Simulation of linear non-Hermitian boundary-value problems with quantum singular value transformation

TL;DR

This paper introduces a quantum algorithm based on quantum singular value transformation to simulate dissipative electromagnetic waves in one-dimensional media, addressing boundary-value problems with outgoing conditions.

Contribution

The work develops a novel quantum circuit for boundary-value wave simulation using QSVT, highlighting its potential and limitations in modeling dissipative systems.

Findings

Quantum circuit models wave propagation with outgoing boundary conditions.

Limitations arise due to large condition numbers in dispersion matrices.

The measurement procedures for the quantum simulation are discussed.

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.