This paper introduces a hybrid two-dimensional Quantum Fourier Transform (2D hybrid QFT) method for image analysis and synthesis. The QFT and Inverse QFT (IQFT) functions enable analysis-synthesis implementation using frequency spectrum-based selection approaches for compression. We study the resolution and precision of the QFT by comparing its outputs against classical two-dimensional Fast Fourier Transform (FFT) techniques using pixel-level Signal to Noise Ratio (SNR) as a metric. Formative and summative assessments have been deployed as a laboratory exercise in two National Science Foundation (NSF) workforce development programs. Preliminary evaluation results are presented in this paper.
This paper introduces a hybrid two-dimensional Quantum Fourier Transform (2D hybrid QFT) method for image analysis and synthesis. The QFT and Inverse QFT (IQFT) functions enable analysis-synthesis implementation using frequency spectrum-based selection approaches for compression. We study the resolution and precision of the QFT by comparing its outputs against classical two-dimensional Fast Fourier Transform (FFT) techniques using pixel-level Signal to Noise Ratio (SNR) as a metric. Formative and summative assessments have been deployed as a laboratory exercise in two National Science Foundation (NSF) workforce development programs. Preliminary evaluation results are presented in this paper.
This paper presents the development of Quantum Fourier transform (QFT) education tools in the object-oriented Java-DSP (J-DSP) simulation environment. More specifically, QFT and Inverse QFT (IQFT) user-friendly J-DSP functions are developed to expose undergraduate students to quantum computing. These functions provide opportunities to examine QFT resolution, precision (qubits), and the effects of quantum measurement noise. In our study, we also describe a laboratory exercise on QFT-based speech analysis-synthesis which has been deployed in our senior-level DSP class and in our NSF workforce development programs. The software and the laboratory exercise are evaluated using formative and summative assessments.
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.
This survey presents a comprehensive analysis of the quantum Fourier transform (QFT), a fundamental tool in quantum computing, in comparison to its classical counterpart, the fast Fourier transform (FFT). The study begins with an introduction to the classical Fourier transform, which is widely used in different disciplines such as signal and image processing. The article introduces the QFT as a quantum version of the Fourier transform, detailing how it leverages quantum parallelism and superposition to reduce the time complexity of the operation, and highlighting its crucial role in quantum algorithms like Shor’s algorithm for integer factorization. The analysis also addresses the mathematical foundations of the QFT, its implementation in quantum circuits, and the key advantages and challenges associated with its use, such as measurement precision and quantum decoherence. Finally, it concludes with an exploration of the current and potential applications of QFT in quantum computing.
This work explores the practical application of the Quantum Fourier Transform (QFT) for image alignment, focusing on the estimation of rotation angles in grayscale images containing structured line patterns and text. Motivated by the need to demonstrate quantum computing’s potential in addressing real-world image processing tasks, we develop a hybrid approach that combines classical pre-processing with quantum computation. We demonstrate that QFT can be applied to a concrete image processing task, illustrating the practical utility of quantum computing beyond theoretical examples. A classical baseline using the Fast Fourier Transform (FFT) is implemented via the ToolIP framework, achieving fast and accurate angle estimation. In parallel, a quantum version replaces the FFT with a simulated QFT on IBM’s Qiskit platform, using the Quantum Image Encoding Probability scheme to reduce qubit requirements. The classical method delivers results in milliseconds, while the quantum implementation, constrained by simulation and encoding overhead, demands significantly greater computational effort. Nonetheless, our findings show that QFT-based angle estimation is feasible and can yield results comparable to classical techniques. This study demonstrates the applicability of quantum algorithms to real-world image processing and underscores both the theoretical promise of QFT and the practical limitations faced in the current Noisy Intermediate-Scale Quantum (NISQ) era.
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.
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.