The joint photographic expert group algorithm compresses a digital image by filtering its high spatial-frequency components. Similarly, we introduce a quantum algorithm that uses the quantum Fourier transform to discard the high spatial-frequency qubits of an image, downsampling it to a lower resolution. This allows one to capture, compress, and send images even with limited quantum resources for storage and communication. We show under which conditions this protocol is advantageous with respect to its classical counterpart.
The joint photographic expert group algorithm compresses a digital image by filtering its high spatial-frequency components. Similarly, we introduce a quantum algorithm that uses the quantum Fourier transform to discard the high spatial-frequency qubits of an image, downsampling it to a lower resolution. This allows one to capture, compress, and send images even with limited quantum resources for storage and communication. We show under which conditions this protocol is advantageous with respect to its classical counterpart.
Abstract In signal processing, resampling algorithms can modify the number of resources encoding a collection of data points. Downsampling reduces the cost of storage and communication, while upsampling interpolates new data from limited one, e.g., when resizing a digital image. We present a toolset of quantum algorithms to resample data encoded in the probabilities of a quantum register, using the quantum Fourier transform to adjust the number of high-frequency encoding qubits. We discuss advantage over classical resampling algorithms.
Quantum image processing has been a hot topic. The first step of it is to store an image into qubits, which is called quantum image preparation. Different quantum image representations may have different preparation methods. In this paper, we use GQIR (the generalized quantum image representation) to represent an image, and try to decrease the operations used in preparation, which is also known as quantum image compression. Our compression scheme is based on JPEG (named from its inventor: the Joint Photographic Experts Group) --- the most widely used method for still image compression in classical computers. We input the quantized JPEG coefficients into qubits and then convert them into pixel values. Theoretical analysis and experimental results show that the compression ratio of our scheme is obviously higher than that of the previous compression method.
Image processing is a fascinating field for exploring quantum algorithms. However, achieving quantum speedups turns out to be a significant challenge. In this work, we focus on image filtering to identify a class of images that can achieve a substantial speedup. We show that for images with efficient encoding and a lower bound on the signal-to-noise ratio, a quantum filtering algorithm can be constructed with a polynomial complexity in terms of the qubit number. Our algorithm combines the quantum Fourier transform with the amplitude amplification technique. To demonstrate the advantages of our approach, we apply it to three typical filtering problems. We highlight the importance of efficient encoding by illustrating that for images that cannot be efficiently encoded, the quantum advantage will diminish. Our work provides insights into the types of images that can achieve a substantial quantum speedup.
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.
Multi-qubit encoding is a quantum encoding technique that uses multiple qubits to represent information, enabling higher data throughput. This study explores its application in compressed image transmission, comparing its performance to single-qubit encoding in both uncoded and channel-coded configurations. For image compression, JPEG and HEIF formats are used, with source coding rates adjusted to ensure similar bandwidth utilization. The compressed bitstream is optionally protected by channel coding before undergoing quantum encoding using qubit sizes from 1 to 8 for quantum channel transmission. At the receiver, quantum decoding reconstructs classical bits, followed by optional channel decoding, and finally, source decoding restores the image. Image quality is assessed using peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM) and universal quality index (UQI). Results show that increasing the qubit encoding size improves noise resilience, with eight-qubit encoding achieving a maximum channel SNR gain of 15 dB for JPEG and 17 dB for HEIF under channel coding, demonstrating greater robustness compared to single-qubit encoding but with higher computational complexity. To address this, an adaptive multi-qubit encoding process is proposed, dynamically adjusting qubit usage by utilizing fewer qubits for lower noise levels and higher qubits for higher noise conditions while balancing noise resilience and computational complexity under the assumption of perfect channel estimation.
We investigate the storage and retrieval of an image in a multi-particle quantum mechanical system. Several models are studied and compared with corresponding classical digital methods. We consider a situation in which qubits replace classical bits in an array of pixels and show several advantages. For example, we consider the situation in which 4 different values are randomly stored in a single qubit and show that quantum mechanical properties allow better reproduction of original stored values compared with classical (even stochastic) methods. The retrieval process is uniquely quantum (involves measurement in more than one bases). The independence and the finiteness of the stored copies of the image play an important role in the quantum protocol being better than the classical one. Other advantages of quantum storage of an image are found in its security.