Quantum Algorithms Intern: Differential Equations

IBM; Dublin; Hybrid; EUR 17,000 - 23,000; Part time

Job summary

IBM Ireland Limited invites a PhD-level intern to design and analyze quantum algorithms for differential equations. You will embed differential operators into quantum-ready forms and benchmark against classical methods, working across dynamical systems and numerical linear algebra to drive breakthroughs.

Preferred background includes PDE/ODE theory, numerical analysis, and experience with Python and Qiskit. Hybrid work arrangement with mentorship from IBM Research scientists is offered.

Qualifications

• Deep research background in applied mathematics or related fields.
• Experience with differential equations and operator-theoretic methods.
• Prototyping in Python and interest in quantum frameworks (Qiskit).

Responsibilities

• Time-evolution & simulation: develop end-to-end quantum time-evolution algorithms for sparse Hamiltonians and dissipative dynamics.
• Operator embeddings: design embeddings of differential operators into block-encodings and QSP/LCU forms.
• Numerics-aware design: connect discretization choices to quantum complexity and study conditioning and error propagation.
• Resource estimation: perform query complexity, qubits, T-depth, and budgets; identify bottlenecks and improvements.
• Benchmarking: compare quantum pipelines to classical baselines using reasonable accuracy criteria.
• Community engagement: collaborate across dynamical systems, numerical linear algebra, and quantum computing groups.

Skills

Applied Mathematics

Quantum Algorithms

Python (NumPy/SciPy/Matplotlib)

Differential Equations

Education

Doctorate Degree

Tools

Qiskit

Python (NumPy/SciPy/Matplotlib)

Job description

IBM Ireland Limited invites a PhD-level intern to design and analyze quantum algorithms for differential equations. You will embed differential operators into quantum-ready forms and benchmark against classical methods, working across dynamical systems and numerical linear algebra to drive breakthroughs.

Preferred background includes PDE/ODE theory, numerical analysis, and experience with Python and Qiskit. Hybrid work arrangement with mentorship from IBM Research scientists is offered.