Preprints

  1. Yu Cao. Counter-examples for tensorization property of strong data processing inequality for quantum divergences, 2026. arXiv

  2. Yu Cao, Shi Jin, and Nana Liu. Quantum neural ordinary and partial differential equations, 2025. arXiv

Publications

  1. Zhiqiang Cai, Yu Cao, Yuanfei Huang, and Xiang Zhou. Weak Generative Sampler to Efficiently Sample Invariant Distribution of Stochastic Differential Equation. SIAM J. Sci. Comput., 48(4):C708–C735, 2026. arXivDOI

  2. Yu Cao, Mingfeng He, and Xiantao Li. Dynamically optimal unraveling schemes for simulating Lindblad equations. J. Phys. A: Math. Theor., 59(16):165301, 2026. arXivDOI

  3. Yu Cao, Shi Jin, and Nana Liu. Unifying framework for quantum simulation algorithms for time-dependent Hamiltonian dynamics. Phys. Rev. Res., 7(4):043186, 2025. arXivDOI

  4. Yu Cao, Shi Jin, and Nana Liu. Quantum simulation for time-dependent Hamiltonians—with applications to non-autonomous ordinary and partial differential equations. J. Phys. A: Math. Theor., 58(15):155304, 2025. arXivDOI

  5. Yu Cao and Jianfeng Lu. Structure-preserving numerical schemes for Lindblad equations. J. Sci. Comput., 102(1):27, 2025. arXivDOI Code

  6. Yu Cao, Jingrun Chen, Yixin Luo, and Xiang Zhou. Exploring the optimal choice for generative processes in diffusion models: ordinary vs stochastic differential equations. Advances in Neural Information Processing Systems, 2023. arXivPDF Code

  7. Yu Cao, Jianfeng Lu, and Lihan Wang. On explicit $L^2$-convergence rate estimate for underdamped Langevin dynamics. Arch. Ration. Mech. Anal., 247(5):90, 2023. arXivDOI

  8. Yu Cao and Eric Vanden-Eijnden. Learning optimal flows for non-equilibrium importance sampling. Advances in Neural Information Processing Systems, 2022. arXivPDF Code

  9. Yu Cao, Jianfeng Lu, and Lihan Wang. Complexity of randomized algorithms for underdamped Langevin dynamics. Commun. Math. Sci., 19(7):1827–1853, 2021. arXivDOI

  10. Yu Cao and Jianfeng Lu. Tensorization of the strong data processing inequality for quantum chi-square divergences. Quantum, 3:199, 2019. arXivDOI

  11. Yu Cao, Jianfeng Lu, and Yulong Lu. Exponential decay of Rényi divergence under Fokker-Planck equations. J. Stat. Phys., 176(5):1172–1184, 2019. arXivDOI

  12. Yu Cao, Jianfeng Lu, and Yulong Lu. Gradient flow structure and exponential decay of the sandwiched Rényi divergence for primitive Lindblad equations with GNS-detailed balance. J. Math. Phys., 60(5):052202, 2019. arXivDOI

  13. Yu Cao and Jianfeng Lu. Stochastic dynamical low-rank approximation method. J. Comput. Phys., 372:564–586, 2018. arXivDOI

  14. Yu Cao and Jianfeng Lu. Lindblad equation and its semiclassical limit of the Anderson-Holstein model. J. Math. Phys., 58(12):122105, 2017. arXivDOI

  15. Yu Cao, Ling Lin, and Xiang Zhou. Explore stochastic instabilities of periodic points by transition path theory. J. Nonlinear Sci., 26(3):755–786, 2016. arXivDOI