Tensor network methods strike a middle ground between fully-fledged quantum computing and classical computing, as they take inspiration from quantum systems to significantly speed up certain classical operations. Their strength lies in their compressive power and the wide variety of efficient algorithms that operate within this compressed space. In this work, we focus on applying these methods to fundamental problems in image compression and processing and classical optics such as wave-front propagation and optical image formation, by using directly or indirectly parallels with quantum mechanics and computation. These quantum-inspired methods are expected to yield faster algorithms with applications ranging from astronomy and earth observation to microscopy and classical imaging more broadly.
Tensor network methods strike a middle ground between fully-fledged quantum computing and classical computing, as they take inspiration from quantum systems to significantly speed up certain classical operations. Their strength lies in their compressive power and the wide variety of efficient algorithms that operate within this compressed space. In this work, we focus on applying these methods to fundamental problems in image compression and processing and classical optics such as wave-front propagation and optical image formation, by using directly or indirectly parallels with quantum mechanics and computation. These quantum-inspired methods are expected to yield faster algorithms with applications ranging from astronomy and earth observation to microscopy and classical imaging more broadly.
Computer vision is confronted with increasing computational bottlenecks and memory requirements hard to scale by normal convolutional neural networks. Quantum-inspired architectures are inspired by quantum mechanics, superposition, entanglement as well as interference to redesign visual information processing in a more efficient way. Quantum convolutional neural networks are one of the biggest improvements as they apply parameterized quantum circuits to explore several input states at a time. Quantum-inspired pruning algorithms have lowered the processing time, and quantum optical neural networks have used the wave nature of light to have parallel characteristics of features. Tensor network architectures are based on quantum physics and can be used to convert high-dimensional image data into information-rich elements and model multi-scale interactions. Hybrid quantum-classical systems can be described as using quantum-inspired processing and the reliability of established deep learning. Attention systems ensure that quantum circuits are dedicated to informative parts of an image, whereas knowledge transfer of classical models stabilizes quantum training. Nonetheless, basic constraints limit applications: the barren plateau problem, measurement overhead, preparation complexity of states and decoherence are all major challenges. The existing applications include quantum-inspired classical algorithms to physical hardware experiments. Thorough benchmarking demonstrates that the classical approaches can be much more effective than the quantum ones. Frameworks such as PennyLane extend accessibility, although best practice and careful consideration of the architecture involving the integration of quantum-inspired and classical computing is critical to realistic computer vision systems.
Classical computational simulations of biological systems, particularly at the cellular level, face significant limitations due to the exponential growth in computational requirements with system complexity. This work proposes a novel approach to simulating cellular processes utilizing quantum-inspired algorithms, specifically tensor network methods, to overcome these limitations. These algorithms mimic key aspects of quantum computation – superposition and interference – to efficiently model intricate molecular interactions and resulting emergent phenomena. The core idea is to represent complex biological systems using tensor networks, enabling parallel processing and capturing correlations inherent in quantum systems. This approach provides a computationally feasible pathway for simulating dynamic cellular behavior, offering potential breakthroughs in areas such as drug discovery, disease modeling, and understanding fundamental biological mechanisms. The presented framework focuses on the theoretical foundations and algorithmic design, without necessitating access to quantum hardware, making it immediately applicable for high-performance computing environments. We explore the mathematical formalism underpinning the method, detailing the key equations and operations involved in simulating cellular processes. The ultimate goal is to establish a robust and scalable simulation technique capable of tackling the complexities of biological systems.
Quantum network is an emerging type of network structure that leverages the principles of quantum mechanics to transmit and process information. Compared with classical data reconstruction algorithms, quantum networks make image reconstruction more efficient and accurate. They can also process more complex image information using fewer bits and faster parallel computing capabilities. Therefore, this paper will discuss image reconstruction methods based on our quantum network and explore their potential applications in image processing. We will introduce the basic structure of the quantum network, the process of image compression and reconstruction, and the specific parameter training method. Through this study, we can achieve a classical image reconstruction accuracy of 97.57%. Our quantum network design will introduce novel ideas and methods for image reconstruction in the future.
Quantum-inspired algorithms can deliver substantial speedups over classical state-of-the-art methods by executing quantum algorithms with tensor networks on conventional hardware. Unlike circuit models restricted to unitary gates, tensor networks naturally accommodate non-unitary maps. This flexibility lets us design quantum-inspired methods that start from a quantum algorithmic structure, yet go beyond unitarity to achieve speedups. Here we introduce a tensor-network approach to compute the discrete Laplace transform, a non-unitary, aperiodic transform (in contrast to the Fourier transform). We encode a length-N signal on two paired n-qubit registers and decompose the overall map into a non-unitary exponential Damping Transform followed by a Quantum Fourier Transform, both compressed in a single matrix-product operator. This decomposition admits strong MPO compression to low bond dimension resulting in significant acceleration. We demonstrate simulations up to N=230 input data points, with up to 260 output data points, and quantify how bond dimension controls runtime and accuracy, including precise and efficient pole identification.
Abstract Image segmentation remains one of the most extensively studied problems in computer vision, with applications ranging from medical image analysis and autonomous driving to remote sensing and industrial inspection. While deep learning approaches currently dominate the field, interest in quantum computing has motivated the development of quantum and quantum-inspired segmentation techniques that explore alternative strategies for image representation, optimization, and learning. This survey provides a comprehensive review of quantum and quantum-inspired image segmentation methods within the broader context of modern segmentation research. To establish this context, we first examine the evolution of image segmentation methodologies, covering classical image processing techniques, machine learning approaches, and contemporary deep learning architectures.We then organize the existing quantum image segmentation literature into four categories: quantum-inspired, tensor network-based, hybrid quantum-classical, and fully quantum methods. Across these categories, we analyze computational principles, image encoding and representation strategies, application domains, and datasets. We further compare quantum and quantum-inspired approaches with established segmentation paradigms in terms of supervision, scalability, and hardware requirements. Our analysis indicates that quantum-inspired methods currently represent the most developed direction, while hybrid approaches are emerging and fully quantum methods remain constrained by quantum hardware, data encoding costs, and scalability challenges. By connecting quantum image segmentation with the broader evolution of segmentation research, this survey provides a unified perspective on the field. It identifies current trends, open challenges, and promising future directions for researchers exploring the emerging role of quantum computing in image segmentation.
Tensor networks were developed in the context of many-body physics as compressed representations of multiparticle quantum states. These representations mitigate the exponential complexity of many-body systems by capturing only the most relevant dependencies. Due to the formal similarity between quantum entanglement and statistical correlations, tensor networks have recently been integrated in machine learning, operating both as alternative learning architectures and as decompositions of components of neural networks. The expectation is that the theoretical understanding of tensor networks developed within quantum many-body physics leads to novel methods that offer advantages in terms of computational efficiency, explainability, or privacy. Here we review the use of tensor networks in the context of machine learning, providing a critical assessment of the state of the art, the potential advantages, and the challenges that must be overcome.