Research

My current research can be categorized into two main directions:

• Quantum computing: I am interested in developing new quantum algorithms based on the connections between quantum and classical computing. Specifically, I aim to design efficient classical post-processing subroutines for quantum problems and create new quantum algorithms analogous to their classical counterparts. In this direction, my current interest lies in quantum phase estimation and quantum sampling.

• Classical numerical analysis: In the classical setting, I am interested in applying traditional techniques from numerical analysis and optimization to study, develop, and improve algorithms. My current interests in this direction include mean-field analysis, mean-field control and game theory, optimization, and sampling problems.

Publications:

Preprints:

[6] Z Ding, I. Ekren, Y. Han, A. Zitridis, Quantitative homogenization of convex Hamilton-Jacobi equations in the Wasserstein space, arXiv/2606.22103, 2026.

[5] K. Wang, Z. Jia, S. Veerapaneni, Z. Ding, Quantum Algorithms for Nonlinear Differential Equations via Pivot-Shifted Carleman Linearization, arXiv/2605.20071, 2026. 

[4] H. Chen, Z. Ding, R. Zhang, Overcoming the Lamb Shift in System-Bath Models via KMS Detailed Balance: High-Accuracy Thermalization with Time-Bounded Interaction, arXiv/2604.15615, 2026. 

[3] E. Bayraktar, Z. Ding, I. Ekren, H. Zhou, Uniform-in-time propagation of chaos for consensus-based minimax algorithm, arXiv/2602.14403, 2026. 

[2] K. Wang, Z. Ding, Beyond Lindblad Dynamics: Rigorous Guarantees for Thermal and Ground State Preservation under System Bath Interactions, arXiv/2512.03457, 2025.

[1] Z. Chen, J. Basso, Z. Ding, L. Lin, Quantum Replica Exchange, arXiv/2510/07291, 2025. 

Peer reviewed papers:

[34] Z. Huang, Z. Ding, K. Wang, J. Kaye, X. Li, L. Lin, Provably Efficient Long-time Exponentil Decompositions of Non-Markovnian Gaussian Baths, Physical Review Research, accepted, 2026.

[33] Z. Ding*, Y. Zhan*, J. Preskill, L. Lin, Simple and efficient end-to-end thermal and ground state preparation, Nature Physics, 2026.

[32] Z. Ding, Y. Dong, Y. Tong, L. Lin, Robust ground-state energy estimation under depolarizing noise, APL Computational Physics, 2, 026111, 2026.

[31] Z.Ding, Z. Landau, B. Li, L. Lin, R. Zhang, Polynomial-Time Preparation of Low-Temperature Gibbs States for 2D Toric Code, Journal of Mathematical Physics, 67, 052201, 2026.

[30] Z. Ding, L. Lin, Y. Yang, R. Zhang, Quantum Filtering and Analysis of Multiplicities in Eigenvalue Spectra, PRX Quantum, 7, 020318, 2026.

[29] J. Leng, Z. Ding, Z. Chen, L. Lin, Operator-Level Quantum Acceleration of Non-Logconcave Sampling, PNAS,  123 (e), 2026.

[28] Y. Zhan*, Z.Ding*, J. Huhn, J. Gray, J. Preskill, G. Chan, L. Lin, Rapid quantum ground state preparation via dissipative dynamics, Physical Review X, 06, 011004, 2025.

[27] Z. Ding, M. Junge, P. Schleich, P. Wu, Lower bound for simulation cost of open quantum systems: Lipschitz continuity approach, Communications in Mathematical Physics, 407(3), 60, 2025. 

[26] Z. Ding, B. Li, L. Lin, Efficient quantum Gibbs samplers with Kubo-Martin-Schwinger detailed balance condition, Communications in Mathematical Physics, 407, 67, 2025.

[25] Z. Ding, H. Li, L. Lin, H. Ni, L. Ying, R. Zhang, Quantum Multiple Eigenvalue Gaussian filtered Search: an efficient and versatile quantum phase estimation method, Quantum, 8, 1487, 2024.

[24] Z.Ding, M. Guerra, Q. Li, E. Tadmor, Swarm-based gradient descent meets simulated annealing, SINUM, 62(6), 2024.

[23] Z. Ding, C. Chen, L. Lin, Single-ancilla ground state preparation via Lindbladians, Physical Review Research, 06, 033147, 2024.

