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arXiv:2203.06196 · Physical Review A

Efficient quantum interpolation of natural data

Sergi Ramos-Calderer

Published Dec 21, 2022• 9 citations
arXivHTMLPDF

Abstract

We present efficient methods to interpolate data with a quantum computer to complement uploading techniques and quantum postprocessing. The quantum algorithms make use of the efficient quantum Fourier transform (QFT) as well as classical signal and imaging processing techniques, and may facilitate quantum advantages for some relevant families of data. We showcase a QFT interpolation method, a quantum cosine transform (QCT) interpolation geared towards natural data, and we improve upon them by utilizing a quantum circuit's capabilities of processing data in superposition. A circuit for the QCT is presented. We illustrate the methods on probability distributions and quantum encoded images, and discuss the precision of the resulting interpolations.

DOI
10.1103/physreva.106.062427

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The quantum Fourier transform (QFT) is the important operation in quantum computing. It is used in many algorithms, including the Shor's quantum algorithm for finding the prime factors of integers. Color image encryption, processing and representation of quantum images are areas where the QFT is also used. In this paper, we discuss the quantum superpositions of the images and methods of calculation of the analogues of the quantum 2-D discrete Fourier transform of images. The quantum algorithms and circuits will be described, and examples of calculation of the 2-D QFT of images of 8×8 and 16×16 pixels will be given in detail.
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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 paper explores the application of quantum quantumization for image processing, aiming to improve image compression ratios and quality. The core concept involves transforming images into quantum quantumized information, leveraging the unique properties of quantum computing to perform image processing operations. This approach facilitates both image compression and enhancement. We propose a novel framework utilizing quantum techniques to represent and manipulate image data, offering potential advantages over classical methods, particularly for high-resolution images and complex scenes. The theoretical underpinnings of this work are detailed, focusing on the mathematical formulations involved in the quantum encoding, processing, and decoding stages. We demonstrate the feasibility of this approach and suggest future research directions.