Caminhadas quânticas em tempo discreto sob influência de ruído correlacionado

Abstract

Quantum walks on a lattice have been indicated as a powerful platform for the development of quantum algorithms, offering a versatile and intuitive frame- work for executing any quantum computations. Furthermore, quantum walks have been shown ideal testbeds for investigating and exploring quantum systems. Consequently, the design and control of quantum processes for long-time dynamics represent a fundamental challenge that demands a thorough comprehension. The presence of quantum noises poses a significant obstacle to enhancing the performance of quantum computing, as they can disrupt a crucial element: the fragile quantum state of qubits. Prior studies have demonstrated that stochastic noise can induce either walker localization or diffusive behavior, depending on whether the noise is spatial or temporal in nature. Here, we study how discrete- time quatum 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 assuption: binary pair correla- tions manifesting in the random distribution. The transport properties for both spatial and temporal noise regimes were examined, taking into account different quantum gates. For spatial inhomogeneities, we show noise correlations driving quantum walks from the well-known exponentially localized regime (stochastic and uncorrelated noise) to superdiffusive spreading. This scenario display an interesting performance, in which the superdiffusive exponent is almost invariant to the inhomogeneity degree. Both the time-asymptotic regime and the finite-size scaling unveilan emergent superdiffusive behavior also for quantum walks undergoing temporal noise correlation, replacing the diffusive regime ex- hibited when noise is random and uncorrelated. However, results report some quantum gates insensitive to correlations, contrasting with the spatial noise scenario. Outcomes and discussions help us understand the underlying mechanism behind superdiffusive quantum walks, including those with deterministic aperiodic inhomogeneities.