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.
An em- pirical analysis on the effectiveness of the variational quantum linear solver
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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.
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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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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.