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.
A Linear Combination of Unitaries Decomposition for the Laplace Operator
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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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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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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.