Efficiently representing and compressing large-scale images in quantum circuits remains a challenge due to increasing circuit complexity. This paper proposes an innovative approach called NZ-NEQR (Non-Zero Novel Quantum Representation) to tackle this issue. Eliminating zero connections from the existing NEQR approach significantly reduces the complexity of state label preparation. The proposed NZ-NEQR approach achieves remarkable improvements in both image representation and compression, leading to a substantial reduction in required bits per pixel. To further enhance compression, Block Truncation Coding (BTC) is adopted as a compression scheme, which effectively truncates images into two labels suitable for quantum compression and reconstruction. Notably, the proposed method requires fewer bits per pixel compared to existing NEQR approaches. Additionally, NZ-NEQR combined with BTC employs only 5 qubits for representing a $1024 \times 1024$ image, and compression using a $4 \times 4$ quantum BTC block represents a significant advancement. Computational results demonstrate the superior effectiveness of the proposed NZ-NEQR approach combined with BTC for quantum image representation and compression, surpassing the performance of NEQR and JPEG approaches.
Efficiently representing and compressing large-scale images in quantum circuits remains a challenge due to increasing circuit complexity. This paper proposes an innovative approach called NZ-NEQR (Non-Zero Novel Quantum Representation) to tackle this issue. Eliminating zero connections from the existing NEQR approach significantly reduces the complexity of state label preparation. The proposed NZ-NEQR approach achieves remarkable improvements in both image representation and compression, leading to a substantial reduction in required bits per pixel. To further enhance compression, Block Truncation Coding (BTC) is adopted as a compression scheme, which effectively truncates images into two labels suitable for quantum compression and reconstruction. Notably, the proposed method requires fewer bits per pixel compared to existing NEQR approaches. Additionally, NZ-NEQR combined with BTC employs only 5 qubits for representing a 1024×1024 image, and compression using a 4×4 quantum BTC block represents a significant advancement. Computational results demonstrate the superior effectiveness of the proposed NZ-NEQR approach combined with BTC for quantum image representation and compression, surpassing the performance of NEQR and JPEG approaches.
Quantum computing draws huge attention due to its faster computational capability compared to classical computing to represent and compress the classical image data into the quantum domain. The main idea of quantum domain representation is to convert pixel intensities and their coordinates i.e. state label preparation using quantum bits i.e. Qubits. For a bigger size image, the state label preparation takes more Qubits. To address more Qubits issues, a novel SCMNEQR (State Connection Modification Novel Enhanced Quantum Representation) approach has been proposed that uses fewer qubits to map the arbitrary size of the grayscale image using block-wise state label preparation. The proposed SCMNEQR approach introduces the state connection using a reset gate rather than repeating the use of the Toffoli gate used in the existing approach. The experimental results show that the proposed approach outperforms the existing methods in terms of compression.
Quantum computing draws huge attention due to the multidimensional information processing capability of the processor at the same time. The main idea of quantum imaging is to represent pixel intensities and their state using standard quantum circuits. For a medium or larger size image, the state label circuit takes more qubits as well as requires a huge connection leading to circuit complexity. In this work, a block-wise lossy SCMNEQR (state connection modification novel enhanced quantum representation) approach has been proposed to address more qubit connection issues. The average computation time decreased by 99.66% and 7.39% compared to the JPEG and DCT-EFRQI approaches respectively. The experimental results show that it outperforms the DCT-EFRQI (discrete cosine transform- efficient flexible representation of the quantum image) approach in terms of both representation and compression due to the use of block-wise division of transfer coefficient and state label alongside a novel reset gate.
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.
We introduce a novel and uniform framework for quantum pixel representations that overarches many of the most popular representations proposed in the recent literature, such as (I)FRQI, (I)NEQR, MCRQI, and (I)NCQI. The proposed QPIXL framework results in more efficient circuit implementations and significantly reduces the gate complexity for all considered quantum pixel representations. Our method scales linearly in the number of pixels and does not use ancilla qubits. Furthermore, the circuits only consist of [Formula: see text] gates and [Formula: see text] gates making them practical in the NISQ era. Additionally, we propose a circuit and image compression algorithm that is shown to be highly effective, being able to reduce the necessary gates to prepare an FRQI state for example scientific images by up to 90% without sacrificing image quality. Our algorithms are made publicly available as part of QPIXL++, a Quantum Image Pixel Library.
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.