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CRC Press eBooks

Quantum Image Compression

Zhixin Zhang, Xianhua Song, Ahmed A. Abd El‐Latif, Basma Abd El-Rahiem

Published May 15, 2026• 0 citations
Publisher

Abstract

From the quantum images and their preparation methods described in Chapter 2, it can be seen that preparing a quantum image requires a large number of basic quantum gates. For example, to prepare a quantum color image Quantum Image Representation based on HSI (QIRHSI) with a size of https://www.w3.org/1998/Math/MathML" display="inline"> 2 8 × 2 8 pixels and an intensity value range of https://www.w3.org/1998/Math/MathML" display="inline"> 0 ∼ 2 8 − 1 , approximately the number of basic quantum gates required is 2 64 . Therefore, in this chapter, the resources for image preparation will be optimized. The principle of Boolean expression minimization will be used to simplify the quantum circuit in the quantum image QIRHSI. In essence, it is to replace the original preparation of the quantum image with a new unitary transformation that has fewer quantum logic gates.

DOI
10.1201/9781003621423-6

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From the quantum images and their preparation methods described in Chapter 2, it can be seen that preparing a quantum image requires a large number of basic quantum gates. For example, to prepare a quantum color image Quantum Image Representation based on HSI (QIRHSI) with a size of https://www.w3.org/1998/Math/MathML" display="inline"> 2 8 × 2 8 pixels and an intensity value range of https://www.w3.org/1998/Math/MathML" display="inline"> 0 ∼ 2 8 − 1 , approximately the number of basic quantum gates required is 2 64 . Therefore, in this chapter, the resources for image preparation will be optimized. The principle of Boolean expression minimization will be used to simplify the quantum circuit in the quantum image QIRHSI. In essence, it is to replace the original preparation of the quantum image with a new unitary transformation that has fewer quantum logic gates.
Quantum image representation is an essential component of quantum image processing and plays a critical role in quantum information processing. Flexible Representation of Quantum Images (FRQI) presents pixel colors and associated locations as a state to represent images on quantum computers. A fundamental part of the quantum image processing system is quantum image compression (QIC), which is utilized to maintain and retrieve binary images. This compression allows us to minimize the number of controlled rotation gates in the quantum circuits. This paper designed optimized quantum circuits and simulated them using Qiskit on a real quantum computer based on minimum boolean expressions to retrieve the 8×4 binary single-digit images. To demonstrate the feasibility and efficacy of quantum image representation, quantum circuits for images were developed using FRQI, and quantum image representation experiments were done on IBM Quantum Experience (IBMQ). We were able to visualize quantum information by doing the quantum measurement on the image information that we had prepared. Without utilizing this method, the number of controlled rotation gates is equal to the number of pixels in the image; however, we showed that by using the QIC algorithm, we could decrease the number of gates significantly. On these images, the maximum and minimum compression ratios of QIC are 90.63% and 68.75%, respectively.
Quantum image computing has attracted attention due to its vast storage and faster processing of image data than classical computers. Although classical computing power has grown substantially in the last decade, its abilities have plateaued, struggling to meet the needs of huge datasets. Quantum computers, on the other hand, take advantage of unique qualities like quantum parallelism, superposition, and entanglement to provide faster solutions to complicated problems. Managing huge image data in classical systems necessitates significant memory and hardware resources, which makes quantum computing a possible alternative. Several approaches have arisen for encoding and compressing classical images in the quantum processor. However, one of the most significant limitations is the complexity of quantum state preparation, which translates pixel coordinates to corresponding quantum circuits. Current approaches for representing large-scale images require a huge number of quantum resources including qubit, and qubit connection, which presents significant hurdles. Therefore, this article aims to overview the pixel intensity and state preparation circuit that needs fewer connections, i.e., quantum gates to represent quantum image data, and then explore and design effective compression and processing methods for medium and high-resolution images. This work specializes in emerging quantum models’ potential for enhancing image representation and compression capabilities. It also conducts a comprehensive study of quantum image representation and compression techniques, categorizing existing methods by grayscale and color image types and evaluating their methods, strengths, and limitations. It focuses on crucial difficulties, such as high qubit requirements and complex state preparation, that limit scalability for huge images. This paper also assesses each model’s compression efficacy, which will help future research focus on efficient circuit designs with lower complexity for medium to high-resolution images. It is an essential reference for advancing quantum image processing research since it provides a systematic framework for evaluating quantum image compression and representation algorithms.
Quantum image processing has recently received much attention due to the opportunity to place image data in quantum mechanics systems. The literature survey has shown that the complexity of preparing image data raises the question of how and in what efficient way a medium- and high-size image is represented inside the quantum domain, which is still a big question. Quantum properties such as entanglement, superposition, and parallelism make the quantum system faster and more robust. Qubit is the central basic unit that maps the image data in the quantum processor, which propagates from left to right. The number of qubits and their connection determine the efficiency of the circuit architecture. This chapter aims to investigate the performance of the transformed coefficient-based quantum image representation and compression approaches in terms of the required number of gates and PSNR values. Moreover, the challenges and prospects of quantum image compression and processing will be discussed as a future research direction.
This chapter first presents the general framework structure of quantum image representation, and then introduces some research results on quantum color image representation in our group. In this study, quantum color image representation based on the HSI color space (QIRHSI) is a quantum color image representation based on the hue, saturation, and intensity (HSI) color space in the right-angle coordinate system, novel color quantum image (NCQI) and Color Quantum Image based on Phase Transform (CQIPT) are quantum color image representations based on the RGB color space in the right-angle coordinate system, and MLCPQI is a quantum color image representation based on the RGB color space in the polar coordinate system. In addition, the preparation scheme on a quantum computer and the computational complexity of the prepared image are provided for each quantum color image representation method. Ultimately, a general framework and preparation strategy for quantum video representation are proposed based on quantum image representation.
The negative effects caused by geometric distortion can be removed to the maximum extent possible through appropriate geometric transformations, allowing us to focus on the image content itself in subsequent processing and recognition. Therefore, geometric transformations are often used as a pre-processing step for other image processing applications. In this paper, quantum algorithms are designed to implement geometric transformations, including two-point swapping, circular translation, flipping transformations and right-angle rotation, across a quantum image representation QIRHSI (Quantum Image Representation based on HSI color space) which is built on HSI (Hue-Saturation-Intensity) color space. The above geometric transformations are realized by quantum circuits composed of elementary quantum gates. By analyzing the complexity of the fundamental quantum gates needed for the above geometric transformations, it is found that the global transformations (circular translation, flip transformation and right-angle rotation) are lower than the local transformation (two-point swapping). The proposed geometric transforms are used to facilitate the applications of quantum images with low complexity and high efficiency.
Flexible Representation of Quantum Images (FRQI) is proposed to provide a representation of images that enables efficient preparation and image processing operators on quantum computers. FRQI captures colors and their corresponding positions in an image into a quantum state. The preparation with polynomial simple operations for FRQI turning a quantum computer from the initialized state to the FRQI state is done by using Hadamard and controlled rotation gates. The Quantum Image Compression (QIC) algorithm reduces simple operations used in the preparation process based on the minimization of Boolean equations are from same color groups of positions. Quantum image processing operators on FRQI based unitary transforms dealing with only colors, colors at some positions and the combination by the quantum Fourier transform of both colors and positions are addressed. The experiments for the storage and retrieval of images using FRQI are implemented in Matlab. The compression ratio of QIC among same color groups ranges from 6.67% to 31.62% on the Lena image.