Research

Broadly speaking, I am interested in the following topics (non-exhaustive):

• Hamiltonian simulation
• Simulating differential equations
• Numerical optimization
• Machine learning for quantum computing
• Circuit compilation and optimization

Here is a list of research projects I have worked on.

• Quantum Hamiltonian Descent. Jiaqi Leng, Ethan Hickman, Joseph Li, and Xiaodi Wu. Manuscript, 2023. (Website, arXiv)
• Expanding hardware-efficiently manipulable Hilbert space by Hamiltonian embedding. Jiaqi Leng*, Joseph Li*, Yuxiang Peng, and Xiaodi Wu. Quantum 9, 1857 (2025).
  • AWS Quantum Blog Post: Leveraging near-term quantum hardware for simulating high-dimensional dynamics
  
• Resource-efficient quantum simulation of transport phenomena via Hamiltonian embedding. Joseph Li, Gengzhi Yang, Jiaqi Leng, and Xiaodi Wu. Manuscript, 2026. (arXiv)
• Efficient Quantum Circuits for the Hilbert Transform. Henry Zhang and Joseph Li. IEEE Signal Processing Letters (2026).