Abstract Quantum Diffusion Models (QDMs) are an emerging paradigm in Generative AI that aims to use quantum properties to improve the performances of their classical counterparts. However, existing algorithms are not easily scalable due to the limitations of near-term quantum devices. Following our previous work on QDMs, here we propose and implement two physics-inspired protocols. In the first, we use the formalism of quantum stochastic walks, showing that a specific interplay of quantum and classical dynamics in the forward process produces statistically more robust models generating sets of MNIST images with lower Fréchet Inception Distance (FID) than using totally classical dynamics. In the second approach, we realize an algorithm to generate images by exploiting the intrinsic noise of real IBM quantum hardware with only four qubits. Our work could be a starting point to pave the way for new scenarios for large-scale algorithms in quantum Generative AI, where quantum noise is neither mitigated nor corrected, but instead exploited as a useful resource.
Abstract Quantum Diffusion Models (QDMs) are an emerging paradigm in Generative AI that aims to use quantum properties to improve the performances of their classical counterparts. However, existing algorithms are not easily scalable due to the limitations of near-term quantum devices. Following our previous work on QDMs, here we propose and implement two physics-inspired protocols. In the first, we use the formalism of quantum stochastic walks, showing that a specific interplay of quantum and classical dynamics in the forward process produces statistically more robust models generating sets of MNIST images with lower Fréchet Inception Distance (FID) than using totally classical dynamics. In the second approach, we realize an algorithm to generate images by exploiting the intrinsic noise of real IBM quantum hardware with only four qubits. Our work could be a starting point to pave the way for new scenarios for large-scale algorithms in quantum Generative AI, where quantum noise is neither mitigated nor corrected, but instead exploited as a useful resource.
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.
Abstract Generative models realized with Machine Learning (ML) techniques are powerful tools to infer complex and unknown data distributions from a finite number of training samples in order to produce new synthetic data. Diffusion Models (DMs) are an emerging framework that have recently overcome Generative Adversarial Networks (GANs) in creating high‐quality images. Here, is proposed and discussed the quantum generalization of DMs, i.e., three Quantum‐Noise‐Driven Generative Diffusion Models (QNDGDMs) that could be experimentally tested on real quantum systems. The idea is to harness unique quantum features, in particular the non‐trivial interplay among coherence, entanglement, and noise that the currently available noisy quantum processors do unavoidably suffer from, in order to overcome the main computational burdens of classical diffusion models during inference. Hence, the suggestion is to exploit quantum noise not as an issue to be detected and solved but instead as a beneficial key ingredient to generate complex probability distributions from which a quantum processor might sample more efficiently than a classical one. Three examples of the numerical simulations are also included for the proposed approaches. The results are expected to pave the way for new quantum‐inspired or quantum‐based generative diffusion algorithms addressing tasks as data generation with widespread real‐world applications.
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.
Classical diffusion models have achieved remarkable results in terms of sample quality and variability. The quantum counterpart of these models is still to be explored thoroughly and offers a promising research direction in the field of quantum generative models. In this work, we introduce two versions of a quantum diffusion model, using parameterized quantum circuits to sample from quantum state distributions, while performing training via classical simulations. The first model is a quantum-hardware-oriented design, based on denoising diffusion probabilistic models, for which we demonstrate an implementation on real quantum hardware. The second model is a hybrid approach, based on denoising diffusion implicit models, that uses a classical neural network to enhance the expressive power. We show that the second version produces samples of higher quality and variability, but requires additional classical-quantum encoding and decoding overhead, underscoring a trade-off between expressive power and hardware efficiency. We demonstrate our method on MNIST images encoded as quantum states, as sample quality is easier to visualize and objective metrics are more widely available. While our results do not surpass classical diffusion models in the generation of classical samples, this study suggests the viability of using quantum diffusion models for learning quantum state distributions.
In recent years, machine learning models like DALL-E, Craiyon, and Stable Diffusion have gained significant attention for their ability to generate high-resolution images from concise descriptions. Concurrently, quantum computing is showing promising advances, especially with quantum machine learning which capitalizes on quantum mechanics to meet the increasing computational requirements of traditional machine learning algorithms. This paper explores the integration of quantum machine learning and variational quantum circuits to augment the efficacy of diffusion-based image generation models. Specifically, we address two challenges of classical diffusion models: their low sampling speed and the extensive parameter requirements. We introduce two quantum diffusion models and benchmark their capabilities against their classical counterparts using MNIST digits, Fashion MNIST, and CIFAR-10. Our models surpass the classical models with similar parameter counts in terms of performance metrics FID, SSIM, and PSNR. Moreover, we introduce a consistency model unitary single sampling architecture that combines the diffusion procedure into a single step, enabling a fast one-step image generation.
Quantum generative models offer a promising new direction in machine learning by leveraging quantum circuits to enhance data generation capabilities. In this study, we propose a hybrid quantum-classical image generation framework that integrates variational quantum circuits into a diffusion-based model. To improve training dynamics and generation quality, we introduce two novel noise strategies: intrinsic quantum-generated noise and a tailored noise scheduling mechanism. Our method is built upon a lightweight U-Net architecture, with the quantum layer embedded in the bottleneck module to isolate its effect. We evaluate our model on MNIST and MedMNIST datasets to examine its feasibility and performance. Notably, our results reveal that under limited data conditions (fewer than 100 training images), the quantum-enhanced model generates images with higher perceptual quality and distributional similarity than its classical counterpart using the same architecture. While the quantum model shows advantages on grayscale data such as MNIST, its performance is more nuanced on complex, color-rich datasets like PathMNIST. These findings highlight both the potential and current limitations of quantum generative models and lay the groundwork for future developments in low-resource and biomedical image generation.