A Universal Quantum Circuit Design for Periodical Functions

Abstract

We propose a universal quantum circuit design that can estimate any arbitrary one-dimensional periodic functions based on the corresponding Fourier expansion. The quantum circuit contains Nqubits to store the information on the different N-Fourier components and M + 2 auxiliary qubits with M = log 2 N for control operations. The desired output will be measured in the last qubit qN with a time complexity of the computation of O(N 2 log 2 N 2 ). We illustrate the approach by constructing the quantum circuit for the square wave function with accurate results obtained by direct simulations using the IBM-QASM simulator. The approach is general and can be applied to any arbitrary periodic function.