Noise correlations behind superdiffusive quantum walks

Abstract: 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 uncorrelated stochastic noise assumption: binary pair correlations manifesting in the random distribution. Considering different quantum gates, we examined the transport properties for both spatial and temporal noise regimes. For spatial inhomogeneities, we show noise correlations driving quantum walks from the well-known exponentially localized condition to superdiffusive spreading. This scenario displays an exciting performance in which the superdiffusive exponent is almost invariant to the inhomogeneity degree. 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, results report some quantum gates insensitive to correlations, contrasting with the spatial noise scenario. Results and following discussions help us understand the underlying mechanism of superdiffusive quantum walks, including those with deterministic aperiodic inhomogeneities.