Research Scientist – Quantum Algorithms for Differential Equations

About the role

IBM Research is looking for a Research Scientist to advance quantum algorithms that solve classical differential equations. You will work at the intersection of quantum information, high‑performance computing and algorithmic theory, turning mathematical formulations of ODEs/PDEs into quantum‑ready circuits.

Key responsibilities

• Embed nonlinear dynamics into linear (potentially infinite‑dimensional) systems using Koopman/Carleman lifts and semigroup formalisms.
• Design efficient quantum circuits for time‑evolution of linear dynamics (block‑encodings, qubitization, LCU, QSP/SVT).
• Translate problem statements into query‑model formulations, define oracles and state‑preparation assumptions.
• Develop fault‑tolerant resource estimates (qubits, T‑count, depth) under realistic error‑correction models.
• Benchmark quantum pipelines against classical baselines with matched accuracy and data‑loading assumptions.
• Analyze query and gate complexity, robustness to conditioning, and establish lower bounds where applicable.

Required profile

• Strong background in quantum information theory and quantum algorithms.
• Experience with Hamiltonian and dissipative simulation techniques.
• Ability to formalize oracle models and data‑access assumptions for quantum algorithms.
• Proven research track record in algorithm design and complexity analysis.

Required skills

• Quantum Information
• Quantum Algorithms
• Hamiltonian simulation
• Dissipative dynamics simulation
• Block‑encoding
• Linear Combination of Unitaries (LCU)
• Quantum Signal Processing (QSP) / Singular Value Transformation (SVT)
• Qubitization
• Oblivious amplitude amplification
• Fault‑tolerant resource estimation
• Query‑model formulation
• Oracle definition
• QRAM / streaming data models
• Operator semigroup methods
• Koopman/Carleman lifts
• Sparse Hamiltonians
• Quantum circuit design
• Complexity analysis
• Quantum‑classical benchmarking