Work

Solving the nonlinear Vlasov equation on a quantum computer

Year: 2026

Type: article

Abstract: The practical applicability of a recent Carleman-linearization-based quantum algorithm for solving ordinary differential equations (ODEs) with quadratic nonlinearities is investigated for the nonlinear electrostatic Vlasov equation with Krook-type collision operators. The equation is discretized on a (1+1)-dimensional phase-space grid and mapped onto the input of the quantum algorithm. Upper bounds for the query and gate complexities are derived in the limit of large grid sizes and found to be polynomially larger than the time complexity of the corresponding classical algorithms, primarily due to the dimension, sparsity, and norm of the Carleman-linearized evolution matrix. The convergence criteria are shown to impose severe restrictions on physically relevant plasma applications, requiring dissipation levels far exceeding those provided by the Krook operator.

Source: Quantum

DOI: 10.82444/warw.34590471

Authors: Tamás Vaszary, Animesh Datta, Tom Goffrey, Brian Appelbe

Institution: University of Warwick

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $215

Funders: UK Research and Innovation, Engineering and Physical Sciences Research Council