Quantum circuits for coherent multilayer neural network inference achieve quadratic to polylogarithmic speedups over classical methods depending on quantum data access models for inputs and weights.
Ef- ficient quantum algorithm for nonlinear reaction-diffusion equations and energy estima- tion.Communications in Mathematical Physics, 404(2):963–1020
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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.
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Reduced basis algorithm for solving nonlinear differential equations on quantum computers
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.