Research Scientist - Quantum Algorithms for Differential Equations

Research Scientist - Quantum Algorithms for Differential Equations

IBM

Dublin, Ireland

Your role and responsibilities

IBM Research is seeking a Research Scientist with a strong background in Quantum Information and Quantum Algorithms to design and analyze algorithms for solving classical differential equations on quantum computers. The role focuses on:

• Embedding nonlinear dynamics into linear—potentially infinite-dimensional—systems (e.g., Koopman/Carleman lifts, semigroup formalisms); and
• Encoding 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 include:

• Hamiltonian & dissipative simulation: Develop and refine end-to-end time-evolution algorithms for s‑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.

Required technical and professional expertise

• PhD (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 (s‑sparse or structured cases), LCU, QSP/SVT, qubitization, block-encodings;
  • Amplitude amplification/estimation, phase estimation, or quantum linear systems methods;
  • Query/gate complexity analysis and oracle modeling (data access assumptions, state prep).
• 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-awareconsiderations 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.