Research internship

About the Role

The Algorithms and Applications for PDEs team focuses on quantum-centric supercomputing, combining quantum computing, AI, and conventional numerics to achieve breakthrough performance for forward and inverse problems for PDEs. The team works on quantum solvers, neural operators, and data assimilation methods, with a focus on workflows and algorithms that bridge computational paradigms.

Your Role and Responsibilities

• Actively contribute to the team's research agenda across algorithm and model development, experimentation, and validation.
• Depending on educational background, existing skills, strengths, and research opportunities, responsibilities may include:
• Implementing quantum solvers.
• Training AI models.
• Running validation across computational paradigms.
• Developing cross-platform workflows.
• Contribute to the general discourse within the group and lab, including participating in journal clubs and preparing reports.
• Interact with interns and researchers from other groups across IBM Research, particularly at the Yorktown lab.

Requirements & Tech Stack

• Working understanding of partial differential equations (theoretical or application-oriented).
• Elementary statistics.
• Proven experience prototyping in Python (NumPy).

Qualifications

• One or more of the following:
• Research experience in applied mathematics, specifically regarding differential equations, operator-theoretic methods, or numerical linear algebra for large-scale systems.
• Research experience in AI models for PDEs.
• Research experience in quantum computing.

Preferred Technical and Professional Experience

• One or more of the following:
• Experience with data assimilation methods such as variational data assimilation (3D-Var, 4D-Var), Kalman filtering, or AI data assimilation algorithms (score-based data assimilation).
• Experience with neural operators and/or AI models for inverse problems.
• Demonstrated experience of Hamiltonian simulation, LCU, QSP/SVT, qubitization, block-encodings; amplitude amplification/estimation, phase estimation, or quantum linear systems methods.
• Experience with discretization methods (FEM/FDM/spectral), PDE solvers (CG/GMRES/multigrid), and conditioning/preconditioning analysis.
• Background in model reduction (POD/DMD, balanced truncation) or Koopman/Carleman embeddings.
• Strong software engineering skills.
• Publication record.

Preferred Education

• Master's Degree