We describe how multidimensional linear diffusion with application to image processing could be carried out on a hybrid classical–quantum computer. We present the quantum-lattice-gas-based algorithms, their effective finite difference approximations and representative simulation results. The methods for two-dimensional diffusion processing are particularly relevant to image enhancement tasks. We additionally demonstrate an extension to constrained linear diffusion that provides for non-uniform image smoothing. The simulation results and accompanying analysis support the utility of both classical and classical–quantum lattice gases for image enhancement. The diffusion modelling has applicability to many other fields including biological and physical science.
We describe how multidimensional linear diffusion with application to image processing could be carried out on a hybrid classical–quantum computer. We present the quantum-lattice-gas-based algorithms, their effective finite difference approximations and representative simulation results. The methods for two-dimensional diffusion processing are particularly relevant to image enhancement tasks. We additionally demonstrate an extension to constrained linear diffusion that provides for non-uniform image smoothing. The simulation results and accompanying analysis support the utility of both classical and classical–quantum lattice gases for image enhancement. The diffusion modelling has applicability to many other fields including biological and physical science.
Generative Artificial Intelligence is one of the most relevant technologies of our century, enabling digital machines not only to analyze or classify data but also to generate new content such as images, text, and video. This technology relies on deep learning algorithms designed to capture complex relationships from finite data sets. In this context, Diffusion Models have recently emerged as state-of-the-art in deep generative modeling thanks to their ability to produce high-quality data. Their pipeline typically consists of a forward diffusion process, where data samples are progressively corrupted into pure (classical) noise, and a reverse denoising process, where deep neural networks learn to reverse the diffusion process and then generate new synthetic samples. In parallel, Quantum Machine Learning represents one of the most promising applications of quantum computing. However, currently available quantum processors, known as Noisy Intermediate-Scale Quantum (NISQ) devices, are composed of tens or hundreds of noisy qubits. Therefore, designing scalable and efficient practical quantum algorithms represents a significant challenge. This thesis proposes the first generalization of classical Denoising Diffusion Probabilistic Models to the quantum domain, introducing the novel generative paradigm of Quantum Diffusion Models. In particular, the three possible scenarios are formalized and implemented: (i) classical data corrupted with Gaussian noise and a reverse process implemented via a quantum neural network; (ii) quantum data corrupted with quantum noise and a denoising process through a classical deep neural network; and (iii) a fully quantum approach, where both forward and backward processes are implemented within a quantum framework. Subsequently, the impact of different stochastic dynamics in the forward process is analyzed using the formalism of Quantum Stochastic Walks. We observe that a specific hybrid quantum-classical dynamics produces more statistically robust models, capable of generating sets of images closely resembling real ones compared to purely classical dynamics. Furthermore, we propose a hybrid quantum-classical diffusion model based on Quantum Walks that exploits the intrinsic noise of real quantum processors as a useful resource for generating images. This model is implementable on current NISQ devices and scalable, as it allows the generation of images of any size, requiring q + 1 qubits for grayscale images with pixel intensities in the range [0, 2^q - 1]. Finally, an application in the context of medical imaging is presented, specifically the generation of 64 × 64 color images of blood cells from the BloodMNIST dataset and 200 × 200 brain MRI images from the BraTS2020 dataset.
The integration of quantum computing into image processing represents a significant advancement in computational technology, offering transformative capabilities that enhance performance, efficiency, and accuracy. This chapter explores hybrid quantum-classical algorithms, focusing on how quantum subroutines can be integrated into classical image processing workflows. A comparative analysis of various quantum image encoding techniques highlights their strengths and limitations, paving the way for optimized applications across diverse fields. Key advantages of quantum-enhanced image processing, such as improved speed in high-resolution data analysis and superior optimization methods, are discussed in relation to real-world applications, including medical imaging and computer vision. The chapter anticipates future developments in quantum technology, emphasizing the need for interdisciplinary collaboration to unlock the full potential of quantum computing in digital image applications. By addressing the critical gaps in current methodologies, this work aims to inspire further research and innovation in the realm of quantum-enhanced image processing.
Quantum-enhanced diffusion is a novel approach to image synthesis that utilizes quantum annealing to accelerate the generation process, offering a potential advantage over classical methods, especially when dealing with complex scenes. This paper presents a framework for integrating quantum annealing into the diffusion process, demonstrating its efficacy through simulations and preliminary results. The core claim centers on the ability of quantum annealing to efficiently navigate the parameter space of the diffusion process, thereby reducing computational cost and improving image quality.
Quantum Machine Learning is a novel field of research aimed at devising machine learning approaches exploiting principles of quantum mechanics, such as superposition, entanglement and interference. In this context, we present a scalable hybrid Quantum Diffusion Model, and evaluate its use for medical image analysis. Specifically, our method is based on a Discrete-Time Quantum Walk algorithm, executed on a real quantum device, to model the forward dynamics of the diffusion model. For the backward step of the diffusion model, we devise and evaluate a classical learning model, which is used to reversely denoise the data. In contrast with other existing attempts at applying quantum machine learning for image analysis tasks, severely limited by the size of existing quantum devices, our method allows to process real-world large size medical data. In particular, we present results on grayscale and RGB images, as well as 3D volumes of moderate sizes. We benchmark our results by reproducing an alternative classical counterpart model, based on diffusion models on discrete state spaces. By doing so, we compare the generation capabilities of both models in terms of three distinct state-of-the-art metrics in the field of image generation, showing the competitive, promising results of our approach.
A diffusion probabilistic model (DPM) is a generative model renowned for its ability to produce high-quality outputs in tasks such as image and audio generation. However, training DPMs on large, high-dimensional datasets such as high-resolution images or audio incurs significant computational, energy, and hardware costs. In this work, we introduce efficient quantum algorithms for implementing DPMs through various quantum ODE solvers. These algorithms highlight the potential of quantum Carleman linearization for diverse mathematical structures, leveraging state-of-the-art quantum linear system solvers (QLSS) or linear combination of Hamiltonian simulations (LCHS). Specifically, we focus on two approaches: DPM-solver-k which employs exact k-th order derivatives to compute a polynomial approximation of εθ(xλ,λ); and UniPC which uses finite difference of εθ(xλ,λ) at different points (xsm,λsm) to approximate higher-order derivatives. As such, this work represents one of the most direct and pragmatic applications of quantum algorithms to large-scale machine learning models, presumably taking substantial steps towards demonstrating the practical utility of quantum computing.
A lattice-gas algorithm for the one-dimensional diffusion equation is realized using radio frequency pulses in a one-dimensional spin system. The model is a large array of quantum two-qubit nodes interconnected by the nearest-neighbor classical communication channels. We present a quantum protocol for implementation of the quantum collision operator and a method for initialization and reinitialization of quantum states. Numerical simulations of the quantum-classical dynamics are in good agreement with the analytic solution for the diffusion equation.