Quantum Algorithm to Estimate the Mean Value of a Function

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.