DEEP-INセミナー

Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation

2026年5月14日(木) 14:30 - 15:30

ジアン・シュウ (理化学研究所 数理創造研究センター (iTHEMS) 数理展開部門 量子数理科学チーム 特別研究員)

In quantum machine learning (QML), classical data are often encoded as quantum pure states and processed directly as quantum representations, motivating \emph{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 Schr\"odinger 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 Schr\"odinger 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.

会場: セミナー室 (359号室) 3階 359号室 (メイン会場) / via Zoom

イベント公式言語: 英語