Zhijian Lai
I am a postdoctoral researcher at the Beijing International Center for Mathematical Research (BICMR), Peking University, advised by Zaiwen Wen.
Previously, I received my Ph.D. and M.S. in Policy and Planning Sciences from the University of Tsukuba (Japan) in 2024 and 2021, respectively, under the supervision of Prof. Akiko Yoshise, and my B.Mgmt. in Logistics Management from Dongbei University of Finance and Economics (China) in 2017.
Research Interests
My research interests lie in the intersection of the following areas:
- Riemannian optimization
- constrained optimization on manifolds
- nonsmooth and smoothing methods on matrix manifolds
- Quantum algorithms and quantum optimization
- optimization-based quantum search
- Grover-compatible manifold algorithms
- quantum circuit design and state preparation
- Variational quantum algorithms
- parameterized quantum circuits
- parameter-shift rules and derivative estimation
- coordinate descent methods
News and Updates
2026.06.01 · New preprint. Hantao Nie, Zhijian Lai, Dong An. Pauli-structured preconditioning for quantum linear system solvers. arXiv:2606.01733.
2026.03.27 · New preprint. Zhijian Lai, Dong An, Jiang Hu, Zaiwen Wen. Achieving double-logarithmic precision dependence in optimization-based quantum unstructured search. arXiv:2603.26039.
2026.02.25 · New preprint. Zhijian Lai, Hantao Nie, Jiayuan Wu, Dong An. Quantum circuit design from a retraction-based Riemannian optimization framework. arXiv:2602.20605.
2026 · New publication. Zhijian Lai, Jiang Hu, Dong An, Zaiwen Wen. Extended parameter-shift rules with minimal derivative variance for parameterized quantum circuits. Physical Review Applied 25(1), 014005.
2026 · New publication. Zhijian Lai, Jiang Hu, Taehee Ko, Jiayuan Wu, Dong An. Interpolation-based coordinate descent method for parameterized quantum circuits. Communications Physics 9, 41.
2025.12.11 · New preprint. Chenyi Li, Zhijian Lai, Dong An, Jiang Hu, Zaiwen Wen. Advancing Mathematical Research via Human-AI Interactive Theorem Proving. arXiv:2512.09443.
2025.12.09 · New preprint. Zhijian Lai, Dong An, Jiang Hu, Zaiwen Wen. A Grover-compatible manifold optimization algorithm for quantum search. arXiv:2512.08432.
2025.08.27 · Grant. Granted the NSFC Young Scientists Fund (Category C), project Manifold Optimization Theory and Algorithms in Quantum Information Science.
2025.06.13 · Lecture notes. It has been one year since I started my postdoc at PKU. During this time, I taught Calculus B for two semesters and prepared over a thousand pages of lecture notes in Chinese. AM-B-1 collected notes, course homepage; AM-B-2 collected notes, course homepage.
2024.10.21 · New publication. Xin Yang, Heng Chang, Zhijian Lai, Jinze Yang, Xingrun Li, Yu Lu, Shuaiqiang Wang, Dawei Yin, Erxue Min. Hyperbolic contrastive learning for cross-domain recommendation. CIKM 2024.
2024.08.04 · Software. My PhD work, the Interior Point Newton Method on manifolds, has been implemented in Manopt.jl. See the documentation.
2024.05.14 · Milestone. I started my postdoctoral life at Peking University. Photo.
2024.03.25 · Graduation. I obtained my Ph.D. certificate and graduated from the Graduate School of Systems and Information Engineering, University of Tsukuba. Many thanks to my supervisor Prof. Akiko Yoshise.
2024.03.05–2024.05.13 · Visit. I was a research visitor at BICMR, Peking University.
2024.03.04 · New publication. Zhijian Lai, Akiko Yoshise. Riemannian Interior Point Methods for Constrained Optimization on Manifolds. Journal of Optimization Theory and Applications, 201(1), 433–469.
2024.01.22 · Graduation. I finished my PhD final defense. Slides, photo.
2023.08 · Conference. I gave an oral presentation at ICIAM 2023 at Waseda University, Tokyo, Japan. Photo. Many thanks to Prof. Hiroyuki Sato for inviting and organizing the minisymposium.
2023.08 · Conference. I presented a poster at the Summer School on Continuous Optimization and Related Fields at the Institute of Statistical Mathematics in Tachikawa, Tokyo. Photo.
2023.06 · Website. Opened this website.
