Quantum Algorithms and Quantum Enhanced Machine Learning for Transient Simulations in Large Scale Nonlinear Dynamical Systems
PI: Xiantao Li (Mathematics), Yan Li (Electrical Engineering and Computer Science)
Specific areas of expertise:
Experiences with simulation and control algorithms for dynamical systems and data-driven methods. Programming skills for quantum computing algorithms on quantum simulators or cloud quantum computing platforms.
Other requirements:
post-comp graduate students.
Specific objectives of this work:
Building on the team’s foundational theoretical breakthroughs and f indings, we will engage graduate students in developing a pipeline that adapts established simulation, machine-learning, and control algorithms to quantum hardware. The project will deliver preliminary insights into the capabilities of today’s quantum computers, including: the largest dynamical-system dimensions they can tackle; performance differences between digital and analog devices; head-to-head comparisons of direct-simulation and quantum QI/ML algorithms; the predictive power of quantum-enabled data-driven methods; and accuracy gains achievable through noise-mitigation techniques.
Medium to long-term goals:
Leveraging the PIs’ direct access to quantum hardware from IBM (superconducting digital quantum hardware), QuEra (neutral-atom systems supporting both analog and digital modes), and IQM (superconducting digital-analog processors), our team will reformulate classical numerical methods for dynamical systems into quantum algorithms and deploy them on both analog and digital platforms to evaluate performance speedup and scalability. The resulting preliminary data will enable a rigorous comparison of competing strategies for quantum simulation. Armed with these insights, we will craft compelling full-scale proposals for submission to major funding agencies, including the DOE and NSF.
Connection of the project to ICDS’s mission:
Our project directly advances ICDS’s mission by uniting expertise in dynamical models of many physical systems, machine learning, and quantum computing—disciplines that rarely converge—into a cohesive research team. By reformulating classical numerical algorithms as quantum workflows and benchmarking them on state-of-the-art IBM, QuEra, and IQM hardware, we leverage the very “advanced computational and data-science approaches” ICDS seeks to promote. The work will both train graduate students and generate open benchmarks that guide society-relevant applications, aligning with ICDS’s goal of addressing questions of scientific and societal importance. Finally, the project will rely on ICDS’s network to accelerate code development and cross-college collaboration, exemplifying the center’s role as a catalyst for interdisciplinary research.
Team’s engagement with ICDS.
In 2022, PI X.Li received an ICDS Seed Grant for the project “Machine Learning with QuantumSpeedup.”Building onthat award, Li participated in the ICDS-Quantinuum industry event, served on the 2023 ICDS Symposium panel “The Past, Present, and Future of Quantum Computing,” and will co-organize the mini-symposium “Advances in Computational Mathematics with Machine Learning” at the ICDS workshop in October 2025. PI Y.Li’s group regularly uses ICDS Roar resources and actively participates in research discussions with ICDS-affiliated faculty and ICDS-hosted webinars.
Project Description.
Nonlinear dynamical systems underlie phenomena across engineering and the physical sciences—from power-grid stability and turbulent flows to protein conformational changes in biology and many-body quantum dynamics in quantum physics and material science. Recent advances in quantum computing now offer a promising path for simulating such high-dimensional models beyond classical limits.
Challenges.
A clear roadmap for exploiting quantum hardware in large-scale dynamical simulation is still lacking. Major obstacles include:
• Algorithmic reformulation: Classical time-integration schemes must be recast as quantum algorithms and subsequently mapped to quantum circuits, demanding new mathematical frameworks.
• Data-driven extensions: Koopman analysis, dynamic mode decomposition, and machine-learning methods remain almost entirely classical, with few quantum counterparts.
• Algorithm selection: Direct (time-marching) quantum algorithms and variational quantum algorithms (VQAs) have complementary strengths; their relative merits across dynamical regimes are poorly understood.
• Hardware heterogeneity: Analog and digital quantum devices impose distinct gate, connectivity, and noise constraints whose impact on simulation fidelity is largely unexplored.
• Compilation bottlenecks: Tool chains that translate high-level algorithms into pulse-level instructions are still primitive, limiting practical deployment.
Project Objectives.
Leveraging ICDS resources and the PIs’ direct access to IBM, QuEra, and IQM hardware, we will assemble a team of two PIs and three graduate students to pursue the following oneyear goals:
1. Identify “quantum-friendly” algorithms that require few ancilla qubits, simple quantum operations, and remain robust under gate errors.
2. Develop quantum analogs of data-driven methods that exploit superposition-based data access.
3. Benchmarkdirect versus variational approaches, fully accounting for training overheads and measurement costs in quantum ML/AI methods.
4. Assessanalogvs.digital platforms onrepresentative nonlinear models, quantifying resource–performance trade-offs.
5. Design model-specific quantum error-mitigation schemes for key PDEs such as the Navier–Stokes and nonlinear Schrödinger equations.
6. Study ML-based post-processing techniques that reduce circuit error and numerical error.
7. Release an open-source pipeline that automates compilation and execution across devices.
8. Demonstrate quantum advantages by pinpointing use-cases where quantum algorithms outperform classical ones in accuracy, runtime, and resource utilization on large-scale dynamical simulation.
Team Management.
Two PIs and three graduate students—spanning applied mathematics, data science, and software engineering—will meet weekly to coordinate tasks, using Slack for daily exchanges and GitHub for version control. Findings will be shared through ICDS seminars and external conferences, broadening impact and fostering community feedback.
Path to External Funding.
Upon completing the one-year effort, we will leverage the resulting benchmarks, error-mitigation strategies, and open-source tools to develop full-scale proposals for submission to major funding agencies, including the DOE and NSF. The team, including the two PIs and scientists from QuEra and IQM, already has one joint paper and two DOE grants pending; securing this ICDS award will further strengthen their collaboration and establish a robust foundation for future large-scale federal funding.