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.
From the completions in (63) and using rows 1 and 5 from Table II, we find 3X i=1 G[CL1,i] = log ntG[CX ] + G[CS nt +1] = 12 log 2nt
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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.