The reduced basis algorithm exactly reproduces the nonlinear dynamics of polynomial ODEs and PDEs over m timesteps using a linear quantum operator on a reduced monomial basis, with qubit scaling logarithmic in grid size for PDEs.
Towards simulating fluid flows with quantum computing,
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Second-order Carleman linearization recovers steady-state solutions for low-Re fluid flows, proved analytically for a logistic model and shown numerically for 2D Kolmogorov flow below Re ~10.
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Lowest order Carleman linearization for low Reynolds long-term behaviour of fluid flow simulations
Second-order Carleman linearization recovers steady-state solutions for low-Re fluid flows, proved analytically for a logistic model and shown numerically for 2D Kolmogorov flow below Re ~10.