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.
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.
Generative quantum machine learning has gained significant attention for its ability to produce quantum states with desired distributions. Among various quantum generative models, quantum denoising diffusion probabilistic models (QuDDPMs) [Zhang et al., Phys. Rev. Lett. 132, 100602 (2024)] provide a promising approach with stepwise learning that resolves the training issues. However, the requirement of high-fidelity scrambling unitaries in QuDDPMs poses a challenge to near-term implementation. We propose a mixed-state quantum denoising diffusion probabilistic model (MSQuDDPM) to eliminate the need for scrambling unitaries. Our approach focuses on adapting the quantum noise channels to the model architecture, which integrates depolarizing noise channels in the forward diffusion process and parameterized quantum circuits with projective measurements in the backward denoising steps. We also introduce several techniques to improve MSQuDDPM, including a cosine-exponent schedule of noise interpolation, the use of a single-qubit random ancilla, and superfidelity-based cost functions to enhance the convergence. We evaluate MSQuDDPM on quantum ensemble generation tasks, demonstrating its successful performance.
Quantum generative models exploit quantum superposition and entanglement to enhance learning efficiency for both classical and quantum data. Recently, inspired by classical diffusion frameworks, the quantum denoising diffusion probabilistic model has emerged as a powerful tool for learning correlated noise models, many-body phases, and topological data structures. However, we demonstrate that this framework is currently restricted to small-scale systems. As the system size increases, a severe barren plateau problem emerges, fundamentally limiting the model's scalability. We provide rigorous theoretical proofs and experimental validation to identify the origin of this barren plateau, distinct from previously known causes. To restore trainability, we introduce an enhanced architecture that effectively mitigates the barren plateau phenomenon and guarantees the model's trainability in the tested settings. Building on this architecture, we further propose a conditional quantum denoising diffusion probabilistic model, capable of generating ground states based on Hamiltonian parameters, expanding the utility of quantum generative models for complex quantum state preparation to a certain extent. Our approach not only holds the potential to address the scalability and trainability bottlenecks of quantum diffusion models, but also provides a robust tool for exploring complex quantum matter and state preparation in the NISQ era.
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.
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 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.
Abstract Quantum denoising diffusion models have recently emerged as a powerful framework for generative quantum machine learning. In this work, we extend these models by introducing a conditioning mechanism that enables the generation of quantum states drawn from multiple target distributions. By sharing parameters across distinct classes of quantum states, our approach avoids the need to train separate models for each distribution. We validate our method through numerical simulations that span single-qubit generation tasks, entangled state preparation, and many-body ground state generation. Across these tasks, conditioning significantly reduced the error of targeted state generation by more than an order of magnitude. Finally, we perform an ablation study to quantify the effect of key hyperparameters on the model performance.