Probing coherence and noise tolerance in discrete-time quantum walks: Unveiling self-focusing and breathing dynamics

Abstract

The sensitivity of quantum systems to external disturbances is a fundamental problem for the implementation of functional quantum devices, quantum information, and computation. Based on remarkable experimental progress in optics and ultracold gases, we study the consequences of a short-time (instantaneous) noise while an intensity-dependent phase acquisition is associated with a qubit propagating on an $N$ cycle. By employing quantum coherence measures, we report emerging unstable regimes in which quantum walks arise, such as self-focusing and breathing dynamics. Our numerical and analytical results unveil appropriate settings which favor the stable regime, with the asymptotic distribution surviving for weak nonlinearities and disappearing in the thermodynamic limit with $1/N$. The diagram showing the threshold between different regimes reveals the quantum gates close to Pauli-Z as more noise tolerant. As we move towards the Pauli-X quantum gate, such aptness dramatically decreases and the threshold to the self-focusing regime becomes almost unavoidable. Quantum gates close to Hadamard exhibit an unusual aspect, in which an increment of the nonlinear strength can remove the dynamics from the self-focusing regime.