Second quantization of nonlinear Vlasov-Poisson system for quantum computation

2025/06/02 by Michael Q. May, Hong Qin, May, Michael Q. +1 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Advanced Fiber Laser Technologies #FOS: Physical sciences #Photonic and Optical Devices #Plasma Physics (physics.plasm-ph) #Quantum Information and Cryptography #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2506.01895

openalex publication_date 2025/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Citations

• Quantum Calculation for Two-Stream Instability and Advection Test of Vlasov-Maxwell Equations: Numerical Evaluation of Hamiltonian Simulation
• From Vlasov-Poisson to Schrödinger-Poisson: dark matter simulation with a quantum variational time evolution algorithm
• Hamiltonian simulation using quantum singular value transformation: complexity analysis and application to the linearized Vlasov-Poisson equation
• Improved quantum algorithms for linear and nonlinear differential equations
• Quantum algorithm for nonlinear differential equations
• Plasma Physics in Strong Field Regimes

Cited by

• Trotter-based quantum algorithm for solving transport equations with exponentially fewer time-steps

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