Research Research Scientist - Quantum Algorithms for Differential Equations Dublin, IE

At IBM Research, we explore what's next in computing to shape the technologies that will power tomorrow. Working in Research means accelerating discovery at the intersection of high performance computing, AI, quantum, and cloud, and turning ideas into reality.

Role and Responsibilities

• Embed nonlinear dynamics into linear (potentially infinite dimensional) systems (e.g., Koopman/Carleman lifts, semigroup formalisms), and
• Encode linear dynamics as efficient quantum circuits for time evolution (e.g., block encodings, qubitization, LCU, QSP/SVT).

You will translate problem formulations (ODEs/PDEs, operator semigroups, discretizations) into query model statements, define oracle and state preparation assumptions, and design fault tolerant compatible circuits with end to end resource estimates. You'll benchmark quantum pipelines against classical baselines under matched accuracy and data loading assumptions.

Key Responsibilities

• Hamiltonian & dissipative simulation: develop and refine end to end time evolution algorithms for sparse Hamiltonians and linear dissipative dynamics (e.g., dissipative perturbations of Hamiltonian flows).
• Block encodings & signal processing: construct block encodings of discretized operators; employ LCU, QSP/SVT, qubitization, and oblivious amplitude amplification for evolution, solvers, and transforms.
• Oracles & data access models: formalize oracle definitions for operator sparsity/structure, boundary conditions, right hand sides/initial data, and state preparation (incl. amplitude encoding and alternatives), articulating QRAM/streaming or other data assumptions.
• Complexity & lower bounds: analyze query and gate complexity, robustness vs. conditioning and precision, and-where appropriate-connect to Hamiltonian complexity and reductions that inform feasibility or limitations.
• Fault tolerant resource estimation: produce qubit/T count/depth estimates under plausible error correction assumptions (e.g., LDPC code parameters, target logical error rates), identify bottlenecks, and pursue complexity and constant factor improvements.
• Benchmarking & validation: establish fair quantum-classical comparisons (accuracy targets, discretization choices, conditioning/preconditioning) and run prototype benchmarks in Python/Qiskit.
• Community engagement: collaborate across quantum information, numerical algorithms, and dynamical systems communities; contribute to working groups, open source artifacts, and publications.

Qualifications

Required education: Doctorate Degree

Required technical and professional expertise:

• Ph.D. (or equivalent research experience) in Quantum Information/Quantum Computing, Quantum Algorithms, Theoretical Computer Science, or a closely related field.
• Demonstrated experience in at least two of:
  • Hamiltonian simulation (sparse or structured), LCU, QSP/SVT, qubitization, block encodings
  • Amplitude amplification/estimation, phase estimation, or quantum linear system methods
  • Query/gate complexity analysis and oracle modeling (data access assumptions, state preparation)
• Proficiency prototyping in Python; experience with Qiskit or willingness to ramp quickly.

Preferred technical and professional experience:

• Publications in quantum algorithms/quantum information or related top tier venues.
• Experience formulating oracles for discretized operators and state preparation pipelines (e.g., for PDE RHS/IC/BC).
• Familiarity with fault tolerant costing (T count/T depth, surface code logical qubits, target logical error budgets) and noise aware considerations for earlier prototypes.
• Comfort engaging with numerical analysis concepts (conditioning, preconditioning, discretization error) sufficient to set fair benchmarks vs. classical methods.
• Hands on with Git/GitHub and collaborative research workflows.
• Experience running quantum demonstrations or building precise classical baselines for comparison.
• Experience contributing to proposals and grants.

IBM is an equal opportunity employer. All qualified applicants will receive consideration for employment without regard to race, color, religion, sex, gender, gender identity or expression, sexual orientation, national origin, genetics, pregnancy, disability, neurodivergence, age, or other characteristics protected by applicable law. IBM is also committed to fair employment practices regarding citizenship and immigration status.