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.
Understanding the training dynamics of quantum neural networks is a fundamental task in quantum information science with wide impact in physics, chemistry and machine learning. In this work, we show that the late-time training dynamics of quantum neural networks with a quadratic loss function can be described by the generalized Lotka-Volterra equations, which lead to a transcritical bifurcation transition in the dynamics. When the targeted value of loss function crosses the minimum achievable value from above to below, the dynamics evolve from a frozen-kernel dynamics to a frozen-error dynamics, showing a duality between the quantum neural tangent kernel and the total error. In both regions, the convergence towards the fixed point is exponential, while at the critical point becomes polynomial. We provide a non-perturbative analytical theory to explain the transition via a restricted Haar ensemble at late time, when the output state approaches the steady state. Via mapping the Hessian to an effective Hamiltonian, we also identify a linearly vanishing gap at the transition point. Compared with the linear loss function, we show that a quadratic loss function within the frozen-error dynamics enables a speedup in the training convergence. The theory findings are verified experimentally on IBM quantum devices.
Artificial intelligence (AI) and quantum information (QI) are rapidly co-evolving. AI is becoming a practical tool for learning, designing, controlling, and verifying quantum systems, while QI offers new computational models, representational structures, and learning-theoretic questions for AI. This survey reviews the interface from both directions. In the AI for QI direction, we organize recent progress around the central tasks of extracting information from limited measurements, training and discovering quantum algorithms, stabilizing noisy hardware, automating experimental and programming workflows, and extending learning-based methods to sensing and networking. In the QI for AI direction, we examine how quantum computation and quantum-inspired structures affect learning through algorithmic speedups, expressivity, trainability, generalization, neural-network design, and tensor-network representations. We close by identifying cross-cutting challenges in reproducibility, scalability, hardware realism, and co-design, arguing that progress will depend on tighter integration of theory, experiment, and hybrid quantum--classical systems.
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) [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 QuDDPM poses a challenge in near-term implementation. We propose the \textit{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 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.
Bosonic continuous-variable Variational quantum circuits (VQCs) are crucial for information processing in cavity quantum electrodynamics and optical systems, widely applicable in quantum communication, sensing and error correction. The trainability of such VQCs is less understood, hindered by the lack of theoretical tools such as $t$-design due to the infinite dimension of the physical systems involved. We overcome this difficulty to reveal an energy-dependent barren plateau in such VQCs. The variance of the gradient decays as $1/E^{Mν}$, exponential in the number of modes $M$ but polynomial in the (per-mode) circuit energy $E$. The exponent $ν=1$ for shallow circuits and $ν=2$ for deep circuits. We prove these results for state preparation of general Gaussian states and number states. We also provide numerical evidence that the results extend to general state preparation tasks. As circuit energy is a controllable parameter, we provide a strategy to mitigate the barren plateau in continuous-variable VQCs.