Quantum Algorithms for Scientific Computing

Recent News & Momentum

• Early 2026 Presentation at the IPAM workshop: A general dilation framework for non-Hermitian dynamics.

Our Research

Scalable Hamiltonian Simulations

Developing highly efficient, mathematically rigorous quantum circuits for unitary evolution U = e^-iHt. By establishing strict error bounds and optimizing resource estimates, we provide the foundational algorithmic infrastructure for exact ground-state and dynamical simulations in physical chemistry and materials science.

Open Quantum Systems

Real-world materials and near-term hardware are inherently dissipative. We build rigorous mathematical frameworks to simulate complex Lindbladian and non-Markovian dynamics, unlocking practical quantum utility for open systems by bridging theoretical continuous-time models with NISQ hardware reality.

Next-Generation Materials & DFT

Transitioning quantum advantage into first-principle materials design. Our quantum-enhanced Density Functional Theory (DFT) solvers are engineered to overcome classical scaling bottlenecks, enabling high-fidelity electronic structure predictions for complex, strongly correlated materials.

Quantum Solvers for PDEs

Translating classical fluid and wave dynamics onto quantum architectures. Utilizing breakthrough dilation frameworks and Schrödingerisation, we engineer mathematically well-posed quantum solvers designed to break the curse of dimensionality in macroscopic physics simulations.

System Identification & Control

Transforming measurement data into actionable hardware calibration. We develop robust learning algorithms to infer Hamiltonian interactions and dissipative environmental parameters, directly enabling advanced control protocols for noisy quantum devices.

Accelerated Statistical Sampling

Overcoming classical optimization and sampling limits. By leveraging quantum walks and amplitude amplification, our quantum MCMC algorithms drastically reduce mixing times, providing a strategic computational advantage in traversing complex, non-convex optimization landscapes.

Hardware-Algorithm Co-Design

Treating hardware noise as a solvable mathematical parameter. We pioneer rigorous error extrapolation (ZNE) and non-Markovian mitigation strategies that natively exploit hardware topologies to simultaneously suppress algorithmic bias and physical circuit errors.

Hybrid Quantum-Classical Optimization

Optimizing the classical-quantum interface. We design and rigorously analyze hybrid optimization schemes—such as random coordinate descent and fast-forwarded Hamiltonian diagonalization—ensuring stable, scalable convergence for variational quantum algorithms.

Quantum Stochastic SDEs

Natively embedding randomness into quantum processors. Our unitary dilation frameworks rigorously propagate second-order statistics, unlocking the ability to simulate complex diffusive dynamics, open system limits, and stochastic transport phenomena directly on quantum hardware.

