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.
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.
Quantum algorithms have emerged as a transformative approach to address the computational challenges of high-dimensional image processing tasks. This research investigates the integration of quantum computing principles, such as Quantum Fourier Transform (QFT) and Quantum Principal Component Analysis (QPCA), to optimize processes like edge detection, noise reduction, and image segmentation. These quantum-enhanced techniques promise significant improvements in computational efficiency and accuracy compared to classical methods, especially when handling complex visual data in real-time applications like medical imaging, satellite imagery, and autonomous systems. Additionally, the study explores hybrid quantum-classical architectures to bridge current limitations in noisy intermediate-scale quantum (NISQ) devices, ensuring resource optimization and scalability. The potential of quantum algorithms to provide faster, more precise solutions is evaluated alongside challenges like error mitigation and algorithmic stability. This research highlights the future role of quantum computing in revolutionizing image processing, paving the way for breakthroughs in computer vision and artificial intelligence.
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.
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 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.
Synthetic Aperture Radar (SAR) has played an important role in Earth observation, with applications in disaster monitoring, agriculture, forestry, ice surveillance, defense, and planetary exploration. The reconstruction of SAR images is a costly operation that uses Fourier Transform, while quantum computing has some key advantages that potentially enhance the algorithm to make it faster. Therefore, in the first part of the thesis, a major image processing method used in SAR systems is studied, known as the Range Doppler Algorithm (RDA). RDA is implemented on a simulated data set and a real data set from ICEYE Oy. In the second half of the thesis, quantum computing basic is studied and reviewed, including qubits, 1-qubit gate and 2-qubits gates, as well as the Quantum Fourier Transform (QFT) that are specific to replace the classical Fourier Transform. A framework for implementing the Range Doppler Algorithm (RDA) on a quantum computer, referred to as the Quantum Range Doppler Algorithm (QRDA), is proposed. In addition, the required resources under ideal quantum-computing assumptions are analyzed, including time complexity (algorithmic scaling) and space complexity (the number of qubits required). Lastly, the potential applicability of the proposed. QRDA in the context of current quantum device, Noisy Intermediate-Scale Quantum (NISQ) machine, is discussed.
Quantum Image Processing (QIP)is an exciting new field showing a lot of promise as a powerful addition to the arsenal of Image Processing techniques. Representing image pixel by pixel using classical information requires an enormous amount of computational resources. Hence, exploring methods to represent images in a different paradigm of information is important. In this work, we study the representation of images in Quantum Information. The main motivation for this pursuit is the ability of storing N bits of classical information in only log(2N) quantum bits (qubits). The promising first step was the exponentially efficient implementation of the Fourier transform in quantum computers as compared to Fast Fourier Transform in classical computers. In addition, images encoded in quantum information could obey unique quantum properties like superposition or entanglement.