Quantum Algorithm to Estimate the Mean Value of a Function

TL;DR

This paper introduces a quantum algorithm that efficiently estimates the mean value of a function using quantum superposition and entanglement, achieving logarithmic complexity and minimal black-box queries.

Contribution

It presents a novel quantum circuit for mean estimation that significantly reduces complexity compared to classical methods.

Findings

Achieves $ ext{O}( ext{log} N)$ complexity in mean estimation

Requires only $ ext{O}(1)$ black-box queries

Utilizes quantum superposition, interference, and entanglement

Abstract

This paper proposes a quantum circuit for computing the mean value from a given set of numbers or function evaluations. Suppose a Quantum Random Access Memory is given as a black-box function, which allows us to store and read the values of a set as quantum states. The proposed quantum algorithm estimate the mean value of the function by using superposition, interference, and entanglement phenomena, in $\mathcal{O}(\log{N})$ complexity or in $\mathcal{O}(1)$ query of the black-box.