Simulations of dissipative electromagnetic waves using quantum singular value transformation

Quantum Singular Value Transformation (QSVT) is a state-of-the-art quantum algorithm for solving linear vector equations of the form Ax = b, including those with non-Hermitian matrices A. We report an application of the QSVT to the modeling of classical electromagnetic waves in a one-dimensional system with outgoing boundary conditions. We show how to encode the corresponding non-Hermitian boundary-value problem into a quantum circuit and also propose how to extract classical information from this circuit using quantum measurements. In particular, we show how the absorption power can be measured using an oracle emulating the electric conductivity. The potential speedup and the drawbacks of QSVT applications to classical waves are also discussed.