Step-dependent quantum walks on odd and even cyclic graphs produce gapped and gapless topological phases, rotationally symmetric flat bands in 4n-site graphs, and robust edge states at phase interfaces.
,Experimental two-dimensional quan- tum walk on a photonic chip, SCIENCE ADVANCES 4, eaat3174 (2018)
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Quantum walks reveal topological flat bands, robust edge states and topological phase transitions in cyclic graphs
Step-dependent quantum walks on odd and even cyclic graphs produce gapped and gapless topological phases, rotationally symmetric flat bands in 4n-site graphs, and robust edge states at phase interfaces.