Two Dimensional Quantum Walk with Non Hermitian Skin Effects
We construct a two dimensional, discrete time quantum walk exhibiting non Hermitian skin effects under open boundary conditions. As a confirmation of the non Hermitian bulk boundary correspondence, we show that the emergence of topological edge states are consistent with Floquet winding numbers calculated using a non Bloch band theory invoking time dependent generalized Billouin zones. Further, the non Bloch topological invariants associated with the Floquet bands are captured by a non Hermitian local Chern marker in real space, defined through local biorthogonal eigen wave functions of the non unitary Floquet operator. Our work suggests the possibility of directly measuring non Bloch topological invariants in quantum walk dynamics, and would stimulate further studies of non Hermitian Floquet topological phases where skin effects play a key role.