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We study how discrete-time quantum walks behave under short-range correlated noise. By considering noise as a source of inhomogeneity of quantum gates, we introduce a primitive relaxation in the assumption of uncorrelated stochastic noise: binary pair correlations manifesting in the random distribution. Using different quantum gates, we examined the transport properties for both spatial and temporal noise regimes. For spatial inhomogeneities, we unveil noise correlations driving quantum walks from the well-known exponentially localized regime to superdiffusive spreading. This scenario displays an intriguing performance in which the superdiffusive exponent is almost invariant to the degree of inhomogeneity. The time-asymptotic regime and the finite-size scaling also unveil an emergent superdiffusive behavior for quantum walks undergoing temporal noise correlation, replacing the diffusive regime exhibited when noise is random and uncorrelated. However, some quantum gates are insensitive to correlations, contrasting with the spatial noise scenario. Numerical and analytical results provide valuable insights into the underlying mechanism of superdiffusive quantum walks, including those arising from deterministic aperiodic inhomogeneities.
Almeida et al. (Mon,) studied this question.