Research Internship: Quantum Computing and AI for Partial Differential Equations (2027) – IBM Research

Team & Research Overview

Role & Responsibilities

• Algorithm & Model Development: Design, prototype, and validate algorithms across quantum PDE solvers, neural operators, and hybrid computational paradigms.
• Cross-Platform Workflows: Implement and benchmark workflows combining classical numerical linear algebra, data assimilation, AI surrogate models, and quantum algorithms.
• Prototyping & Experimentation: Write clean, modular experimental code in Python (NumPy, PyTorch/SciPy) to test theoretical scaling advantages against classical baselines.
• Research Dissemination: Contribute to lab-wide discourse, present at journal clubs, author technical reports, and collaborate with researchers and fellow interns across the Thomas J. Watson Research Center.

Qualification Requirements

Required Technical Expertise (All Required)

• Partial Differential Equations: Solid theoretical or applied understanding of PDEs (forward/inverse problem formulations).
• Mathematics & Statistics: Foundational understanding of elementary statistics and probability.
• Python Prototyping: Proven experience prototyping numerical or scientific algorithms in Python (NumPy).
• Domain Focus (At least ONE required):
  • Research experience in applied mathematics (differential equations, operator-theoretic methods, or large-scale numerical linear algebra).
  • Research experience in AI models applied to PDEs (e.g., Fourier Neural Operators, Physics-Informed Neural Networks).
  • Research experience in quantum computing algorithms and quantum information.

Preferred Experience & Tooling (One or More)

• Quantum Algorithms: Hamiltonian simulation, Linear Combinations of Unitaries (LCU), Quantum Signal Processing / Singular Value Transformation (QSP/SVT), Qubitization, Block-Encodings, Amplitude Amplification/Estimation, Quantum Phase Estimation, or Quantum Linear Systems Algorithms (HHL/Childs et al.).
• Data Assimilation: Variational data assimilation (3D-Var, 4D-Var), Kalman filtering, or AI-driven score-based data assimilation.
• AI & Operator Learning: Neural operators (FNO, DeepONet) and deep learning for physics-informed inverse problems.
• Numerical Methods: Discretisation (FEM, FDM, Spectral methods), iterative solvers (CG, GMRES, Multigrid), and preconditioning/conditioning analysis.
• Model Order Reduction: Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DMD), Balanced Truncation, or Koopman/Carleman embeddings.
• Publication Track Record: Proven track record of scientific peer-reviewed publications in machine learning, quantum computing, or computational physics.

Role Summary