# Effects of Imperfect Gate Operations in Shor's Prime Factorization Algorithm

## TL;DR

This paper investigates how different types of gate imperfections affect the performance of Shor's prime factorization algorithm, highlighting its robustness to systematic errors but vulnerability to random errors, and providing error thresholds.

## Contribution

It classifies gate errors into systematic, random, and combined, and analyzes their impact on Shor's algorithm, offering insights into error tolerance levels.

## Key findings

- Shor's algorithm is robust against systematic errors.
- Shor's algorithm is vulnerable to random errors.
- An error threshold is established for successful factorization.

## Abstract

The effects of imperfect gate operations in implementation of Shor's prime factorization algorithm are investigated. The gate imperfections may be classified into three categories: the systematic error, the random error, and the one with combined errors. It is found that Shor's algorithm is robust against the systematic errors but is vulnerable to the random errors. Error threshold is given to the algorithm for a given number $N$ to be factorized.