Initialization Errors in Quantum Data Base Recall

TL;DR

This paper investigates how initialization errors affect the recall accuracy in the Grover quantum search algorithm, revealing a linear relationship between initial error variance and successful memory retrieval.

Contribution

It provides a novel analysis linking initialization error variance to recall probability, demonstrating high recall even with significant initial deviations.

Findings

High probability of correct memory retrieval despite large initialization errors

Linear relationship between initial error variance and recall success

Quantitative analysis of error impact on quantum database search

Abstract

This paper analyzes the relationship between initialization error and recall of a specific memory in the Grover algorithm for quantum database search. It is shown that the correct memory is obtained with high probability even when the initial state is far removed from the correct one. The analysis is done by relating the variance of error in the initial state to the recovery of the correct memory and the surprising result is obtained that the relationship between the two is essentially linear.