Quantum Signal Processing for simulating cold plasma waves

TL;DR

This paper proposes a quantum algorithm using Quantum Signal Processing to simulate cold plasma waves, specifically X waves in inhomogeneous plasma, demonstrating potential for faster plasma modeling on quantum computers.

Contribution

It introduces a quantum algorithm for plasma wave simulation using quantum signal processing and block-encoding, advancing quantum computational methods in plasma physics.

Findings

Quantum circuit simulation agrees with classical calculations.

The method scales with resolution, indicating potential for high-resolution modeling.

Emulation on classical computers validates the quantum approach.

Abstract

Numerical modeling of radio-frequency waves in plasma with sufficiently high spatial and temporal resolution remains challenging even with modern computers. However, such simulations can be sped up using quantum computers in the future. Here, we propose how to do such modeling for cold plasma waves, in particular, for an X wave propagating in an inhomogeneous one-dimensional plasma. The wave system is represented in the form of a vector Schr\"odinger equation with a Hermitian Hamiltonian. Block-encoding is used to represent the Hamiltonian through unitary operations that can be implemented on a quantum computer. To perform the modeling, we apply the so-called Quantum Signal Processing algorithm and construct the corresponding circuit. Quantum simulations with this circuit are emulated on a classical computer, and the results show agreement with traditional classical calculations. We also discuss how our quantum circuit scales with the resolution.