Subspace Methods in Era of Quantum Computing

"I am asking essential questions about the place of classical computing algorithms in light of the quantum supremacy claimed by GOOGLE. GOOGLE claimed they could generate the bonafide quantum states via an iteration of a matrix on a vector. I expect that someday prepared states will be used in another stage of quantum algorithms. However, is there a place for understanding as another tool besides the dominant properties of the oracle? In particular, if one writes down a subspace of active dynamical dimensions with exact quantum operators, could this understanding be faster than state preparation? I have been experimenting with cheaper solutions using a company meerkat (system76) computer. The same algorithm on HPC, which I have time on Lonestar 6, could computer bigger subspaces and more Qbits. In the figure, reporting the timing of ground state computations as a function of Qbit size shows power-law scaling with increasing Qbits. Subspaces dropped into QuTip can achieve fast computation of time dependence with Lindband and dissipation. The limiting factor is the subspace's linear dependence (quality), which has routinely been suitable for other problems. I ask the reader to consider the value of subspace methods irrespective of the quality of my production. Unlike most methods to diagonalize on the market, this method uses forward matrix-vector multiplication on Sums Of Products vector representations. The method was originally designed to work with Coloumb forces on digital lattices. Recent work recognizes the application of classical computation beside quantum computing technologies. Quantum Galaxies Corporation is a startup from Texas Tech University for classical computing based on patents for quantum computing."