Second quantization of nonlinear Vlasov-Poisson system for quantum computation

TL;DR

This paper introduces a second quantization approach to linearize and discretize the nonlinear Vlasov-Poisson system, enabling quantum computation to efficiently simulate plasma dynamics with promising scalability.

Contribution

The work develops a second quantization framework for the Vlasov-Poisson equations, establishing conditions for correspondence and demonstrating quantum simulation of nonlinear plasma phenomena.

Findings

Quantum simulations can capture nonlinear plasma dynamics.

Scaling relations suggest efficient quantum computation for these equations.

Numerical results validate the approach's accuracy and potential.

Abstract

The Vlasov-Poisson equations, fundamental in plasma physics and astrophysical applications, are rendered linear, finite-dimensional, and discrete by second quantization. Conditions for correspondence between the pre-quantized and quantized equations are derived, and numerical simulations demonstrating the quantized linear system can capture nonlinear dynamics are presented. Finally, encouraging scaling relations emphasizing the prospect of using quantum computers to efficiently integrate the second quantized Vlasov-Poisson equations as a model for the usual Vlasov-Poisson equations are derived.