Research Internship: Quantum Computing & AI for PDEs

Research Internship: Quantum Computing and AI for Partial Differential Equations 2027

The Algorithms and Applications for PDEs team focuses on the paradigm of quantum centric supercomputing. The idea is to combine the state of the art in quantum computing, AI, and conventional numerics to achieve breakthrough performance gains for forward and inverse problems involving PDEs. Our global team actively works on quantum solvers, neural operators, and data assimilation methods, with a particular focus on workflows and algorithms that bridge computational paradigms.

Partial differential equations appear throughout scientific and industrial problems. The study of forward and inverse problems has been a cornerstone of scientific computing from its earliest days. While this has led to a rich landscape of powerful numerical methods and tools, many challenges remain, especially where scaling limits are encountered or underlying dynamics are not fully known. The AI revolutions of the 2010s and 2020s started addressing these challenges. In some domains, data-driven solvers match or surpass the performance of conventional approaches, often while running on a smaller computational footprint. Quantum methods, with their exponential state spaces and scaling advantages, hold the promise of much more rapid advances. Unlocking this promise requires addressing questions such as state preparation and read-out, to name just two.

Bridging these gaps is at the heart of our team's research. By combining expertise in scientific computing, machine learning, and quantum algorithms, we develop workflows that leverage the strengths of each paradigm and investigate their potential for real-world PDE applications.

Your Role

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 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 includes participating in journal clubs and preparing reports, as well as interacting with interns and researchers from other groups across IBM Research in general and the Yorktown lab in particular.

Required Technical and Professional Expertise

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

Preferred Technical and Professional Expertise

At least one of the following:

• Research experience in applied mathematics, particularly 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.

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 with 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.