  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 $1\times10^7$ 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 $\chi=\mathcal{O}(\text{poly}(1/\epsilon))$
for the maximum bond dimension $\chi$ of MPS representing turbulent flow
fields, with an error $\epsilon$, based on the spectral distribution of
turbulent kinetic energy. Our findings motivate further exploration of related
quantum algorithms and other tensor network methods.
