How fast can a quantum computer search?

TL;DR

This paper provides a refined proof establishing the minimum number of queries a quantum computer requires to search an unsorted list, confirming the optimality of Grover's algorithm with a specific lower bound.

Contribution

The paper offers a simplified and improved proof of the lower bound on quantum search complexity, tightening the known query requirement from 0.707 to 0.785 times the square root of N.

Findings

Quantum search requires at least 0.785 sqrt(N) queries.

The proof confirms Grover's algorithm is optimal.

Lower bound matches the number of queries used by Grover's algorithm.

Abstract

This paper gives a simple proof of why a quantum computer, despite being in all possible states simultaneously, needs at least 0.707 sqrt(N) queries to retrieve a desired item from an unsorted list of items. The proof is refined to show that a quantum computer would need at least 0.785 sqrt(N) queries. The quantum search algorithm needs precisely this many queries.