Stochastic Schrodinger Diffusion Models for Pure-State Ensemble Generation

arXiv:2605.03573v1 Announce Type: cross Abstract: 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 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 CP^{d-1} and the intractability of transition densities. We propose Stochastic Schrodinger Diffusion Models (SSDMs), an intrinsic score-based generative framework on CP^{d-1} endowed with the Fubini--Study (FS) metric. SSDMs formulate a forward Riemannian diffusion with a stochastic Schrodinger equation (SSE) realization, and derive reverse-time dynamics driven by the Riemannian score nabla_{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.

Source: arXiv cs.LG | 2026-05-06