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 N-qubits to store the information on the different N-Fourier components and $M+2$ auxiliary qubits with $M = \lceil{ \log_2{ N}}\rceil$ for control operations. The desired output will be measured in the last qubit $q_N$ with a time complexity of the computation of $O(N^2\lceil \log_2N\rceil^2)$. 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.
Categories: quant-ph