CS-1

Changpeng Shao (邵长鹏)

506 Siyuan Building, NO 55 Zhongguancun East Road, Beijing China changpeng.shao@amss.ac.cn
北京市,中关村东路55号,中科院数学院,思源楼-506

Associate Professor, Key Laboratory of Mathematics Mechanization, Chinese Academy of Sciences. (Prior to this, I was a research associate at the School of Mathematics, University of Bristol working with Ashley Montanaro and Noah Linden. I received my PhD from the University of Chinese Academy of Sciences under the supervision of Prof. Hongbo Li.)

Research interests: quantum computation, quantum algorithms, quantum complexity theory and some relevant mathematics

My research aims to better understand the power of quantum computers. I am especially interested in quantum algorithms, quantum query, communication and circuit complexity. I am also interested in symbolic computation, where I use tools from Clifford algebra, computational algebraic geometry, and invariant theory to automated reasoning. Some other interesting research topics include the Kaczmarz method and randomised numerical linear algebra.

"If you can't do great things, do small things in a great way. Don't wait for great opportunities. Seize common, everyday ones and make them great." --- Napoleon Hill

Students

  • Yuxin Zhang (张宇欣) 2023.10-2026.06 (then a postdoctoral researcher of András Gilyén).

    Papers

    Google Scholar, arXiv, Some talks, A full list of publications, the following is a list of preprints

    1. Low-ancilla block encodings via Hamiltonian simulation
      with Yuxin Zhang
      arXiv:2607.01843

    2. Worst-case Harrow-Hassidim-Lloyd algorithm with average-case correct quantum Fourier transform
      arXiv:2604.10428

    3. DQC1-completeness of normalized trace estimation for functions of log-local Hamiltonians
      with Zhengfeng Ji, Tongyang Li, Xinzhao Wang, Yuxin Zhang
      to appear in FOCS 2026
      arXiv:2604.01519

      In our paper, Theorem 2.10 is the key theorem underlying all our results. We spent too much time—maybe half a year—trying to prove a general result, but failed and only obtained a conditional result in the end, before turning to AI. Recently, with the help of GPT-5.6 Sol, we proved more general results (see this note and this revised note, which were written by GPT). The first result is a little surprising, because it only uses a uniform periodic Jacobi matrix with $a_i=0,b_i=1/2$ of dimension depending on the input function. In our paper, the choices of $a_i,b_i$ highly depend on the input function. Interestingly, this Jacobi matrix is indeed the case used in all previous results for some specific functions. This particular Jacobi matrix corresponds to Chebyshev polynomials, and from the findings of our paper, it seems to be a natural object in DQC1-hardness. The extra condition for DQC1-hardness is much weaker than the one in our paper. The second result is quite impressive: it says that DQC1-hardness holds for all Lipschitz functions. Note that previously, the DQC1 quantum algorithm given by Cade and Montanaro was also for Lipschitz functions (arXiv:1706.09279). The proof is quite different from our current proof in the paper. I may have missed some points, but I checked the proofs and did not find any serious issues.

    4. DQC1-hardness of estimating log-determinants [Notes]
      with Xinzhao Wang

      In this short note, we prove that estimating the log-determinant of log-local Hamiltonians is DQC1-complete.

    5. Randomized Quantum Singular Value Transformation
      with Xinzhao Wang, Yuxin Zhang, Soumyabrata Hazra, Tongyang Li, Shantanav Chakraborty
      arXiv:2510.06851

    6. Quantum singular value transformation without block encodings: Near-optimal complexity with minimal ancilla
      with Shantanav Chakraborty, Soumyabrata Hazra, Tongyang Li, Xinzhao Wang, Yuxin Zhang
      arXiv:2504.02385

    7. Low-degree approximation of QAC0 circuits
      with Ashley Montanaro, Dominic Verdon
      arXiv:2411.00976 (withdrawn)
      There is a bug in the paper that will take some time to fix.

    8. Quantum speedup of leverage score sampling and its application
      arXiv:2301.06107

    Quantum and beyond

    Visiting scholars (访问学者)