[22]  Z. Ding, E. N. Epperly, L. Lin, R. Zhang, The ESPRIT algorithm under high noise: Optimal error scaling and noisy super-resolution, FOCS 2024, 2024.

[21] S. Chen, Z. Ding, Q. Li, Bayesian sampling using interacting particles, Active Particles, Volume 4, Birkhäuser Cham, 2024.

[20] Z. Ding, T. Ko, J. Hao, L. Lin, X. Li, Random coordinate descent: a simple alternative for optimizing parameterized quantum circuits, Physical Review Research, 6, 033029, 2024.

[19] N. Abrahamsen, Z. Ding, G. Goldshlager, L. Lin, Convergence of variational Monte Carlo simulation and scale-invariant pre-training, Journal of Computational Physics, 513, 113-140, 2024.

[18] Z. Ding, X. Li, L. Lin, Simulating open quantum systems using hamiltonian simulations, PRX Quantum, 5, 020332, 2024.

[17] Z. Ding, L. Lin, Simultaneous estimation of multiple eigenvalues with short-depth quantum circuit on early fault-tolerant quantum computers, Quantum 7, 1136, 2023.

[16] Z. Ding, L. Lin, Even shorter quantum circuit for phase estimation on early fault-tolerant quantum computers with applications to ground-state energy estimation, PRX Quantum, 4(2), 2023.

[15] S. Chen, Z. Ding, Q. Li, L. Zepeda-Núñez, High-frequency limit of the inverse scattering problem: asymptotic convergence from inverse Helmholtz to inverse Liouville, SIAM Journal on Imaging Sciences, 16(1), 111-143, 2023.

[14] S. Chen, Z. Ding, Q. Li, S. Wright, A reduced order Schwarz method for nonlinear multiscale elliptic equations based on two-layer neural networks, Journal of Computational Mathematics, 2023.

[13] Z. Ding, S. Chen, Q. Li, S. Wright, Overparameterization of deep ResNet: zero loss and mean-field analysis, Journal of Machine Learning Research, 23(48): 1-65, 2022.

[12] Z. Ding, Q. Li, Constrained Ensemble Langevin Monte Carlo, Foundations of Data Science, 4(1): 37-70, 2022.

[11] Z. Ding, Q. Li, Langevin Monte Carlo: random coordinate descent and variance reduction, Journal of Machine Learning Research, 22(205): 1-51, 2021.

[10] Z. Ding, Q. Li, J. Lu, S. Wright, Random Coordinate Underdamped Langevin Monte Carlo, 24th International Conference on Artificial Intelligence and Statistics (AISTATS 2021), 2021.

[9] Z. Ding, Q. Li, J. Lu, S. Wright, Random Coordinate Langevin Monte Carlo, 34th Annual Conference on Learning Theory (COLT 2021), 2021

[8] Z. Ding, Q. Li, J. Lu, Ensemble Kalman Inversion for nonlinear problems: weights, consistency, and variance bounds, Foundations of Data Science, 3(3): 371-411, 2021.

[7] Z. Ding, Q. Li, Ensemble Kalman Sampler: mean-field limit and convergence analysis, SIAM Journal on Mathematical Analysis, 53(2): 1546–1578, 2021.

[6] Z. Ding, Q. Li, Ensemble Kalman Inversion: mean-field limit and convergence analysis, Statistics and Computing, 31, 9, 2021.

[5] Z. Ding, L. Einkemmer, Q. Li, Dynamical low-rank integrator for the linear Boltzmann equation: Error analysis in the diffusion limit, SIAM Journal on Numerical Analysis, 59, 4, 2021. 

[4] Z. Ding, H. Hajaiej, On a Fractional Schrödinger equation in the presence of Harmonic potential, Electronic Research Archive, 29(5): 3449-3469, 2021.

[3] Z. Ding, S. Ha, S. Jin, A local sensitivity analysis in Landau Damping for the kinetic Kuramoto equation with random inputs, Quarterly of Applied Mathematics, 79, 229-264, 2021.

[2] Z. Ding, Q. Li, Variance reduction for Random Coordinate Descent-Langevin Monte Carlo, 34th Conference on Neural Information Processing Systems (NeurIPS 2020), 2020.

[1] Z. Ding, S. Jin, Random regularity of a nonlinear Landau Damping solution for the Vlasov-Poisson equations with random inputs, International Journal for Uncertainty Quantification, 9, 123-142, 2019.