Research internship: Quantum computing and AI for partial differential equations 2027

IBM is a research and technology company developing quantum computing, artificial intelligence, and scientific computing solutions. This internship supports research on quantum solvers, AI models, numerical methods, and cross-platform workflows for forward and inverse partial differential equation problems, including algorithm development, experimentation, validation, reporting, and collaboration with researchers.

What you'll do:

• The successful candidate will actively contribute to the team's research agenda across the entire vertical of algorithm and model development, experimentation and validation. Depending on educational background, existing skills and strengths as well as research opportunities, this can mean implementing quantum solvers, training AI models, running validation across computational paradigms or developing cross-platform workflows
• Beyond the work on a primary project, the candidate will contribute to and be part of the general discourse within the group and lab. This means participating in journal clubs and preparing reports; yet also interacting with interns and researchers from other groups across IBM Research in general and the Yorktown lab in particular

What they're looking for:

• Bachelor's Degree
• Working understanding of partial differential equations -- from a theoretical or application-oriented perspective
• Elementary statistics
• Proven experience prototyping in python (numpy)
• Research experience in applied mathematics. In particular regarding differential equations and operator-theoretic methods or numerical linear algebra for large-scale systems
• Research experience in AI models for PDEs
• Research experience in quantum computing
• Master's Degree
• 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

Benefits:

• Supplemental 1 employees may be eligible for up to 8 paid holidays
• Supplemental 1 employees may be eligible for a minimum of 56 hours paid sick time
• Supplemental 1 employees may be eligible for the IBM Employee Stock Purchase Plan
• IBM offers paid family medical leave to eligible employees where required by applicable law
• IBM offers disability benefits to eligible employees where required by applicable law