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We propose a universal quantum circuit design that can estimate any arbitraryone-dimensional periodic functions based on the corresponding Fourierexpansion. The quantum circuit contains N-qubits to store the information onthe different N-Fourier components and $M+2$ auxiliary qubits with $M =\lceil{\log_2{N}}\rceil$ for control operations. The desired output will bemeasured 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 thequantum circuit for the square wave function with accurate results obtained bydirect simulations using the IBM-QASM simulator. The approach is general andcan be applied to any arbitrary periodic function.

A Universal Quantum Circuit Design for Periodical Functions