Two Notes on Grover's Search: Programming and Discriminating

TL;DR

This paper explores practical implementation of Grover's algorithm for database search and analyzes its effectiveness when the database size is uncertain, highlighting limitations in state distinguishability.

Contribution

It introduces a quantum model of an unordered database with programmable queries and analyzes the impact of state distinguishability on algorithm success.

Findings

Quantum database model with programmable queries

Success rate decreases with uncertain database size

Unambiguous discrimination yields limited success

Abstract

In this work we address two questions concerning Grover's algorithm. In the first we give an answer to the question how to employ Grover's algorithm for actual search over database. We introduce a quantum model of an unordered phone book (quantum database) with programmable queries to search in the phone book either for a number, or for a name. In the second part we investigate how successful the algorithm can be if the number of elements of the database is not known precisely. This question reduces to analysis of the distinguishability of states occurring during Grover's algorithm. We found that using unambiguous discrimination scheme even a seemingly good guess, that is close to the optimal one can result in a rather small success rate.