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.
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.
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.
In recent years, quantum image computing has gained significant attention due to its ability to provide more data storage and process faster than classical computation. These are possible due to the unique properties of quantum mechanism of parallelism, superposition, and entanglement. Compressing and representing classical image data in the quantum domain, as well as state label preparation complexity, is still a challenging issue. The existing techniques typically directly connect the pixel values and their corresponding state label connection without exploring quantum bits i.e. qubits and connection pattern correlation. As a result, the required number of quantum resources, such as gates and qubits to implement quantum circuits, is quite high. This thesis proposes several novel approaches by exploiting correlations within qubits/connections in the state preparation within pixel domain and transform domain. The existing quantum methods need qubits, and quantum gates to represent both pixel intensity and their corresponding position i.e. state preparation information. To reduce the number of qubits and gates required for state preparation, transformation and quantization are applied to the image data. This is because the transformed coefficients are concentrated in a smaller region compared to the pixel domain, allowing the number of state-preparation qubits to be significantly lower. Theoretical analysis and experimental results show that it provides better compression and representation than existing approaches. To represent the quantized transformed coefficient using the existing quantum representing approach, two control gates are needed, one for opening and another for closing the connection to locate each quantized transformed state value. Due to the repetitive use of the same control gates to locate each quantized state connection, a significant number of quantum resources are still required. Furthermore, resetting the output effect of each quantized transformed coefficient state connection on the qubit introduces redundancy in control gate usage and increases circuit complexity. To address state complexity challenges of the quantized transform coefficient approach, a novel reset gate is introduced that can perform the same task for closing the connection of state position. It modifies the closing state connection that nullifies the previous quantized transformed coefficient state connection effect on the next one, eliminating the need for repetitive use of control gates. Although using the reset gate instead of control gate, the proposed approach improves the compression performance, still, this approach requires higher quantum resources to locate the state position of the quantized transformed coefficient alongside. To address this, a novel control gate state connection approach is proposed. It modifies the quantized transformed coefficient connections by discarding ‘0’ values in the state preparation stage, since only input ‘1’ influences the output. This approach significantly reduces the circuit complexity. The experimental results confirm its superior performance in quantum image compression and representation. The required number of qubits for representing large magnitude of coefficient is sometimes higher for high quality images. To address this, a non-zero state connection of pixel values circuit is proposed on top of the block truncation coding compression approach. This approach is easy to implement, cost-effective, and memory-efficient and requires fewer qubits compared to the transformed-based approach. However, this approach requires more connections to complete the whole image circuit. Recently, an autoencoder-based approach has been used to compress quantum images. The main limitation of the autoencoder approach is that it is only applicable to small-scale images with unclear state compression mechanisms. To overcome this limitation, a parameterized position-aware lossy quantum autoencoder is proposed by utilizing the least significant bit (LSB) as a control qubit for optimized state-label information management. We have used a block-based position-aware LSB control qubit approach to improve further compression efficiency. Comparative analysis shows that it outperforms the existing quantum autoencoder approach in terms of gate efficiency as well as image quality.
In recent years, quantum image computing draws a lot of attention due to storing and processing image data faster compared to classical computers. A number of approaches have been proposed to represent the quantum image inside a quantum computer. Representing and compressing medium and big-size images inside the quantum computer is still challenging. To address this issue, we have proposed a block-wise DCT-EFRQI (Direct Cosine Transform Efficient Flexible Representation of Quantum Image) approach to represent and compress the gray-scale image efficiently to save computational time and reduce the quantum bits (qubits) for the state preparation. In this work, we have demonstrated the capability of block-wise DCT and DWT transformation inside the quantum domain to investigate their relative performances. The Quirk simulation tool is used to design the corresponding quantum image circuit. In the proposed DCT-EFRQI approach, a total of 17 qubits are used to represent the coefficients, the connection between coefficients and state (i.e., auxiliary), and their position for representing and compressing grayscale images inside a quantum computer. Among those, 8 qubits are used to map the coefficient values and the rest are used to generate the corresponding coefficient XY-coordinate position including one auxiliary qubit. Theoretical analysis and experimental results show that the proposed DCT-EFRQI scheme provides better representation and compression compared to DCT-GQIR, DWT-GQIR, and DWT-EFRQI in terms of rate-distortion performance.
