropy Hα(p) of a discrete probability distribution p = (pi)ni=1 within additive error ϵ with success probability at least 2/3.
These results improve upon the previous state-of-the-art algorithms in terms of the joint dependence on n and 1/ϵ.
The algorithms combine quantum singular value transformation, quantum annealing, and variable-time amplitude estimation to achieve the improved complexity.
The techniques can also be applied to estimate the Rényi entropy of quantum density matrices, and the authors provide corresponding corollaries.
The paper discusses open questions, such as whether quadratic quantum speedup in n is possible for α > 1 Rényi entropy estimation, and the potential application of the framework to other statistical problems like partition function estimation.
A otro idioma
del contenido fuente
arxiv.org
Ideas clave extraídas de
by Xinzhao Wang... a las arxiv.org 04-04-2024
https://arxiv.org/pdf/2212.01571.pdfConsultas más profundas