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.
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.
The Radon transform constitutes the conventional tool for tomosynthesis, i.e., the composition of cross-sections of an object from its projections. It is actually a version of the Fourier Transform, which is accompanied by the appropriate digital high pass filters for correct distribution of energy among the reconstructed frequency components. The Radon transform and its inverse are employed in their 2D and 3D versions, respectively, and the whole procedure is verified by the a priori known cross-sections to be reconstructed (known fandom). Usually, 3D medical image cubes, which are to be reconstructed, require powerful computational tools since the 2D projections are of high-resolution containing millions of pixels. Although the 3D FFT is very fast, the large number of projections will result in a 3D spectrum of very large dimensions. Inverting this spectrum with the inverse 3D FFT is extremely time consuming. In this work, the implementation of the 2D Radon transform using the 2D Quantum Fourier Transform is analytically presented. Simultaneously, its inverse version is realized by means of the Quantum inverse 3D FFT. For this purpose, a review of the necessary quantum computational units is presented for the implementation of the quantum 3D FFT and simultaneously simple examples of tomosynthesis are given by means of the quantum version of the 2D Radon transform and its inverse 3D counterpart. The whole procedure of the quantum tomosynthesis is analytically described.
Particle Image Velocimetry (PIV) is the prime image-processing technique to measure and visualize velocity fields of laminar and turbulent flows. The velocity field vectors are obtained with sub-pixelaccuracy by analyzing cross-correlations, empowered by Fast Fourier Transforms (FFT). Here, we present a quantum algorithm with multidimensional quantum Fourier Transforms, termed Quantum-based PIV (QuPIV), to replace the classical computation of up to millions of velocity vectors. Our end-to-end quantum algorithm includes a novel state preparation, modified amplitude amplification, and the output extraction. We enhance amplitude amplification by a contracted ground-state projector, which allows a significant reduction of the number of gates in the quantum circuit. We justify the end-to-end capability with numerical studies on all stages of the algorithm on both synthetic and experimental data.
signals into frequency-domain forms is the Fourier Transform (FT). It is extensively utilized in several fields, such as spectrum analysis, audio and video processing, and 5G networks. Effective frequency analysis is essential for channel optimization, signal reliability, and noise reduction in 5G networks. The FFT is appropriate for real-time applications since it greatly increases processing speed. However, the Quantum Fourier Transform makes use of quantum entanglement and superposition, providing exciting new developments for secure data transfer and high-speed communication in the future. Furthermore, both the Inverse Fast Fourier Transform (IFFT) and the Inverse Quantum Fourier Transform are used to correctly recreate the signal. Implementation of Quantum's real valued computing of quantum-based signal processing is also covered in the survey.
In digital signal processing, the finite impulse response (FIR) filter is a fundamental tool for processing discrete-time signals. This paper explores the implementation of FIR filters using quantum computation methods. In this study, a quantum circuit for the FIR filter is designed using a normalized filter coefficient vector, orthogonal triangular decomposition commonly known as QR decomposition, and the transpilation tools provided by IBM’s software Qiskit SDK V2.3. Then, each block of the input signal is normalized to a unit-norm vector, loaded into a quantum register, and processed by the FIR filter quantum circuit to produce an output state. Quantum measurement is then performed on the output state to obtain a histogram, from which the first-bin data are scaled to compute the output sample of the filter. Finally, signal filtering experiments using FIR mean filters are conducted to demonstrate the effectiveness of the proposed quantum computation approach.
Fourier Transform (FT) is an important signal processing technique that translates time-domain signals to frequency-domain forms. It is widely used in several applications, including 5G networks, image processing, & spectrum analysis. In 5G networks, efficient frequency analysis is critical for noise reduction, channel optimisation, and signal dependability.This study explores the implementation of Classical Fourier Transform, Fast Fourier Transform, and Quantum Fourier Transform using Python (NumPy, Pandas, Matplotlib) and Qiskit. The FFT significantly improves processing speed, making it suitable for real-time applications. On the other hand, QFT leverages quantum superposition and entanglement, offering promising advancements for future high-speed communication and secure data transmission. Additionally, the signal is successfully reconstructed using both the Inverse Fast Fourier Transform (IFFT) and the Inverse Quantum Fourier Transform (IQFT). While IFFT efficiently restores the original signal with minimal numerical artifacts, IQFT ensures exact reconstruction without errors. The study also includes execution on IBM Quantum’s real hardware, showcasing the practical feasibility of quantum-based signal processing.
In this paper we address the emerging field of Quantum Image Processing. We investigate the use of quantum computing systems to represent and manipulate images. In particular, we consider the basic task of image filtering. We prove that a quantum version for this operation can be achieved, even though the quantum convolution of two sequences is physically impossible. In our approach we use the principle of the quantum oracle to implement the filter function. We provide the quantum circuit that implements the filtering task and present the results of several simulation experiments on grayscale images. There are important differences between the classical and the quantum implementations for image filtering. We analyze these differences and show that the major advantage of the quantum approach lies in the exploitation of the efficient implementation of the quantum Fourier transform.