Research Scientist – Quantum Algorithms for Differential Equations

About the Role

Join IBM Research in Dublin, part of the global innovation hub advancing AI, hybrid cloud, and practical quantum computing. As a Research Scientist specializing in Quantum Information and Quantum Algorithms, you will focus on developing quantum algorithms to solve classical differential equations, including ordinary and partial differential equations.

Key Responsibilities

• Embed nonlinear dynamics into linear frameworks using techniques such as Koopman or Carleman lifts and semigroup formalisms.
• Translate dynamics into efficient quantum circuits for time evolution leveraging methods like block-encodings, qubitization, linear combination of unitaries (LCU), and quantum signal processing (QSP)/singular value transformation (SVT).
• Formulate problem statements into quantum query models, design oracle and state-preparation assumptions, and create fault-tolerant compatible circuit implementations with resource estimates.
• Develop and refine time-evolution algorithms for sparse Hamiltonians and dissipative linear systems.
• Build block-encodings of discretized operators and use advanced quantum algorithmic tools including amplitude amplification and oblivious amplitude amplification for simulation and transformation tasks.
• Define oracle models for operator sparsity, boundary conditions, initial data, and state preparation considering different data-loading approaches such as QRAM or streaming.
• Conduct rigorous analyses of query complexity, gate complexity, and robustness, relating to algorithm feasibility and computational lower bounds.
• Estimate quantum resource costs including qubit counts, T-gate counts, and circuit depths within plausible error-correction frameworks like low-density parity check (LDPC) codes.
• Perform benchmarking against classical approaches, ensuring fair comparisons on accuracy, conditioning, and data assumptions using Python and Qiskit prototypes.
• Engage with the quantum information, numerical algorithms, and dynamical systems communities through collaboration, contributions to open-source projects, working groups, and scientific publications.

Qualifications and Experience

• PhD or equivalent research experience in Quantum Information, Quantum Computing, Quantum Algorithms, Theoretical Computer Science, or related disciplines.
• Demonstrated expertise in at least two of the following: Hamiltonian simulation (sparse/structured), LCU, QSP/SVT, qubitization, block-encodings.
• Experience with amplitude amplification or estimation, phase estimation, or quantum linear system algorithms.
• Strong background in query and gate complexity analysis and oracle modeling including state preparation and data access assumptions.
• Proficiency in Python programming and experience or readiness to work with Qiskit.

Preferred Skills and Experience

• Published research in quantum algorithms or quantum information in reputed journals or conferences.
• Practice in designing oracles for discretized operators and pipelines for state preparation of PDEs initial and boundary conditions.
• Knowledge of fault-tolerant quantum resource costing including T-gate metrics and error budget management.
• Understanding of numerical analysis principles related to conditioning, preconditioning, and discretization errors to benchmark against classical methods.
• Familiarity with collaborative research tools such as GitHub.
• Experience conducting quantum demonstrations or developing accurate classical baselines.
• Contributions to research proposals and grant writing.

Location

This role is based in Dublin, Ireland primarily for EU candidates. Exceptional candidates from the US might be considered for other IBM Research locations within the United States.