A Universal Quantum Circuit Design for Periodical Functions
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.
Junxu Li Sabre Kais