NVQLS introduces the first hybrid quantum-classical unsupervised operator learning method for parametric PDEs via Legendre-Galerkin weak form, sign ambiguity resolution, and neural embedding.
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Presents LCNU-plus-embedding data loading for any polynomial Carleman-linearized autonomous system and applies it to the 3D LBE, yielding Ns ~ O(α²Q²) terms and explicit T-gate resource estimates for two solvers.
Pauli-structured preconditioning enables regrouped Pauli representations that reduce coefficient weight of the preconditioned operator and alter normalization parameters in quantum linear system solvers.
Hybrid VQLS pipeline with Carleman linearization recovers high-fidelity solutions to the weakly nonlinear Duffing equation on IBM and Xanadu hardware using symmetry-grouped measurements and optimized ansatzes.
citing papers explorer
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Neural Quantum Spectral Operator Learning for Solving Partial Differential Equations
NVQLS introduces the first hybrid quantum-classical unsupervised operator learning method for parametric PDEs via Legendre-Galerkin weak form, sign ambiguity resolution, and neural embedding.
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Quantum Data Loading for Carleman Linearized Systems: Application to the Lattice-Boltzmann Equation
Presents LCNU-plus-embedding data loading for any polynomial Carleman-linearized autonomous system and applies it to the 3D LBE, yielding Ns ~ O(α²Q²) terms and explicit T-gate resource estimates for two solvers.
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Pauli-structured preconditioning for quantum linear system solvers
Pauli-structured preconditioning enables regrouped Pauli representations that reduce coefficient weight of the preconditioned operator and alter normalization parameters in quantum linear system solvers.
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Measurement-Efficient Variational Quantum Linear Solver for Carleman-Linearized Nonlinear Dynamics
Hybrid VQLS pipeline with Carleman linearization recovers high-fidelity solutions to the weakly nonlinear Duffing equation on IBM and Xanadu hardware using symmetry-grouped measurements and optimized ansatzes.