Ternary Quantum Image Processing (TQIP) leverages the power of qutrits to enhance Quantum Image Processing (QIP) by enabling higher information density, reducing error rates, and simplifying circuit complexity compared to traditional binary quantum systems. Inspired by the ENEQR binary model, this paper introduces the Ternary Novel Colored Quantum Representation (TNCQR), a qutrit-based model for encoding RGB digital images in a ternary quantum system. The TNCQR model requires fewer qutrits than the number of qubits needed in equivalent binary models. By incorporating a single ancilla qutrit, the model reduces the depth of high-complexity gates, thereby lowering the overall quantum cost and improving time complexity. To simplify the constructed circuits, an optimization algorithm is presented, consisting of 2 general phases applicable to any image size and one conditional phase specific to each image. This makes TNCQR an efficient, scalable, and resource-optimized quantum image representation model.
Ternary Quantum Image Processing (TQIP) leverages the power of qutrits to enhance Quantum Image Processing (QIP) by enabling higher information density, reducing error rates, and simplifying circuit complexity compared to traditional binary quantum systems. Inspired by the ENEQR binary model, this paper introduces the Ternary Novel Colored Quantum Representation (TNCQR), a qutrit-based model for encoding RGB digital images in a ternary quantum system. The TNCQR model requires fewer qutrits than the number of qubits needed in equivalent binary models. By incorporating a single ancilla qutrit, the model reduces the depth of high-complexity gates, thereby lowering the overall quantum cost and improving time complexity. To simplify the constructed circuits, an optimization algorithm is presented, consisting of 2 general phases applicable to any image size and one conditional phase specific to each image. This makes TNCQR an efficient, scalable, and resource-optimized quantum image representation model.
Ternary quantum image processing (TQIP) integrates qutrit-based quantum computing with image representation, offering a promising pathway for efficient image encoding models. This paper introduces Novel Qutrit Quantum Representation (NQQR) model, a scalable and optimized ternary model for representing grayscale and RGB images of size [Formula: see text] in a ternary quantum system. The proposed model encodes pixel positions using the superposition of 2n qutrits and assigns grayscale or color intensity values using 6 qutrits, while an additional color qutrit and an ancilla qutrit are employed to reduce the complexity of multi-controlled N-qutrit gates, thereby lowering the overall quantum cost. Experimental results show that the NQQR achieves a time complexity of [Formula: see text] and the optimized NQQR model significantly reduces quantum cost, with improvements up to [Formula: see text] for grayscale images and [Formula: see text] for RGB images when compared to equivalent non-optimized qubit/qutrit-based encoding models. In addition, the performance of the proposed model is evaluated under quantum depolarizing noise using MSE and PSNR metrics computed between the original and reconstructed images under different noise levels. These results demonstrate the efficiency and scalability of the proposed NQQR model at the representation level and suggest its potential as a building block for future research in TQIP.
Abstract Quantum computation is growing in significance and proving to be a powerful tool in meeting the high real-time computational demands of classical digital image processing. However, extensive research has been done on quantum image processing, mainly rooted in binary quantum systems. In this paper, we propose a new quantum ternary image circuit based on the analysis of the existing qutrit representation of quantum images. The proposed design utilizes ternary shift gates and ternary Muthukrishnan–Stroud gates, with the belief that this circuit can be used for ternary quantum image processing. This study makes a significant improvement compared to the existing counterpart in terms of quantum cost, the number of constant inputs, and garbage outputs, which are all essential parameters in quantum circuit design.
Quantum image processing is an emerging topic in the field of quantum information and technology. In this paper, we propose a new quantum image representation of RGB images with deterministic image retrieval, which is an improvement over all the similar existing representations in terms of using minimum resource. We use two entangled quantum registers constituting of total 7 qutrits to encode the color channels and their intensities. Additionally, we generalize the existing encoding methods by using both qubits and qutrits to encode the pixel positions of a rectangular image. This hybrid-qudit approach aligns well with the current progress of NISQ devices in incorporating higher dimensional quantum systems than qubits. We then describe the image encoding method using higher-order qubit-qutrit gates, and demonstrate the decomposition of these gates in terms of simpler elementary gates. We use the Google Cirq's quantum simulator to verify the image preparation in both the ideal noise-free scenario and in presence of realistic noise modelling. We show that the complexity of the image encoding process is linear in the number of pixels. Lastly, we discuss the image compression and some basic RGB image processing protocols using our representation.
