Research internship Quantum computing and AI for partial differential equations 2027

IBM

Town of Yorktown (NY)

On-site

USD 89,000 - 164,000

Full time

3 days ago

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Job summary

IBM Research Yorktown Heights invites applications for a Research internship focused on quantum computing and AI for partial differential equations. You will contribute to the development and validation of solvers, with emphasis on cross-domain workflows across quantum, AI, and numerics.

The role suits candidates with a strong PDE background, statistical foundation, and experience prototyping in Python. Collaborations with interns and researchers across IBM Research are expected in a dynamic

Qualifications

Working understanding of PDEs from theory or applications.
Elementary statistics.
Proven experience prototyping in Python (NumPy).
At least one of: research in applied mathematics, AI models for PDEs, or quantum computing.

Responsibilities

Contribute to algorithm and model development, experimentation and validation.
Prototype quantum solvers, train AI models, or develop cross-platform workflows.
Collaborate with IBM Research Yorktown lab and mentor interns.

Skills

PDE knowledge

Statistics

Python prototyping

Education

Bachelor's Degree

Master's Degree

Tools

Python (numpy)

Quantum computing basics

Job description

Introduction

The Algorithms and Applications for PDEs team focusses on the paradigm of quantum centric supercomputing. Here, the idea is to mix and match the state of the art in all three areas -- quantum computing, AI and conventional numerics -- to yield breakthrough performance increases for forward and inverse problems for 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, there are still many challenges -- in particular where scaling limits are encountered or underlying dynamics not fully known. The AI revolutions of the 2010s and 2020s started addressing these challenges. In some domains, data-driven solvers equal or surpass the performance of conventional approaches, frequently while running on an arguably smaller computational footprint. Quantum methods with their exponential state spaces and scaling advantages hold the tantalizing promise of much more rapid advances. Yet 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 and responsibilities

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.

Required education

Bachelor's Degree

Preferred education

Master's Degree

Required technical and professional expertise

All of:

Working understanding of partial differential equations -- from a theoretical or application-oriented perspective.
Elementary statistics.
Proven experience prototyping in python (numpy).

At least one of:

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.

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 engineerins skills.
Publication record.

ABOUT BUSINESS UNIT

IBM Research is the organic growth engine of IBM and an innovation engine for our customers and partners. As part of this mission, IBM Research anticipates and examines 'What's Next in Computing' to ultimately create and integrate the technologies the world relies upon to solve big challenges and unlock new opportunities. We create and pioneer new markets for IBM, our partners and customers as exemplified in our ongoing quest to reach practical and large-scale quantum computing. Across IBM Research, we realize the power and potential to accelerate discovery with our partners and clients by combining the power of high performance computing, AI, and Quantum, all integrated through the hybrid cloud.

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OTHER RELEVANT JOB DETAILS

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

This position was posted on the date cited in the key job details section and is anticipated to remain posted for 15 days from this date or less if not needed to fill the role.

We consider qualified applicants with criminal histories, consistent with applicable law.

The compensation range and benefits for this position are based on a full‑time schedule for a full calendar year. The salary will vary depending on your job‑related skills, experience and location. Pay increment and frequency of pay will be in accordance with employment classification and applicable laws. For part time roles, your compensation and benefits will be adjusted to reflect your hours. Benefits may be pro‑rated for those who start working during the calendar year.

Job Title

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

Date posted

18-Sep-2026

Job ID

133430

City / Township / Village

Yorktown Heights

State / Province

New York

Country

United States