A fast quantum mechanical algorithm for estimating the median

TL;DR

This paper introduces a quantum algorithm that estimates the median of N items with high precision using significantly fewer steps than classical methods, leveraging quantum superposition for efficiency.

Contribution

It presents a novel quantum algorithm achieving O(1/epsilon) complexity for median estimation, improving upon classical sample complexity.

Findings

Quantum median estimation algorithm with O(1/epsilon) steps

Outperforms classical O(1/epsilon^2) sample complexity

Demonstrates quantum advantage in statistical estimation tasks

Abstract

Consider the problem of estimating the median of N items to a precision epsilon, i.e., the estimate should be such that, with a high probability, the number of items, with values both smaller than and larger than this estimate, is less than N*(1+epsilon)/2. Any classical algorithm to do this will need at least O(1/epsilon^2) samples. Quantum mechanical systems can simultaneously carry out multiple computations due to their wave like properties. This paper describes an O(1/epsilon) step algorithm for the above estimation.