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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.03573 |
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| _version_ | 1866911671510892544 |
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| author | Xu, Jian Chen, Wei Li, Shigui Li, Chao Zheng, Jingyuan Zeng, Delu Paisley, John Zhao, Qibin |
| author_facet | Xu, Jian Chen, Wei Li, Shigui Li, Chao Zheng, Jingyuan Zeng, Delu Paisley, John Zhao, Qibin |
| contents | In quantum machine learning (QML), classical data are often encoded as quantum pure states and processed directly as quantum representations, motivating representation-level generative modeling that samples new quantum states from an underlying pure-state ensemble rather than re-preparing them from perturbed classical inputs. However, extending \emph{score-based} diffusion models with well-defined reverse-time samplers to quantum pure-state ensembles remains challenging, due to the non-Euclidean geometry of the complex projective space $\mathbb{CP}^{d-1}$ and the intractability of transition densities. We propose \emph{Stochastic Schrödinger Diffusion Models} (SSDMs), an intrinsic score-based generative framework on $\mathbb{CP}^{d-1}$ endowed with the Fubini--Study (FS) metric. SSDMs formulate a forward Riemannian diffusion with a stochastic Schrödinger equation (SSE) realization, and derive reverse-time dynamics driven by the Riemannian score $\nabla_{\mathrm{FS}} \log p_t$. To enable training without analytic transition densities, we introduce a local-time objective based on a local Euclidean Ornstein--Uhlenbeck approximation in FS normal coordinates, yielding an analytic teacher score mapped back to the manifold. Experiments show that SSDMs faithfully capture target pure-state ensemble statistics, including observable moments, overlap-kernel MMD, and entanglement measures, and that SSDM-generated quantum representations improve downstream QML generalization via representation-level data augmentation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03573 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation Xu, Jian Chen, Wei Li, Shigui Li, Chao Zheng, Jingyuan Zeng, Delu Paisley, John Zhao, Qibin Machine Learning In quantum machine learning (QML), classical data are often encoded as quantum pure states and processed directly as quantum representations, motivating representation-level generative modeling that samples new quantum states from an underlying pure-state ensemble rather than re-preparing them from perturbed classical inputs. However, extending \emph{score-based} diffusion models with well-defined reverse-time samplers to quantum pure-state ensembles remains challenging, due to the non-Euclidean geometry of the complex projective space $\mathbb{CP}^{d-1}$ and the intractability of transition densities. We propose \emph{Stochastic Schrödinger Diffusion Models} (SSDMs), an intrinsic score-based generative framework on $\mathbb{CP}^{d-1}$ endowed with the Fubini--Study (FS) metric. SSDMs formulate a forward Riemannian diffusion with a stochastic Schrödinger equation (SSE) realization, and derive reverse-time dynamics driven by the Riemannian score $\nabla_{\mathrm{FS}} \log p_t$. To enable training without analytic transition densities, we introduce a local-time objective based on a local Euclidean Ornstein--Uhlenbeck approximation in FS normal coordinates, yielding an analytic teacher score mapped back to the manifold. Experiments show that SSDMs faithfully capture target pure-state ensemble statistics, including observable moments, overlap-kernel MMD, and entanglement measures, and that SSDM-generated quantum representations improve downstream QML generalization via representation-level data augmentation. |
| title | Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.03573 |