Analyzing XOR-Forrelation through stochastic calculus

TL;DR

This paper offers a simplified stochastic calculus-based analysis of the quantum and classical complexities involved in the $k$-XOR Forrelation problem, providing insights into its computational difficulty.

Contribution

It introduces a stochastic interpretation of the Forrelation distribution to analyze the problem's complexity, simplifying previous approaches.

Findings

Quantum and classical complexities are characterized using stochastic calculus.

The analysis reveals new insights into the difficulty of the $k$-XOR Forrelation problem.

The approach simplifies understanding of Forrelation's computational properties.

Abstract

In this note we present a simplified analysis of the quantum and classical complexity of the $k$-XOR Forrelation problem (introduced in the paper of Girish, Raz and Zhan) by a stochastic interpretation of the Forrelation distribution.