Creating superpositions that correspond to efficiently integrable probability distributions

TL;DR

This paper presents a straightforward method for creating quantum superpositions that approximate efficiently integrable probability distributions, enabling more effective quantum sampling and analysis.

Contribution

It introduces a simple, efficient process for generating quantum superpositions that approximate a wide class of probability distributions, including log-concave ones.

Findings

Enables quantum approximation of efficiently integrable distributions

Provides a practical method for quantum sampling tasks

Improves efficiency over previous approaches

Abstract

We give a simple and efficient process for generating a quantum superposition of states which form a discrete approximation of any efficiently integrable (such as log concave) probability density functions.