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Potential quantum advantage for simulation of fluid dynamics

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arxiv 2303.16550 v3 pith:HR3HGFE5 submitted 2023-03-29 quant-ph physics.ao-phphysics.flu-dyn

classification quant-phphysics.ao-phphysics.flu-dyn
keywords quantumdynamicsevidencefluidsimulatingachievedadvantageboltzmann
verification ladder T0 review T1 audit T2 compute T3 formal
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Numerical simulation of turbulent fluid dynamics needs to either parameterize turbulence-which introduces large uncertainties-or explicitly resolve the smallest scales-which is prohibitively expensive. Here we provide evidence through analytic bounds and numerical studies that a potential quantum exponential speedup can be achieved to simulate the Navier-Stokes equations governing turbulence using quantum computing. Specifically, we provide a formulation of the lattice Boltzmann equation for which we give evidence that low-order Carleman linearization is much more accurate than previously believed for these systems and that for computationally interesting examples. This is achieved via a combination of reformulating the nonlinearity and accurately linearizing the dynamical equations, effectively trading nonlinearity for additional degrees of freedom that add negligible expense in the quantum solver. Based on this we apply a quantum algorithm for simulating the Carleman-linearized lattice Boltzmann equation and provide evidence that its cost scales logarithmically with system size, compared to polynomial scaling in the best known classical algorithms. This work suggests that an exponential quantum advantage may exist for simulating fluid dynamics, paving the way for simulating nonlinear multiscale transport phenomena in a wide range of disciplines using quantum computing.

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  1. Opportunities and challenges of quantum computing for climate modelling

    quant-ph 2025-02 unverdicted novelty 4.0 of 10

    This position paper maps quantum algorithms to four climate modeling tasks and concludes that near-term QML parameterizations are promising but computationally prohibitive at scale.

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