A matrix decomposition into linear combinations of non-unitaries produces an LCU for any Carleman-linearized polynomial system and yields an O(α² Q²) term count for the 3D lattice Boltzmann equation independent of spatial or temporal grid points.
Variational quantum algorithms for nonlinear problems
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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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Quantum Data Loading for Carleman Linearized Systems: Application to the Lattice-Boltzmann Equation
A matrix decomposition into linear combinations of non-unitaries produces an LCU for any Carleman-linearized polynomial system and yields an O(α² Q²) term count for the 3D lattice Boltzmann equation independent of spatial or temporal grid points.
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Loss-aware state space geometry for quantum variational algorithms
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.
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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.