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@ARTICLE{Hlscher:1038624,
      author       = {Hölscher, Leonhard and Rao, Pooja and Müller, Lukas and
                      Klepsch, Johannes and Luckow, Andre and Stollenwerk, Tobias
                      and Wilhelm, Frank K.},
      title        = {{Q}uantum-inspired fluid simulation of two-dimensional
                      turbulence with {GPU} acceleration},
      journal      = {Physical review research},
      volume       = {7},
      number       = {1},
      issn         = {2643-1564},
      address      = {College Park, MD},
      publisher    = {APS},
      reportid     = {FZJ-2025-01595},
      pages        = {013112},
      year         = {2025},
      abstract     = {Tensor network algorithms can efficiently simulate complex
                      quantum many-body systems by utilizing knowledge of their
                      structure and entanglement. These methodologies have been
                      adapted recently for solving the Navier-Stokes equations,
                      which describe a spectrum of fluid phenomena, from the
                      aerodynamics of vehicles to weather patterns. Within this
                      quantum-inspired paradigm, velocity is encoded as matrix
                      product states (MPS), effectively harnessing the analogy
                      between interscale correlations of fluid dynamics and
                      entanglement in quantum many-body physics. This particular
                      tensor structure is also called quantics tensor train (QTT).
                      By utilizing NVIDIA's cuQuantum library to perform parallel
                      tensor computations on GPUs, our adaptation speeds up
                      simulations by up to 12.1 times. This allows us to study the
                      algorithm in terms of its applicability, scalability, and
                      performance. By simulating two qualitatively different but
                      commonly encountered 2D flow problems at high Reynolds
                      numbers up to 1×107 using a fourth-order time stepping
                      scheme, we find that the algorithm has a potential advantage
                      over direct numerical simulations in the turbulent regime as
                      the requirements for grid resolution increase drastically.
                      In addition, we derive the scaling
                      𝜒=𝒪⁡(poly⁡(1/𝜀)) for the maximum bond dimension
                      𝜒 of MPS representing turbulent flow fields, with an
                      error 𝜀, based on the spectral distribution of turbulent
                      kinetic energy. Our findings motivate further exploration of
                      related quantum algorithms and other tensor network
                      methods.},
      cin          = {PGI-12},
      ddc          = {530},
      cid          = {I:(DE-Juel1)PGI-12-20200716},
      pnm          = {5221 - Advanced Solid-State Qubits and Qubit Systems
                      (POF4-522)},
      pid          = {G:(DE-HGF)POF4-5221},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:001415898000002},
      doi          = {10.1103/PhysRevResearch.7.013112},
      url          = {https://juser.fz-juelich.de/record/1038624},
}