• Abstract 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.
Article Summaries:
- Researchers have introduced QD3PM, a quantum discrete denoising diffusion probabilistic model that overcomes the dimensional‑factorization limitations of classical discrete diffusion models. By exploiting exponentially large Hilbert spaces, the method learns joint probability distributions instead of independent dimension‑wise factors, reducing worst‑case errors that grow linearly with data dimension. The approach employs a quantum circuit with temporal parameter sharing and data‑controlled rotations, enabling single‑step sampling from pure noise and retraining‑free conditional inference-features lacking in many quantum generative models. Simulations show QD3PM outperforms parameter‑matched classical baselines in capturing inter‑dimensional correlations and remains more robust to quantum noise than existing quantum GANs and VAEs.
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