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.

翻译：生成式量子机器学习因其能够产生具有期望分布的量子态而受到广泛关注。在各种量子生成模型中，量子去噪扩散概率模型（QuDDPMs）[Phys. Rev. Lett. 132, 100602 (2024)] 通过逐步学习提供了一种有前景的方法，解决了训练难题。然而，QuDDPM 对高保真度置乱幺正算子的要求给近期实现带来了挑战。我们提出了\textit{混合态量子去噪扩散概率模型}（MSQuDDPM）以消除对置乱幺正算子的需求。我们的方法侧重于将量子噪声信道适配到模型架构中，该架构在前向扩散过程中整合了去极化噪声信道，并在反向去噪步骤中使用了带投影测量的参数化量子电路。我们还引入了若干技术以改进MSQuDDPM，包括噪声插值的余弦指数调度、单量子比特随机辅助比特的使用，以及基于超保真度的代价函数以增强收敛性。我们在量子系综生成任务上评估了MSQuDDPM，证明了其成功的性能。