Quantum Circuit for Calculating Mean Values Via Grover-like Algorithm

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.