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

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.

References in corpus (3)

• Quantum algorithm for solving linear systems of equations
• Time complexity analysis of quantum difference methods for linear high dimensional and multiscale partial differential equations
• Quantum Signal Processing for simulating cold plasma waves

Cited by in corpus (6)

• Quantum algorithm for the advection-diffusion equation and the Koopman-von Neumann approach to nonlinear dynamical systems
• Quantum Computing Perspective for Electromagnetic Wave Propagation in Cold Magnetized Plasmas
• Encoding of linear kinetic plasma problems in quantum circuits via data compression
• Estimating QSVT angles for matrix inversion with large condition numbers
• Simulating plasma wave propagation on a superconducting quantum chip
• An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations