  We propose a quantum algorithm for simulating dissipative waves in
inhomogeneous linear media as a boundary-value problem. Using the so-called
quantum singular value transformation (QSVT), we construct a quantum circuit
that models the propagation of electromagnetic waves in a one-dimensional
system with outgoing boundary conditions. The corresponding measurement
procedure is also discussed. Limitations of the QSVT algorithm are identified
in connection with the large condition numbers that the dispersion matrices
exhibit at weak dissipation.
