Solving Wave Equations on Quantum Computers

I will discuss quantum algorithms for simulating classical wave propagation that achieve superquadratic speedup in the case of three dimensions. These algorithms are based on reductions to Hamiltonian simulation and can be generalized to simulate Maxwell’s equations and the Klein-Gordon equation. I will discuss the quantum algorithms, some concrete estimates on the number of qubits and gates needed for solving problems in the regime that might be challenging for classical supercomputers, and some complexity-theoretic barriers against certain generalizations.