Research Scientist – Quantum Algorithms for Differential Equations

At IBM Research, we are the innovation engine of IBM. Exploring what’s next in computing and shaping the technologies the world will rely on tomorrow. From advancing AI and hybrid cloud to pioneering practical quantum computing, we anticipate challenges and unlock new opportunities for clients, partners, and society. Working in Research means joining a team that accelerates discovery at the intersection of high-performance computing, AI, quantum, and cloud. You’ll collaborate with leading scientists, engineers, and visionaries to push boundaries and turn ideas into reality. With a culture built on curiosity, creativity, and collaboration, IBM Research offers the opportunity to grow your career while contributing to breakthroughs that transform industries and change the world.

Your role and responsibilities

IBM Research is seeking aResearch Scientistwith a strong background inQuantum Information and Quantum Algorithmsto design and analyze algorithms for solvingclassical 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 circuitsfor time evolution (e.g., block-encodings, qubitization, LCU, QSP/SVT).

You will translate problem formulations (ODEs/PDEs, operator semigroups, discretizations) intoquery-model statements, defineoracle and state-preparation assumptions, and designfault-tolerant-compatiblecircuits with end-to-endresource estimates. You’ll benchmark quantum pipelines against classical baselines under matched accuracy and data-loading assumptions.

Key responsibilities include:

• Hamiltonian & dissipative simulation:Develop and refineend-to-end time-evolution algorithmsfors‑sparseHamiltonians andlinear dissipative dynamics(e.g., dissipative perturbations of Hamiltonian flows).
• Block-encodings & signal processing:Constructblock-encodingsof discretized operators; employLCU,QSP/SVT,qubitization, andoblivious amplitude amplificationfor evolution, solvers, and transforms.
• Oracles & data access models:Formalizeoracle definitionsfor operator sparsity/structure, boundary conditions, right-hand sides/initial data, andstate preparation(incl. amplitude encoding and alternatives), articulatingQRAM/streamingor other data assumptions.
• Complexity & lower bounds:Analyzequery and gate complexity, robustness vs.conditioning and precision, and—where appropriate—connect toHamiltonian complexityand reductions that inform feasibility or limitations.
• Fault-tolerant resource estimation:Produce qubit/T-count/depth estimates under plausibleerror-correctionassumptions (e.g., LDPC code parameters, target logical error rates), identify bottlenecks, and pursuecomplexity and constant-factor improvements.
• Benchmarking & validation:Establish fairquantum–classical comparisons(accuracy targets, discretization choices, conditioning/preconditioning) and run prototype benchmarks inPython/Qiskit.
• Community engagement:Collaborate across quantum information, numerical algorithms, and dynamical systems communities; contribute to working groups, open-source artifacts, and publications.

Location:Dublin, Ireland (primary, for EU candidates)
Check you match the skill requirements for this role, as well as associated experience, then apply with your CV below.
Note:Exceptional US candidates may be considered for roles at select US IBM Research locations.

Required education

Doctorate Degree

Preferred education

Doctorate Degree

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, orquantum linear systemsmethods
  • Query/gate complexityanalysis and oracle modeling (data access assumptions, state prep)
• Proficiency prototyping inPython; experience withQiskitor willingness to ramp quickly.

• 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.

IBM Research is the organic growth engine of IBM and an innovation engine for our customers and partners. As part of this mission, IBM Research anticipates and examines 'What's Next in Computing' to ultimately create and integrate the technologies the world relies upon to solve big challenges and unlock new opportunities. We create and pioneer new markets for IBM, our partners and customers as exemplified in our ongoing quest to reach practical and large-scale quantum computing. Across IBM Research, we realize the power and potential to accelerate discovery with our partners and clients by combining the power of high performance computing, AI, and Quantum, all integrated through the hybrid cloud.

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For additional information about location requirements, please discuss with the recruiter following submission of your application. xcfaprz

Job Title

Research Scientist – Quantum Algorithms for Differential Equations

Job ID

97419

City / Township / Village

Dublin

State / Province

Dublin

Country

Ireland

Work arrangement

Onsite

Area of work

Research

Employment type

Regular

Position type

Professional

Some travel may be required based on business demand

Company

(0066) IBM Ireland Limited

Shift

General (daytime)

Is this role a commissionable/sales incentive based position?