A new LCNU-to-LCU decomposition enables a generalized quantum framework for Carleman-linearized polynomial systems like the lattice Boltzmann equation, with Ns scaling as O(α² Q²) independent of spatial and temporal discretization 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.
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Quantum Data Loading for Carleman Linearized Systems: Application to the Lattice-Boltzmann Equation
A new LCNU-to-LCU decomposition enables a generalized quantum framework for Carleman-linearized polynomial systems like the lattice Boltzmann equation, with Ns scaling as O(α² Q²) independent of spatial and temporal discretization 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.