Quantum generative models leverage quantum superposition and entanglement to enhance learning efficiency for both classical and quantum data. The quantum denoising diffusion probabilistic model (QuDDPM), inspired by its classical counterpart, has been proposed as a promising framework for quantum generative learning. QuDDPM is capable of efficiently learning and generating quantum data, and it demonstrates excellent performance in learning correlated quantum noise models, quantum many-body phases, and the topological structure of quantum data. However, we show that barren plateaus emerge in QuDDPMs due to the use of 2-design states as the input for the denoising process, which severely undermines the performance of QuDDPM. Through theoretical analysis and experimental validation, we confirm the presence of barren plateaus in the original QuDDPM. To address this issue, we introduce an improved QuDDPM that utilizes a distribution maintaining a certain distance from the Haar distribution, ensuring better trainability. Experimental results demonstrate that our approach effectively mitigates the barren plateau problem and generates samples with higher quality, paving the way for scalable and efficient quantum generative learning.
Quantum generative models leverage quantum superposition and entanglement to enhance learning efficiency for both classical and quantum data. The quantum denoising diffusion probabilistic model (QuDDPM), inspired by its classical counterpart, has been proposed as a promising framework for quantum generative learning. QuDDPM is capable of efficiently learning and generating quantum data, and it demonstrates excellent performance in learning correlated quantum noise models, quantum many-body phases, and the topological structure of quantum data. However, we show that barren plateaus emerge in QuDDPMs due to the use of 2-design states as the input for the denoising process, which severely undermines the performance of QuDDPM. Through theoretical analysis and experimental validation, we confirm the presence of barren plateaus in the original QuDDPM. To address this issue, we introduce an improved QuDDPM that utilizes a distribution maintaining a certain distance from the Haar distribution, ensuring better trainability. Experimental results demonstrate that our approach effectively mitigates the barren plateau problem and generates samples with higher quality, paving the way for scalable and efficient quantum generative learning.
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.
Discrete diffusion models typically rely on dimension-wise factorization to avoid computational intractability. However, we rigorously prove this approach leads to worst-case errors scaling linearly with data dimension, fundamentally failing to capture inter-dimensional correlations. To address this, we propose a quantum discrete denoising diffusion probabilistic model (QD3PM), which enables joint probability learning through diffusion and denoising in exponentially large Hilbert spaces. By deriving posterior states through quantum Bayes’ theorem, we establish a theoretical foundation for quantum-enhanced diffusion models. We design a quantum circuit that utilizes temporal information for parameter sharing and incorporates learnable classical-data-controlled rotations for encoding. Crucially, our approach enables single-step sampling from pure noise to eliminate iterative bottlenecks, while also supporting retraining-free conditional inference, a flexibility often absent in existing quantum generative models such as quantum circuit Born machines. Simulations demonstrate that QD3PM significantly outperforms the parameter-matched classical baseline in modeling inter-dimensional correlations and exhibits superior robustness against quantum noise compared to quantum generative adversarial networks and quantum variational autoencoders. Hence, our work establishes a new theoretical paradigm by leveraging quantum advantages in joint distribution learning.
Generative models for quantum data pose significant challenges but hold immense potential in fields such as chemoinformatics and quantum physics. Quantum denoising diffusion probabilistic models (QuDDPMs) enable efficient learning of quantum data distributions by progressively scrambling and denoising quantum states. However, existing implementations typically rely on circuit-based random unitary dynamics, which can be costly to implement and sensitive to control imperfections, particularly on analog quantum hardware. We propose the chaotic quantum diffusion model, a framework that generates projected ensembles via chaotic Hamiltonian time evolution, providing a flexible and hardware-compatible diffusion mechanism. Requiring only global, time-independent control, our approach substantially reduces implementation overhead across diverse analog quantum platforms while achieving accuracy comparable to QuDDPMs. This method improves trainability and robustness, broadening the applicability of quantum generative modeling.
This thesis addresses one of the central challenges in Quantum Machine Learning: the Barren Plateaus phenomenon, which causes the exponential vanishing of gradients and hin ders the effective training of variational quantum algorithms. We propose the Q-MOLLD method in which we design a hybrid protocol that leverages the generative capabilities of Large Language Models to generate quantum algorithms for optimization problems and to produce informed initializations for quantum circuits to improve their performance. Experimental results demonstrate that the proposed approach can mitigate the Barren Plateaus problem, preserving larger gradient magnitudes during the early stages of training and facilitating convergence compared to random or classical strategies. The findings suggest that Large Language Models can play a crucial role in the design and training of quantum algorithms, especially in the Noisy Intermediate-Scale Quantum era, where hardware limitations and noise pose significant challenges. Future work will focus on extending the analysis to different ansatz architectures, exploring active learning techniques, and evaluating performance under realistic noise conditions on quantum hardware.
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.
Although recent advances in transfer learning have simplified training, fine-tuning big language models remains an energy-intensive and expensive process, with high hardware and energy costs that make it difficult to use and scale. While quantum machine learning (QML) presents a promising theoretical tool to overcome these bottlenecks, the practical implementation is hampered by the barren plateau problem, a phenomenon well established in literature that manifests through exponentially vanishing gradients of deep parameterized quantum circuits (PQCs) with increasing circuit depth, preventing informative parameter updates by rendering the optimization landscape flat. This study presents a hybrid quantum-classical architecture in which a PQC layer is integrated into a pretrained classical LLM backbone and fine-tuned throughout this work. This iterative refinement loop is controlled by an Expected Improvement acquisition function, which actively guides the search process through parameter regimes with obvious non-vanishing gradient variance. The study proposes that this theory-driven initialization scheme reduces the onset of barren plateaus, thereby enabling efficient and stable convergence in hybrid optimization. Experiments show that the proposed method consistently outperforms purely classical fine-tuning baselines and randomly initialized quantum baselines on representative downstream natural language processing tasks. The experimental results show that principled parameter initialization leads to concrete improvements in convergence stability, gradient trainability, and task-level performance. In summary, this research provides a scalable method for integrating near-term noisy intermediate-scale Quantum (NISQ) devices into state-of-the-art deep learning pipelines, fostering the further real-world adoption of hybrid quantum-classical systems for demanding artificial intelligence tasks.