Trainable quantum spectral models with an intermediate parameterized mixer (ε ≈ 0.5) outperform standard variational quantum circuits for PDEs by learning in spectral representation, with HHL-inspired architectures showing fastest convergence.
Variational quantum algorithms for nonlinear problems,
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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.
End-to-end QSP-based quantum circuits solve linear PDEs on IBM hardware with tunable error and handle non-homogeneous Dirichlet boundaries for a plasma Poisson problem.
Loss-aware natural gradient variants are introduced by embedding the loss hypersurface in a statistical manifold or using quantum state overlaps, yielding conformal updates that adjust effective step size.
A survey of variational quantum algorithms, quantum neural networks, and tensor networks for addressing scalability challenges in computational fluid dynamics.
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A review of quantum machine learning and quantum-inspired applied methods to computational fluid dynamics
A survey of variational quantum algorithms, quantum neural networks, and tensor networks for addressing scalability challenges in computational fluid dynamics.