Velocity Filtering Using Quantum 3D FFT

In this work, the quantum version of 3D FFT is proposed for constructing velocity filters. Velocity filters are desirable when we need to separate moving objects with a specific velocity range in amplitude and direction in a rapidly changing background. These filters are useful in many application fields, such as for monitoring regions for security reasons or inspecting processes in experimental physics. A faster and more attractive way to implement this filtering procedure is through 3D FFT instead of using 3D FIR filters. Additionally, 3D FFT provides the capability to create banks of ready-made filters with various characteristics. Thus, 3D filtering is carried out in the frequency domain by rejecting appropriate frequency bands according to the spectral content of the trajectory of the object to be isolated. The 3D FFT procedure and the corresponding inverse one are required in the beginning and end of the filtering process. Although 3D FFT is computationally effective, it becomes time-consuming when we need to process large data cubes. The implementation of velocity filters by means of the quantum version of 3D FFT is investigated in this work. All necessary quantum circuits and quantum procedures needed are presented in detail. This proposed quantum structure results in velocity filtering with a short execution time. For this purpose, a review of the necessary quantum computational units is presented for the implementation of quantum 3D FFT and representative examples of applications of velocity filtering are provided.