Edge states in a two-dimensional quantum walk with disorder

Abstract

Abstract. We investigate the effect of spatial disorder on the edge states localized at the interface between two topologically different regions. Rotation disorder can localize the quantum walk if it is strong enough to change the topology, otherwise the edge state is protected. Nonlinear spatial disorder, dependent on the walker's state, attracts the walk to the interface even for very large coupling, preserving the ballistic transport characteristic of the clean regime.

Entanglement and interaction in a topological quantum walk

“…The exponent depends in general on the interaction strength α = α(φ), vanishing for φ = 0. The self-similar form (25) is borrowed from the one particle quantum walk, for which the ballistic law xt applies [2,35]; this is certainly appropriated when the probability distribution is dominated by the motion of the bounded state of the two particles, and then we have an effective one particle walk, or in the other limit, when there is repulsion (as in the antisymmetric case) and the two particles are almost independent. The fact that the characteristic exponent varies with the interaction can be related to the leak of one particle position probability in correlations with the other degrees of freedom: the effective motion of one particle is no more ballistic.…”

“…Indeed, in a quantum walk a particle at a site moves to the neighboring sites according to its spin state; in the simplest one dimensional walk the spin up projection moves to the right and the spin down projection to the left: after one walk step the particle is in a superposition of two sites and two spin projections. Therefore, it is a natural idea to use quantum walks from quantum information theory to explore topological effects from condensed matter physics [25].…”

Self-trapped quantum walks

“…By using DTQWs which combine zero modes with a particle-conserving nonlinear relaxation mechanism, a conversion of two zero modes of opposite chirality into an attractor-repeller pair of the nonlinear dynamics was reported [33]. By investigating the effect of nonlinear spatial disorder on the edge states at the interface between two topologically different regions, the preservation of the ballistic propagation of the walker has been described even for very strong nonlinear couplings [34]. Nonlinear effects on the quantum walks ruled by Pauli-X gates homogeneously distributed have been revealed the existence a set of stationary and moving breathers with almost compact superexponential spatial tails [35].…”

Parameterization of Translation-Invariant Two-Dimensional Two-State Quantum Walks

“…In this paper, we discuss two-dimensional two-state quantum walks, in which V = Z 2 and H v = C 2 . These have been the subject of some previous studies [1,2,7].…”