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Simulating quantum turbulence with matrix-product states

Felipe Gómez-Lozada1,*, Nicolas Perico-García2, Nikita Gourianov3, Hayder Salman4,5, and Juan José Mendoza-Arenas1,2

  • *Contact author: felipe.gomezlozada@ist.ac.at
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Phys. Rev. Applied 25, 064069 – Published 29 June, 2026

DOI: https://doi.org/10.1103/x5xg-whh1

Abstract

Quantum turbulence spans length scales from the system size L to the healing length ξ, making direct numerical simulations (DNS) of the Gross-Pitaevskii (GP) equation computationally expensive when L≫ξ. We present a matrix-product state (MPS) solver for the GP equation that efficiently compresses the wavefunction by truncating weak interlength-scale correlations. This approach reduces memory usage by factors ranging from 10× to over 10000× compared to DNS. We benchmark our approach on nonlinear excitations, namely dark solitons (1D) and quantized vortices (2D, 3D), capturing key dynamics such as Kelvin-wave propagation and vortex-ring emission in the case of vortex-line reconnection. For turbulent states composed of multiple nonlinear excitations, we find that the memory compression of the MPS representation is directly proportional to the soliton or vortex densities. We also accurately reproduce established results from two-point correlation functions and energy spectra, where we recover the incompressible kinetic energy spectrum with little memory overhead. These results demonstrate the representative capabilities of the MPS ansatz for quantum turbulence and pave the way for studying this nonequilibrium state using previously prohibited system sizes. Moreover, the MPS ansatz can be adapted to existing quantum algorithms, providing a framework to implementing our time-evolution method on near-future quantum processing units.

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Phys. Rev. Applied 25, 064069– Published 29 June, 2026
  • Received 10 September 2025
  • Revised 6 April 2026
  • Accepted 22 April 2026
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