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arXiv:2608.23127

Efficient Quantum Simulation of Linearized Vlasov--Poisson Dynamics Using Trotter and THRIFT Hamiltonian Simulation Methods

Kartick Paul, Rahul V, S. Aravinda, Reetesh K. Gangwar

quant-phphysics.comp-phphysics.plasm-phSubmitted Aug 24, 2026• Announced Aug 25, 2026• 0 citations• Revised Oct 9, 2026 (v2)

v1 · Aug 24, 2026 v2 · Oct 9, 2026

Abstract

The Vlasov--Poisson system provides the fundamental kinetic description of plasma and plays a central role in understanding collective phenomena such as Landau damping and wave--particle interactions. Efficient numerical simulation of these dynamics remains challenging because of the high dimensionality of phase space. In this work, we studied magnetized and non-magnetized plasma using a quantum simulation framework for the linearized Vlasov-Poisson equation by reformulating the discretized system as a Hermitian Hamiltonian suitable for gate-based quantum computation. The time evolution is implemented using first, second and fourth-order Trotter--Suzuki product formulas and the recently proposed Time-Resolved Interaction Framework (THRIFT). The performance of the different simulation methods is systematically evaluated through electric field evolution, state fidelity, convergence behavior, energy conservation, entanglement entropy and quantum resource requirements, including circuit depth and two-qubit gate complexity, for both magnetized and non-magnetized plasma models. To further reduce finite time step errors without increasing circuit depth, Richardson extrapolation is incorporated as a error-mitigation technique. The results provide a comprehensive comparison of Trotter and THRIFT approaches and establish practical guidelines for accurate and resource-efficient quantum simulation of plasma dynamics on gate-based quantum computers.

Comments: 18 pages,11 figures

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The Vlasov-Maxwell system of equations, which describes classical plasma physics, is extremely challenging to solve, even by numerical simulation on powerful computers. By linearizing and assuming a Maxwellian background distribution function, we convert the Vlasov-Maxwell system into a Hamiltonian simulation problem. Then for the limiting case of electrostatic Landau damping, we design and verify a quantum algorithm, appropriate for a future error-corrected universal quantum computer. While the classical simulation has costs that scale as

O({N}_{v}t)

for a velocity grid with

{N}_{v}

grid points and simulation time

t

, our quantum algorithm scales as $O[\text{polylog}({N}_{v})t/\ensuremath{\delta}]$ where $\ensuremath{\delta}$ is the measurement error, and weaker scalings have been dropped. Extensions, including electromagnetics and higher dimensions, are discussed. A quantum computer could efficiently handle a high-resolution, six-dimensional phase-space grid, but the $1/\ensuremath{\delta}$ cost factor to extract an accurate result remains a difficulty. This paper provides insight into the possibility of someday achieving efficient plasma simulation on a quantum computer.

Quantum computers can efficiently simulate many-body systems. As a widely used Hamiltonian simulation tool, the Trotter-Suzuki scheme splits the evolution into the number of Trotter steps

N

and approximates the evolution of each step by a product of exponentials of each individual term of the total Hamiltonian. The algorithmic error due to the approximation can be reduced by increasing

N

, which however requires a longer circuit and hence inevitably introduces more physical errors. In this work, we first study such a trade-off and numerically find the optimal number of Trotter steps

{N}_{\mathrm{opt}}

given a physical error model in a near-term quantum hardware. Practically, physical errors can be suppressed using recently proposed error mitigation methods. We then extend physical error mitigation methods to suppress the algorithmic error in Hamiltonian simulation. By exploiting the simulation results with different numbers of Trotter steps $N\ensuremath{\le}{N}_{\mathrm{opt}}$, we can infer the exact simulation result within a higher accuracy and hence mitigate algorithmic errors. We numerically test our scheme with a five-qubit system and show significant improvements in the simulation accuracy by applying both physical and algorithmic error mitigations.

We extend the regime of convergence of Carleman-embedded quantum algorithms that solve the Vlasov-Poisson equations from kinetic plasma physics. We establish convergence, using both analytical and numerical lower bounds, for physically reasonable collision frequencies using a Fourier-Hermite expansion of the shifted phase-space distribution function. We also show that for a large class of basis functions, the convergence of the Carleman-embedded Vlasov-Poisson system requires increasing collision frequency strength with velocity resolution. The complexity of the quantum algorithm depends strongly on whether we seek time-averaged or -resolved outputs.