A reformulation of geometrical optics using ray time and ray energy as canonical coordinates, with an Airy transform connecting the two phase spaces, yields nonsingular envelope equations near reflection points.
Simulation of linear non-Hermitian boundary-value problems with quantum singular value transformation
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abstract
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.
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Geometrical optics in phase space
A reformulation of geometrical optics using ray time and ray energy as canonical coordinates, with an Airy transform connecting the two phase spaces, yields nonsingular envelope equations near reflection points.