Mitigating Barren plateaus in quantum denoising diffusion probabilistic models

Abstract: 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.