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 ultra-cold gases, we study the consequences of a short-time (instantaneous) noise while an intensity-dependent phase acquisition is associated with a qubit propagating on N -cycle. By employing quantum coherence measures, we report emerging unstable regimes in which hitherto unknown quantum walks arise, such as self-focusing and breathing dynamics. Our 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 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 self-focusing regime.

Asymptotic stability of small bound state of nonlinear quantum walks

“…The importance of solitons can also be seen by soliton resolution conjecture [58], which claims generic solutions decouple into scattering waves and solitons, as in RAGE theorem for the linear case [20,51]. Indeed, many papers studying nonlinear QWs numerically observe solitonic behavior of the solution and focus on the study of its dynamics [8,9,17,34,37,45,63]. For the stability analysis of bound states, related to the study of topological phases [3,4,10,11,28,29,40,60,61,62], Gerasimenko, Tarasinski, and Beenakker [22], followed by Mochizuki, Kawakami and Obuse [44] studied the linear stability of bound states bifurcating from linear bound states.…”