Quantum computing has emerged as a transformative paradigm, with revolutionary potential in numerous fields, including quantum image processing and compression. Applications that depend on large scale image data could benefit greatly from parallelism and quantum entanglement, which would allow images to be encoded and decoded with unprecedented efficiency and data reduction capability. This paper provides a comprehensive overview of the rapidly evolving field of quantum image compression, including its foundational principles, methods, challenges, and potential uses. The paper will also feature a thorough exploration of the fundamental concepts of quantum qubits as image pixels, quantum gates as image transformation tools, quantum image representation, as well as basic quantum compression operations. Our survey shows that work is still sparse on the practical implementation of quantum image compression algorithms on physical quantum computers. Thus, further research is needed in order to attain the full advantage and potential of quantum image compression algorithms on large-scale fault-tolerant quantum computers.
Abstract In recent years, quantum image processing got a lot of attention in the field of image processing due to the opportunity to place huge image data in quantum Hilbert space. Hilbert space or Euclidean space has infinite dimensions to locate and process the image data faster. Moreover, several types of research show that the computational time of the quantum process is faster than classical computers. Encoding and compressing the image in the quantum domain is still a challenging issue. From the literature survey, we have proposed a DCT-EFRQI (Direct Cosine Transform Efficient Flexible Representation of Quantum Image) algorithm to represent and compress gray image efficiently which save computational time and minimize the complexity of preparation. This work aims to represent and compress various gray image sizes in quantum computers using the DCT (Discrete Cosine Transform) and EFRQI (Efficient Flexible Representation of Quantum Image) approaches together. The Quirk simulation tool is used to design the corresponding quantum image circuit. Due to the limitation of qubits, a total of 16 numbers of qubits is used to represent the coefficient and its position of the grayscale image. Among those, 8 number of qubits are used to map the coefficient values and the rest are used to generate the corresponding coefficient XY-coordinate position. Theoretical analysis and experimental results show that the proposed DCT-EFRQI scheme provides better representation and compression compared to DCT-GQIR, DWT-GQIR, and DWT-EFRQI in terms of PSNR(Peak Signal to Noise Ratio), and bit rate.
Quantum image computing has emerged as a groundbreaking field, revolutionizing how we store and process data at speeds incomparable to classical methods. Nevertheless, as image sizes expand, so does the complexity of qubit connections, posing significant challenges in the efficient representation and compression of quantum images. In response, we introduce a modified Toffoli gate state connection using a quantized transform coefficient preparation process. This innovative strategy streamlines circuit complexity by modifying state connection from the state connection information. In our operational control gates, only input 1 impacts the output, allowing us to modify the state connection and dramatically enhance the efficiency of the proposed circuit. As a result, the proposed approach significantly reduces the number of gates required for both image compression and representation. Our findings reveal that it requires an impressive 44.21 percent fewer gates than existing techniques, such as the Direct Cosine Transform Efficient Flexible Representation of Quantum Images (DCTEFRQI), all while maintaining a consistent peak signal-to-noise ratio (PSNR). For an image block size of 2^Sx2^Sy with q gray levels, the complexity of our approach can be succinctly expressed as, O[3q+log2Sx+log2Sy+2q(log2Sx+log2Sy)]. Here, Sx and Sy represent the X and Y positional control gates while q indicates the non-zero transform coefficients. Moreover, experimental evaluations strongly demonstrate that it excels in both compressing and representing quantum images compared to the DCTEFRQI approach, particularly excelling in the essential metrics of gate requirements and PSNR performance. Embrace the future of quantum imaging with our innovative solution, where efficiency meets excellence.