Scalable quantum simulation of continuous-time generative models via tensor networks

Continuous-time flow and diffusion models are widely used across many application domains, from large-scale deployment in computer vision and protein folding to emerging adoption for modeling language, time series, and quantum states. After training, inferring statistical properties from continuous-time models is costly. Wavefunction flows target this cost by recasting learned transport as unitary evolution, whose final Born distribution approximates the target distribution. This prepares a coherent amplitude encoding (a qsample) that can be post-processed by quantum algorithms offering a quadratic advantage over Monte Carlo sampling. We present the first numerical study of these flows, in which we represent time-dependent potentials and states as tensor networks. At spatial dimension $d=8$, storage falls by $\sim 10^7\times$ relative to the dense grid of $N^d$ points, and evolution wall-clock time falls by $\gtrsim 10^3\times$ against a baseline extrapolated from the measured $d\le 5$ scaling. We validate our pipeline by reproducing the $O(1/\sqrt{p_{\rm rare}})$ scaling of rare-event sampling.

Conditional Tropical Cyclogenesis Rates via Rare-Event Sampling in a Neural Weather Emulator

We couple Forward Flux Sampling (FFS), a non-equilibrium rare-event technique from statistical mechanics, to a neural weather emulator (SDL-WXFormer, 1° grid spacing) to estimate conditional tropical cyclogenesis rates, or how often a tropical cyclone achieves a hurricane-level central pressure, without modifying model dynamics. Tropical cyclogenesis rates vary by orders of magnitude across regimes, yet direct ensemble sampling cannot resolve this variability at operationally feasible ensemble sizes. FFS decomposes the rare disturbance to mature cyclone intensification path into a flux through an initial interface pressure and a product of conditional crossing probabilities across four intermediate interface pressures. We use the 1° emulator because FFS requires O(10^4) model trajectories per initial condition, and because the model's calibrated stochastic layers provide the necessary exploratory spread. Applied to 98 Atlantic basin initial conditions spanning 21 August - 8 October 2022, FFS resolves genesis rates spanning nearly three orders of magnitude, capturing a seasonal cycle qualitatively consistent with observations. A self-consistency check comparing FFS rates to independent direct-sampling rates yields a mean ratio of 1.03 +/- 0.15 across all initial conditions. Computational enhancement factors range from 3X (most active environment) to 140X (most suppressed), with a geometric mean of 14X. Three case studies illustrate the physical diagnostics the method provides: the rate-limiting step is initial tropical organization for the Earl environment, uniformly high crossing probabilities for the Fiona precursor environment, and a compound barrier at the final intensification stages for the Ian environment. More efficient emulators would enable application of FFS to finer resolutions.