About the role#
The Algorithms and Applications for PDEs team focuses on quantum centric supercomputing. We combine quantum computing, AI, and conventional numerics to solve forward and inverse problems for partial differential equations. Our work involves developing workflows that bridge these computational paradigms to improve performance where conventional methods hit scaling limits.
What you'll do#
- Contribute to the team research agenda through algorithm and model development.
- Perform experimentation and validation of new methods.
- Implement quantum solvers and train AI models.
- Build cross-platform workflows.
- Participate in journal clubs and prepare research reports.
- Interact with researchers and other interns across the lab.
What you'll need#
- Working understanding of partial differential equations and elementary statistics.
- Proven experience prototyping in Python using NumPy.
- Research experience in at least one of the following: applied mathematics (differential equations, operator-theoretic methods, or numerical linear algebra), AI models for PDEs, or quantum computing.
- Experience in one or more of these areas: data assimilation (3D-Var, 4D-Var, Kalman filtering, or score-based methods), neural operators, inverse problems, Hamiltonian simulation, LCU, QSP/SVT, qubitization, block-encodings, amplitude amplification, phase estimation, or quantum linear systems.
- Proficiency with discretization methods (FEM/FDM/spectral), PDE solvers (CG/GMRES/multigrid), and conditioning analysis.
- Background in model reduction (POD/DMD, balanced truncation) or Koopman/Carleman embeddings.
- Strong software engineering skills and a record of publication.
Location & details#
- Location: Yorktown Heights, New York, United States.
- Term: Summer 2027.
- Status: Full-time internship.
- Modality: On-site.
- This is a paid position.
About IBM
IBM provides IT services and consulting to a global client base. The company develops technology solutions across areas such as cloud computing, security, analytics, and infrastructure. It operates as a public organization with more than 10,001 employees. The corporate headquarters are located in Armonk, New York.
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