Localized State in a Two-Dimensional Quantum Walk on a Disordered   Lattice
  We realize a pair of simultaneous ten-step one-dimensional quantum walks with two walkers sharing coins, which we prove is analogous to the ten-step two-dimensional quantum walk with a single walker holding a four-dimensional coin. Our experiment demonstrates a ten-step quantum walk over an 11x11 two-dimensional lattice with a line defect, thereby realizing a localized walker state. 
Peng Xue, Rong Zhang, Zhihao Bian, Xian Zhan, Hao Qin, and Barry C.   Sanders
quant-ph