As a discrete-time quantum walk model on the one-dimensional integer lattice Z,
the quantum walk recently constructed byWang and Ye [CaishiWang and Xiaojuan Ye, Quantum
walk in terms of quantum Bernoulli noises, Quantum Information Processing 15 (2016), 1897–1908]
exhibits quite different features. In this paper, we extend this walk to a higher dimensional case.
More precisely, for a general positive integer d ≥ 2, by using quantum Bernoulli noises we introduce
a model of discrete-time quantum walk on the d-dimensional integer lattice Z^d, which we call
the d-dimensional QBN walk. The d-dimensional QBN walk shares the same coin space with the
quantum walk constructed by Wang and Ye, although it is a higher dimensional extension of the
latter. Moreover we prove that, for a range of choices of its initial state, the d-dimensional QBN walk
has a limit probability distribution of d-dimensional standard Gauss type, which is in sharp contrast
with the case of the usual higher dimensional quantum walks. Some other results are also obtained.