Author

Xian-Tao Li

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Preprint Aug 2026

From Nonlinear Stochastic Differential Equations to Quantum Channels: The Kolmogorov--Lindblad Mapping

Nonlinear stochastic differential equations (SDEs) underlie molecular modeling and drug discovery, quantitative finance, stochastic learning, and uncertainty quantification. Their expectations, event probabilities, and time correlations are therefore natural targets for quantum computation, but nonlinear drift and aver...

Hsuan-Cheng Wu, Xian-Tao Li · 1 citation

Preprint Jul 2026

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables

A multilevel quantum algorithm that estimates linear and quadratic observables $directly$ and places the fine--coarse cancellation inside the circuit before measurement and gives a non-Fourier realization based on energy-orthogonal dyadic midpoint details in one dimension.

Xian-Tao Li · 2 citations