This invention involves an algorithm that uses quantum fractional Kravchuk-Fourier transform. In the quantum field, the discrete Fourier transform (DFT) is an efficient approximation to the Fourier transform (FT). However, DFT has some bottlenecks, such as not reproducing all essential features of FT. On the other hand, the Fast Fourier Transform (FFT) algorithm helps DFT to be powerful, but there is a problem with FFT, which considerably lowers the number of operations in computing. As a solution, the Quantum Fourier Transform (QFT) enables the implementation of DFT on quantum amplitudes. Additionally, in many applications where signals are typically not periodic and are random in length, the Kravchuk transform (KT) is a useful alternative to FFT, which can be applied to finite signal processing. Yet KT lacks a fast computation algorithm. The solution to this computation algorithm problem is the quantum Kravchuk transform.