Noise correlations behind superdiffusive quantum walks

TL;DR

This paper investigates how short-range correlated noise affects quantum walks, revealing that noise correlations can induce superdiffusive spreading and alter transport regimes, with implications for understanding quantum transport in noisy environments.

Contribution

It introduces a model of correlated noise in quantum walks, demonstrating how spatial and temporal correlations lead to superdiffusive behavior, a novel insight compared to uncorrelated noise models.

Findings

Noise correlations induce superdiffusive spreading in quantum walks.

Spatial inhomogeneities can transition quantum walks from localization to superdiffusion.

Temporal correlations can replace diffusive regimes with superdiffusive behavior.

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 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.