Abstract Color images (i.e. RGB) contain rich visual information essential for object recognition, spatial context analysis, and decision-making across fields such as medical imaging, remote sensing, and computer vision. Processing such data efficiently requires significant computational resources, which can be addressed by the parallelism and speed of quantum computing. Representing RGB image data within quantum states enables efficient and scalable processing compared to classical methods. In recent years, various quantum image representation techniques have been developed based on probabilistic and basis state encoding. Probabilistic encoding methods are efficient for representing quantum binary images but face challenges in accurately reconstructing RGB images. This is due to the randomness introduced by measurement. To overcome this limitation, several basis state encoding approaches have been proposed. These methods map classical pixel values directly to quantum basis states. Thus enabling accurate grayscale and RGB image representation. However, they often require a larger number of qubits and complex gate operations, leading to higher circuit preparation costs. So, there exists substantial potential for quantum probabilistic RGB image representation using randomized measurements. Hence, our objective is to develop a probabilistic quantum image representation, capable of representing RGB images using fewer qubits. This method aims to reconstruct the classical image with high accuracy using randomized measurements, thereby addressing the major limitations of probabilistic methods. To balance image quality with resource efficiency, we propose an Improved Probabilistic Quantum Image Representation (IPQIR) method based on equal superposition states. This approach utilizes a quantum circuit with Hadamard Gate to encode classical pixel values into equal superposition states. The original image is then reconstructed by performing multiple quantum measurements and applying expectation value estimation to average the outcomes. To align with existing research in quantum image representation, quantum state tomography and different applications are utilized as standard evaluation methods to assess the effectiveness of the proposed algorithm. The tomography achieved a fidelity of 97.51%. In addition, various parametric and non-parametric statistical tests were performed to verify the accuracy of the reconstructed classical image. The high Pearson (0.9983) and Spearman (0.9959) correlation coefficients indicate a nearly perfect linear and monotonic relationship between the original and reconstructed images.
Abstract In recent years, quantum computing has emerged as a leading approach for accelerating complex computations, leveraging quantum parallelism and entanglement to surpass classical limits. Although numerous quantum circuits based on reversible gates have been proposed, optimizing circuit efficiency remains a critical challenge, particularly in the noisy intermediate-scale quantum era, where error rates and coherence times constrain performance. Ternary quantum computing, which operates on three-level quantum systems (qutrits), offers a promising alternative by reducing circuit complexity and resource overhead. In particular, balanced ternary logic presents advantages over conventional ternary logic by enhancing resource efficiency and potentially mitigating quantum gate error rates. This paper focuses on two key objectives: first, the synthesis of a reversible 1-qutrit comparator circuit using balanced ternary logic, and second, the extension to a generalized n-qutrit comparator. The proposed 1-qutrit comparator achieves notable improvements over existing unbalanced designs, demonstrating a 65% reduction in quantum cost, 50% fewer constant inputs, and a 33% decrease in garbage outputs. These results highlight the potential of balanced ternary logic to enhance the efficiency of quantum circuits, making it a valuable contribution to the development of scalable and error-resilient quantum hardware.
Quantum image representation plays an important role in quantum image processing. In this paper, a bitplane representation of quantum images (BRQI) is proposed, which uses (n+4) or (n+6) qubits to store a grayscale or RGB color image of 2npixels. Compared with a novel enhanced quantum representation (NEQR), and a novel quantum representation of color digital images (NCQI), the storage capacity of BRQI improves 16 times and 218times, respectively. Next, some quantum operations based on BRQI are proposed, these operations including complement of colors, reverse of bitplanes, and translation of bitplanes. Analyzed the implementation circuits of these operations, the result indicates that these operations based on BRQI have lower quantum cost than NEQR and NCQI. Furthermore, an image scrambling algorithm based on BRQI is presented by combining the above operations. Simulation experiments and performance analysis show that proposed scrambling algorithm is effective and efficient.