Current Themes

  • Numerical methods for Lindblad equations and quantum dynamical equations.
  • Quantum algorithms for time-dependent Hamiltonian systems.
  • Sampling, diffusion models, and stochastic differential equations.
  • Machine learning and optimization in complex dynamical systems.

Preprints

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

  2. Zhiqiang Cai, Yu Cao, Yuanfei Huang, and Xiang Zhou. Weak Generative Sampler to Efficiently Sample Invariant Distribution of Stochastic Differential Equation, 2024. arXiv

Publications

  1. 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

  2. Yu Cao, Shi Jin, Nana Liu. Unifying framework for quantum simulation algorithms for time-dependent Hamiltonian dynamics, Phys. Rev. Res., 2025. arXivDOI

  3. 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., 2025. arXivDOI

  4. Yu Cao and Jianfeng Lu. Structure-preserving numerical schemes for Lindblad equations, J. Sci. Comput., 2025. CodearXivDOI

  5. 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. CodePDF

  6. Yu Cao, Jianfeng Lu, and Lihan Wang. On explicit $L^2$-convergence rate estimate for underdamped Langevin dynamics. Arch Rational Mech Anal, 247(5), 2023. DOI

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

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

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

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

  11. 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. DOI

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

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

  14. 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. DOI