Fig. 7: Favorable resource scaling.
From: Realization of higher-order topological lattices on a quantum computer
Comparison of asymptotic computational time required for the dynamical simulation of d-dimensional, size-L lattice Hamiltonians of similar complexity as our HOT lattices. a With fixed lattice dimension d and increasing lattice size L, the time taken with our approach on a quantum computer (labeled QC) scales with L2, rather than the higher power of L3d through classical ED. b For fixed L and varying d, our approach scales promisingly, scaling like 4d instead of \({({L}^{3})}^{d}\) for ED. We assume conventional Trotterization for circuit construction, and at large L and d, our mapping and quantum simulation approach can provide a resource advantage over classical numerical methods (e.g., ED).
