Quantum boundary-value algorithms for linear dissipative waves in dielectric media and kinetic plasmas

Quantum Singular Value Transformation (QSVT) is a state-of-the-art quantum algorithm for solving linear equations, particularly those that involve non-Hermitian matrices. For high-dimensional problems, this algorithm can provide polynomial speedup with respect to the best-known conjugate-gradient-based classical methods. We discuss applications of the QSVT to solving boundary-value problems for stationary waves in inhomogeneous dielectric media and also kinetic electrostatic waves excited by a monochromatic source in inhomogeneous one-dimensional plasma.