QCPIKAN is a quantum-classical physics-informed KAN that claims exponential high-frequency error convergence and superior accuracy over prior QCPINNs on single-phase, transport, and two-phase seepage PDEs.
Bravo-Prieto, R
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The paper proves feasibility of quantum domain decomposition preconditioning for FEM Poisson problems with the two-level Additive Schwarz method, supplies block-encoding bounds, derives quantum solver complexity, and details a BPX local solver choice.
D-VQLS with FWHT Pauli decomposition and 1% thresholding reduces circuit evaluations by 256x for 10-qubit tridiagonal systems while achieving over 99.99% fidelity and near-ideal scaling on up to 96 GPUs.
PDEs are solved by formulating discretized systems as generalized eigenvalue problems and using annealing to optimize the generalized Rayleigh quotient iteratively for eigenvectors.
citing papers explorer
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Quantum-classical physics-informed Kolmogorov-Arnold networks for PDEs
QCPIKAN is a quantum-classical physics-informed KAN that claims exponential high-frequency error convergence and superior accuracy over prior QCPINNs on single-phase, transport, and two-phase seepage PDEs.
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Quantum Domain Decomposition for Preconditioning the Finite Element Method
The paper proves feasibility of quantum domain decomposition preconditioning for FEM Poisson problems with the two-level Additive Schwarz method, supplies block-encoding bounds, derives quantum solver complexity, and details a BPX local solver choice.
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Distributed Variational Quantum Linear Solver
D-VQLS with FWHT Pauli decomposition and 1% thresholding reduces circuit evaluations by 256x for 10-qubit tridiagonal systems while achieving over 99.99% fidelity and near-ideal scaling on up to 96 GPUs.
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Annealing-based approach to solving partial differential equations
PDEs are solved by formulating discretized systems as generalized eigenvalue problems and using annealing to optimize the generalized Rayleigh quotient iteratively for eigenvectors.