# Sensitivity of quantum PageRank

## TL;DR

This paper analyzes how small changes in the Google matrix affect the quantum PageRank, providing bounds on convergence and error to understand its stability and robustness.

## Contribution

It introduces a method using finite dimensional perturbation theory to estimate the sensitivity and bounds of quantum PageRank under perturbations.

## Key findings

- Derived bounds for quantum PageRank sensitivity
- Estimated lower bounds of convergence radius
- Provided error bounds for perturbation expansion

## Abstract

In this paper, we discuss the sensitivity of quantum PageRank. By using the finite dimensional perturbation theory, we estimate the change of the quantum PageRank under a small analytical perturbation on the Google matrix. In addition, we will show the way to estimate the lower bound of the convergence radius as well as the error bound of the finite sum in the expansion of the perturbed PageRank.