Quantum Computing Research (Xiantao Li's Group, Math Department)

About Us

Quantum computing harnesses many unique properties of quantum mechanics, such as quantum entanglement and superposition, offering distinct capabilities that exceed those of conventional computing apparatus. Our overarching objective is to devise efficient quantum algorithms tailored to address scientific computational issues, particularly those that present formidable challenges to classical computers.

Our Research

Hamiltonian Simulations

Hamiltonian simulation algorithms involve constructing a quantum circuit that performs the unitary transformation U associated with a Hamiltonian operator H. They are important building blocks for many other quantum computing algorithms. Our work focuses on Hamiltonian simulations for multi-scale quantum dynamics [4] and stochastic implementations of quantum dynamics in the second quantization form.

Open Quantum Systems.

In practice, quantum systems are inevitably subject to environmental noise. We design both quantum and classical algorithms to effectively simulate the behavior of these open quantum systems. In addition, we develop mathematical models for quantum dynamics outside the Markovian regime.

Optimal Control.

Quantum systems can be guided to perform specific tasks or maximize certain physical properties. We designed quantum algorithms for QOC problems with precise error bound and complexity estimates.

Applications to material science.

First-principle calculations in material science eliminate the need for empirical assumptions and possess the potential to predict material properties with quantum-level precision. The aim of our projects is to employ quantum algorithms in these first-principle computations, enabling the consideration of significantly larger systems and facilitating a direct connection between electronic structures and macroscale behavior.

Quantum Algorithms for Partial Differential Equations (PDE)

We create quantum algorithms specifically designed to solve partial differential equations, particularly in situations where the numerical discretization results in a high degree of freedom.

Quantum Sampling

Markov chains play a central role in modern data science algorithms. We construct algorithms that mix a Markov chain with quantum speedup.

Quantum Machine Learning

QML uses parameterizing quantum circuits to approximate unknown functions. Our focus is to analyze the role of measurement noise in the learning procedure.

Publications

Zhiyan Ding, Xiantao Li and Lin Lin, Simulating Open Quantum Systems Using Hamiltonian Simulations, PRX Quantum, 2024.
Zhiyan Ding, Taehee Ko, Jiahao Yao, Lin Lin, and Xiantao Li, Random coordinate descent: a simple alternative for optimizing parameterized quantum circuits, Preprint, 2023.
Guneykan Ozgul, Xiantao Li, Mehrdad Mahdavi, Chunhao Wang, Stochastic Quantum Sampling for Non-Logconcave Distributions and Estimating Partition Functions, Preprint, 2023.
With Taehee Ko and Chunhao Wang, Implementation of the Density-functional Theory on Quantum Computers with Linear Scaling with respect to the Number of Atoms, Preprint, 2023.
With Ke Wang, Simulation-assisted learning of open quantum systems, Preprint, 2023.
With Jin, Liu, Yu, Quantum Simulation for Partial Differential Equations with Physical Boundary or Interface Conditions., Journal of Computational Physics, Vol 498, 112707, 2024.
With Jin, Liu, Yu, Quantum Simulation for Quantum Dynamics with Artificial Boundary Condition, SIAM Journal on Scientific Computing, 2024.
With C. Wang, Efficient Quantum Algorithms for Quantum Optimal Control, Proceedings of the 40th International Conference on Machine Learning (ICML), 2023.
With C. Wang, Efficient Simulating Markovian open quantum systems using higher-order series expansion, 50th International Colloquium on Automata, Languages, and Programming (ICALP), 2023.
Enabling Quantum Speedup of Markov Chains using a Multi-level Approach, Preprint, 2022.
With S. Jin and Nana Liu, Hamiltonian Simulation in the semi-classical regime Quantum, Vol 6, pp 739, 2022.
X Li, Some Error Analysis for the Quantum Phase Estimation Algorithms Journal of Physics A: Mathematical and Theoretical, 2022.
With Chunhao Wang, Succinct Description and Efficient Simulation of Non-Markovian Open Quantum Systems Communications in Mathematical Physics, , Vol 401, pages 147–183 2023.
With Shi Jin, A Partially Random Trotter Algorithm for Quantum Hamiltonian Simulations, Communications on Applied Mathematics and Computation, 2023.

Our Team

Xiantao Li

Professor, Penn State.

Taehee Ko

Graduate Student.

Ke Wang

Graduate Student.

Pegah Mohammadipour

Graduate Student.

Ryan Cohen

Undergraduate Student.