A Quantum Algorithm for finding the Maximum

TL;DR

This paper introduces a quantum algorithm that finds the maximum of N items more efficiently than classical methods, reducing the complexity from linear to square root time using quantum superposition.

Contribution

It presents a novel quantum algorithm that achieves a quadratic speedup for the maximum-finding problem compared to classical algorithms.

Findings

Achieves O(√N) query complexity for maximum finding.

Provides a tight upper bound of approximately 6.8√N steps.

Demonstrates quantum advantage in search problems.

Abstract

This paper describes a quantum algorithm for finding the maximum among N items. The classical method for the same problem takes O(N) steps because we need to compare two numbers in one step. This algorithm takes O(sqrt(N)) steps by exploiting the property of quantum states to exist in a superposition of states and hence performing an operation on a number of elements in one go. A tight upper bound of 6.8(sqrt(N)) for the number of steps needed using this algorithm was found. These steps are the number of queries made to the oracle.