Quantum Circuit for Calculating Mean Values Via Grover-like Algorithm

TL;DR

This paper introduces a quantum circuit that efficiently computes the mean value of a function using a Grover-like algorithm, achieving quadratic speedup over classical methods.

Contribution

It presents a novel quantum algorithm based on Grover's algorithm for calculating mean values, differing from previous quantum approaches.

Findings

Quantum circuit computes mean values in O(√2^n) steps

Classical algorithms require O(2^n) steps

Quantum approach offers quadratic speedup

Abstract

In this paper, we give a quantum circuit for calculating the mean value of a function $A(x^n)\in \mathbb{C}$, where $x^n\in \{0,1\}^n$. Known classical algorithms for calculating the mean value of a structureless function $A(x^n)$ take ${\cal O}(2^n)$ steps. Our quantum algorithm is based on a Grover-like algorithm and it takes ${\cal O}(\sqrt{2^n})$ steps. Our algorithm differs significantly from previously proposed quantum algorithms for calculating the mean value of a function via Grover's algorithm.