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We study the response of spreading behavior, of two-dimensional discrete-timequantum walks, to glassy disorder in the jump length. We consider differentdiscrete probability distributions to mimic the disorder, and three types ofcoin operators, viz., Grover, Fourier, and Hadamard, to analyze the scaleexponent of the disorder-averaged spreading. We find that the ballisticspreading of the clean walk is inhibited in presence of disorder, and the walkbecomes sub-ballistic but remains super-diffusive. The resilience todisorder-induced inhibition is stronger in two-dimensional walks, for all theconsidered coin operations, in comparison to the same in one dimension. Thequantum advantage of quantum walks is therefore more secure in two dimensionsthan in one.

Stronger resilience to disorder in 2D quantum walks than in 1D