Mixed-State Quantum Denoising Diffusion Probabilistic Model
This work addresses a bottleneck for near-term quantum machine learning by making quantum generative models more practical, though it is incremental as it builds on existing QuDDPMs.
The paper tackled the challenge of implementing quantum denoising diffusion probabilistic models (QuDDPMs) in near-term quantum devices by eliminating the need for high-fidelity scrambling unitaries, resulting in the proposed mixed-state quantum denoising diffusion probabilistic model (MSQuDDPM) that successfully performs quantum ensemble generation tasks.
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.