Quantum Hardware Access

• IBM Quantum (via NERSC)
• Quantinuum (via ORNL/OLCF)
• IonQ

Publications

1. Z Huang, Z Ding, K Wang, J Kaye, X Li, L Lin, Provably Efficient Long-Time Exponential Decompositions of Non-Markovian Gaussian Baths, preprint, 2026.
2. Xiantao Li, Auxiliary-Field Quantum Monte Carlo on Quantum Hardware via Unitary Dilation, preprint, 2026.
3. Hsuan-Cheng Wu and Xiantao Li, Universal Dilation of Linear Itô SDEs: Quantum Trajectories and Lindblad Simulation of Second Moments, preprint, 2026.
4. Xiantao Li and Chunhao Wang, Quantum Regression Theory and Efficient Computation of Response Functions for Non-Markovian Open Systems, preprint, 2025.
5. Yu Cao, Mingfeng He, Xiantao Li, Dynamically Optimal Unraveling Schemes for Simulating Lindblad Equations, Journal of Physics A: Mathematical and Theoretical, 2026.
6. Pinchen Xie, Ke Wang, Anupam Mitra, Yuanran Zhu, Xiantao Li, Wibe Albert de Jong, Chao Yang, Predict open quantum dynamics with data-informed quantum-classical dynamics, Physical Review Letters, Vol 136, 010402, 2026.
7. Pegah Mohammadipour and Xiantao Li, Reducing Circuit Depth in Lindblad Simulation via Step-Size Extrapolation, Physical Review A, 2025.
8. Xiantao Li, From Linear Differential Equations to Unitaries: A Moment-Matching Dilation Framework with Near-Optimal Quantum Algorithms, preprint, 2025.
9. Taehee Ko, Sangkook Choi, Hyowon Park, Xiantao Li, Classical optimization algorithms for diagonalizing quantum Hamiltonians, Physica Scripta, 2025.
10. Xiantao Li, Exponential Quantum Speedup for Simulating Classical Lattice Dynamics, Physical Review Letters, Accepted, 2025.
11. Guneykan Ozgul, Xiantao Li, Mehrdad Mahdavi, Chunhao Wang, Quantum Speedups for Markov Chain Monte Carlo Methods with Application to Optimization, preprint, 2025.
12. Pegah Mohammadipour and Xiantao Li, Direct Analysis of Zero-Noise Extrapolation: Polynomial Methods, Error Bounds, and Simultaneous Physical-Algorithmic Error Mitigation, Quantum, 9, 1909, 2025.
13. Ke Wang and Xiantao Li, Non-Markovian Noise Mitigation: Practical Implementation, Error Analysis, and the Role of Environment Spectral Properties, preprint, 2025.
14. Zhenning Liu, Xiantao Li, Chunhao Wang, and Jin-Peng Liu, Toward end-to-end quantum simulation for protein dynamics, preprint, 2024.
15. Hsuan-Cheng Wu and Xiantao Li, Structure-preserving quantum algorithms for linear and nonlinear Hamiltonian systems, preprint, 2024.
16. Hsuan-Cheng Wu, Jiayao Wang and Xiantao Li, Quantum Algorithms for Nonlinear Dynamics: Revisiting Carleman Linearization with No Dissipative Conditions, SIAM Journal on Scientific Computing, 2025.
17. Wenhao He, Tongyang Li, Xiantao Li, Zecheng Li, Chunhao Wang and Ke Wang, Efficient Optimal Control of Open Quantum Systems, TQC, 2024.
18. Zhiyan Ding, Xiantao Li and Lin Lin, Simulating Open Quantum Systems Using Hamiltonian Simulations, PRX Quantum, 5, 020332, 2024.
19. Zhiyan Ding, Taehee Ko, Jiahao Yao, Lin Lin, and Xiantao Li, Random coordinate descent: a simple alternative for optimizing parameterized quantum circuits, Physical Review Research, 2024.
20. Guneykan Ozgul, Xiantao Li, Mehrdad Mahdavi, Chunhao Wang, Stochastic Quantum Sampling for Non-Logconcave Distributions and Estimating Partition Functions, ICML, 2024.
21. Taehee Ko, Chunhao Wang, and Xiantao Li, Implementation of the Density-functional Theory on Quantum Computers with Linear Scaling with respect to the Number of Atoms, QEC, 2024.
22. Ke Wang and Xiantao Li, Simulation-assisted learning of open quantum systems, Quantum, 2024.
23. Shi Jin, Nana Liu, Yue Yu, and Xiantao Li, Quantum Simulation for Partial Differential Equations with Physical Boundary or Interface Conditions, Journal of Computational Physics, Vol 498, 112707, 2024.
24. Shi Jin, Nana Liu, Yue Yu, and Xiantao Li, Quantum Simulation for Quantum Dynamics with Artificial Boundary Condition, SIAM Journal on Scientific Computing, 2024.
25. Xiantao Li and Chunhao Wang, Efficient Quantum Algorithms for Quantum Optimal Control, ICML, 2023.
26. Xiantao Li and Chunhao Wang, Efficient Simulating Markovian open quantum systems using higher-order series expansion, ICALP, 2023.
27. Xiantao Li, Enabling Quantum Speedup of Markov Chains using a Multi-level Approach, Preprint, 2022.
28. Shi Jin, Nana Liu, and Xiantao Li, Hamiltonian Simulation in the semi-classical regime, Quantum, Vol 6, pp 739, 2022.
29. Xiantao Li, Some Error Analysis for the Quantum Phase Estimation Algorithms, Journal of Physics A: Mathematical and Theoretical, 2022.
30. Xiantao Li and Chunhao Wang, Succinct Description and Efficient Simulation of Non-Markovian Open Quantum Systems, Communications in Mathematical Physics, Vol 401, pages 147–183, 2023.
31. Shi Jin and Xiantao Li, A Partially Random Trotter Algorithm for Quantum Hamiltonian Simulations, Communications on Applied Mathematics and Computation, 2023.

Our Team