Quantum Algorithms for Differential Equations

Partial differential equations govern much of science and engineering, yet high-fidelity simulation of nonlinear systems pushes classical computing to its limits, motivating the search for quantum approaches. In this talk, we give a broad overview of the state of the art and the open challenges in quantum algorithms for differential equations, which span the full end-to-end pipeline: loading classical data into a quantum state, evolving the dynamics in time together with boundary conditions, handling nonlinearity, and reading out the solution.