Fig. 6: Quantum processor measurements of robustness from HOT edge (or hinge) modes on a 4D tesseract lattice.
From: Realization of higher-order topological lattices on a quantum computer
Our mapping facilitates the realization of any desired HOT modes, beyond the aforementioned corner mode examples. The header row on the left displays the energy spectrum for a configuration of the tesseract harboring topologically non-trivial edges (midgap mode energies in black). Accompanying schematic highlights alternating sites with topological edge wavefunction support. Subsequent columns present site-resolved occupancy density ρ(x, y, z, w) for a 6 × 6 × 6 × 6 lattice mapped onto a 24-qubit chain, measured on quantum hardware at t = 0 (first row) and final simulation time t = 0.6 (second row), for three different experiments. a A corner-localized state along a topological edge is robust, compared to one along a non-topological edge. b On a topologically non-trivial edge, a state localized on a site with topological wavefunction support is robust, compared to one localized on a site without support. c A surface-localized state far away from the topological edges diffuses into a large occupancy cloud. The bottom leftmost summarizes occupancy fidelities for the various initial states, obtained from ED and hardware (labeled HW). Error bars represent standard deviation across repetitions on different qubit chains and devices.
