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.
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.
Generative models have gained attention for their proven effectiveness in various domains, from generating images to producing text. Diffusion models (DMs) have demonstrated superior performance compared to alternative techniques like generative adversarial networks (GANs) or autoencoders (AE). The research about DMs has advanced further with the proposition of latent diffusion models (LDMs), which employ DMs within the latent space to mitigate computational complexity while preserving high quality and flexibility. Quantum computing with its intrinsic characteristics of entanglement and superposition which enable high representational power, arises with the possibility of offering computational advantages over classical generative models. Inspired by current trends of classical generative models, we propose quantum latent diffusion models (QLDMs) to enable computationally efficient DMs with the guidance of conditions on classical data. QLDMs offer solutions to the challenges faced by classical generative models due to their large number of parameters, while still achieving comparable results on datasets.
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.
Generative models have achieved remarkable success in data synthesis, though recent advances driven by increasing model scale have introduced challenges in computational cost and efficiency. Quantum machine learning offers a promising alternative, representing complex data distributions using compact, highly expressive models. Here, we propose QDiffusion-TS, the first quantum generative diffusion model for time series synthesis, and validate it on the IQM quantum processor. The framework extends a classical diffusion architecture by replacing feed-forward components within the denoising transformer with quantum neural networks, yielding a hybrid quantum transformer that reduces the number of trainable parameters in each replaced component by nearly three orders of magnitude. Evaluated on financial time series from Apple and Amazon, the model generates synthetic data that more accurately reproduces the real distributions, reducing Wasserstein distance by approximately 44% relative to its classical counterpart across both datasets. In a downstream forecasting task, augmentation with the generated data improves predictive performance by up to 71% in RMSE over a baseline trained solely on real data. These results show that quantum enhanced architectures can consistently match and frequently surpass classical performance with substantially fewer parameters, establishing a practical framework towards more efficient and scalable data-driven generative modelling.
Deep generative models are key-enabling technology to computer vision, text generation, and large language models. Denoising diffusion probabilistic models (DDPMs) have recently gained much attention due to their ability to generate diverse and high-quality samples in many computer vision tasks, as well as to incorporate flexible model architectures and a relatively simple training scheme. Quantum generative models, empowered by entanglement and superposition, have brought new insight to learning classical and quantum data. Inspired by the classical counterpart, we propose the quantum denoising diffusion probabilistic model (QuDDPM) to enable efficiently trainable generative learning of quantum data. QuDDPM adopts sufficient layers of circuits to guarantee expressivity, while it introduces multiple intermediate training tasks as interpolation between the target distribution and noise to avoid barren plateau and guarantee efficient training. We provide bounds on the learning error and demonstrate QuDDPM's capability in learning correlated quantum noise model, quantum many-body phases, and topological structure of quantum data. The results provide a paradigm for versatile and efficient quantum generative learning.
This paper investigates the application of Quantum Generative Adversarial Networks (QGANs) to data augmentation for machine learning. Traditional Generative Adversarial Networks (GANs) rely on classical neural networks, while this research explores leveraging quantum circuits as generators within a QGAN architecture. The core idea is to train a quantum generator to produce synthetic data samples, supplementing existing datasets with novel instances. The discriminator remains a classical neural network, tasked with distinguishing between real and generated data. We present a theoretical framework for this approach, outlining the mathematical formulation and key components. Specifically, we introduce the notation (x, s_1, s_2, ..., s_K) to represent data samples, generator states, and relevant parameters. The objective function for the QGAN is defined as minimizing the Jensen-Shannon divergence between the real and generated data distributions. The effectiveness of this approach is discussed, highlighting potential advantages and challenges. This work contributes to the emerging field of quantum machine learning and offers a novel strategy for improving the performance of machine learning models, particularly in scenarios with limited training data.
Deep generative models, such as Generative Adversarial Networks (GANs), have demonstrated remarkable success in generating realistic data across various domains. However, a fundamental limitation lies in their reliance on traditional stochastic sampling methods, predominantly uniform or Gaussian distributions. These methods often struggle to accurately represent the complex, high-dimensional structure inherent in real-world data. This work introduces a novel approach – Quantum-Inspired Stochastic Sampling – that draws inspiration from quantum mechanics to overcome these limitations. We propose a parameterized "quantum circuit" that simulates superposition and interference, enabling the generation of stochastic samples from distributions that are not constrained by the limitations of classical sampling techniques. The core idea is to map a random seed into a distribution that mirrors the probabilistic behavior observed within quantum systems. We aim to demonstrate that this quantum-inspired approach can lead to improved sample quality and a more accurate representation of complex data distributions within deep generative models. The theoretical framework and methodology are presented, highlighting the potential for this technique to significantly advance the field of generative modeling.