Quantum Image Processing is a recent highlight in the quantum computing field. All previous methods for representing the images as quantum states were defined using qubits. One Quantum Image Representation (QIR) method using qutrits is present in the literature. Inspired by the qubit methods and the higher state-space available for qutrits, multiple QIR methods using qutrits are worked out in this paper. The ternary quantum gates required for the representations are described, and then the implementation details for five qutrit-based QIR methods are given. All the methods have been simulated in software, and example circuits are provided.
Quantum Image Processing is a recent highlight in the quantum computing field. All previous methods for representing the images as quantum states were defined using qubits. One Quantum Image Representation (QIR) method using qutrits is present in the literature. Inspired by the qubit methods and the higher state-space available for qutrits, multiple QIR methods using qutrits are worked out in this paper. The ternary quantum gates required for the representations are described, and then the implementation details for five qutrit-based QIR methods are given. All the methods have been simulated in software, and example circuits are provided.
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 Representation (QIR) has become a key component of Quantum Image Processing (QIP), enabling the encoding and manipulation of visual data within quantum computing environments.Its integration with Quantum Artificial Intelligence (QAI) and Quantum Machine Learning (QML) has attracted significant research interest due to the potential advantages of quantum parallelism and compact data representation.This survey reviews major QIR techniques, analyzes their encoding strategies and computational characteristics, and examines their opportunities, challenges, and future relevance in quantum AI and machine learning applications.A systematic review of 70 peer-reviewed journal and conference publications published between 1992 and 2025 was conducted.The selected studies were evaluated based on encoding mechanisms, qubit requirements, circuit complexity, retrieval capability, scalability, and suitability for quantum image processing and learning tasks.The review covers prominent QIR models, including FRQI, NEQR, MCQI, QPIE, GQIR, QRMW, and tensor-network-based representations.Comparative analysis reveals important trade-offs between qubit efficiency, encoding complexity, retrieval accuracy, and scalability.Amplitude-based approaches provide compact image encoding but suffer from probabilistic retrieval, whereas basis-state representations offer deterministic recovery at the expense of increased circuit complexity.QIR demonstrates significant potential in image classification, feature extraction, image compression, and hybrid quantum-classical learning frameworks.QIR provides a promising foundation for next-generation quantum-enhanced visual intelligence systems.However, practical implementation remains constrained by state preparation overhead, noise, decoherence, limited qubit availability, and the lack of standardized evaluation frameworks.Future research should focus on scalable encoding methods, fault-tolerant quantum architectures, benchmarking standards, and deeper integration with advanced QML models to accelerate the development of practical quantum image analytics.
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.
Abstract Quantum Image Representation (QIR) is a fundamental concept in quantum image processing. It describes how classical images are converted into quantum states for processing on quantum computers. Researchers proposed several QIR models, with FRQI and NEQR being the most popular ones. These models show the possibilities of the quantum image encoding. Nevertheless, they are also limited in some way. Mostly, pixel intensity accuracy, the required number of qubits, and circuit complexity have trade-offs. Their application to Noisy Intermediate-Scale Quantum (NISQ) devices becomes challenging, the quantum resources being small in such devices, due to this. In the following paper, we introduce our own approach, which is the Intensity-Preserving Quantum image Representation (IP-QIR). The key aim of IP-QIR is to maintain the information about the grayscale intensities and decrease the amount of quantum resources. IP-QIR quantifies pixel intensities by a controlled rotation scheme. The measurement statistics of a single qubit hold the intensity information and the position qubits represent the spatial information. The strategy uses small patches of images rather than complete images to make it easy to implement. This will decrease the depth of circuit design and makes the approach less advanced to the near-term quantum hardware. IBM Qiskit simulations are used in assessing the performance of IP-QIR. The three types of grayscale images of which experiments are run are the synthetic image patches, SAR images and medical TB chest X-ray images. It is revealed that IP-QIR maintains the intensity information compared to the FRQI and NEQR. SAR and medical data can reach values of fidelity of 84.12\%. The other notable point is that the size of a 4 x 4 image patch only needs five qubits which are much lower than in NEQR. Meanwhile, good reconstruction accuracy is achieved. These findings demonstrate the fact that IP-QIR is an effective and realistic approach to quantum image representation on the NISQ-era quantum devices.
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.