Solving the Nonlinear Vlasov Equation on a Quantum Computer
Year: 2024
Type: article
Abstract: We present a mapping of the nonlinear, electrostatic Vlasov equation with Krook type collision operators, discretized on a (1+1) dimensional grid, onto a recent Carleman linearization based quantum algorithm for solving ordinary differential equations (ODEs) with quadratic nonlinearities. We show that the quantum algorithm is guaranteed to converge only when the plasma parameters take unphysical values. This is due to the high level of dissipation in the ODE system required for convergence, that far exceeds the physical dissipation effect provided by the Krook operator. Additionally, we derive upper bounds for the query- and gate complexities of the quantum algorithm in the limit of large grid sizes. We conclude that these are polynomially larger than the time complexity of the corresponding classical algorithms. We find that this is mostly due to the dimension, sparsity and norm of the Carleman linearized evolution matrix.
Author: Vaszary, Tamas
Institution: University of Oxford
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6911684896
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