TY - JOUR

T1 - Quantum walks of SU(2)k anyons on a ladder

AU - Lehman, Lauri

AU - Ellinas, Demosthenes

AU - Brennen, Gavin K.

PY - 2013/7

Y1 - 2013/7

N2 - We study the effects of braiding interactions on single anyon dynamics using a quantum walk model on a quasi-1-dimensional ladder filled with stationary anyons. The model includes loss of information of the coin and nonlocal fusion degrees of freedom on every second time step, such that the entanglement between the position states and the exponentially growing auxiliary degrees of freedom is lost. The computational complexity of numerical calculations reduces drastically from the fully coherent anyonic quantum walk model, allowing for relatively long simulations for anyons which are spin-1/2 irreps of SU(2)k Chern-Simons theory. We find that for Abelian anyons, the walk retains the ballistic spreading velocity just like particles with trivial braiding statistics. For non-Abelian anyons, the numerical results indicate that the spreading velocity is linearly dependent on the number of time steps. By approximating the Kraus generators of the time evolution map by circulant matrices, it is shown that the spatial probability distribution for the k = 2 walk, corresponding to Ising model anyons, is equal to the classical unbiased random walk distribution.

AB - We study the effects of braiding interactions on single anyon dynamics using a quantum walk model on a quasi-1-dimensional ladder filled with stationary anyons. The model includes loss of information of the coin and nonlocal fusion degrees of freedom on every second time step, such that the entanglement between the position states and the exponentially growing auxiliary degrees of freedom is lost. The computational complexity of numerical calculations reduces drastically from the fully coherent anyonic quantum walk model, allowing for relatively long simulations for anyons which are spin-1/2 irreps of SU(2)k Chern-Simons theory. We find that for Abelian anyons, the walk retains the ballistic spreading velocity just like particles with trivial braiding statistics. For non-Abelian anyons, the numerical results indicate that the spreading velocity is linearly dependent on the number of time steps. By approximating the Kraus generators of the time evolution map by circulant matrices, it is shown that the spatial probability distribution for the k = 2 walk, corresponding to Ising model anyons, is equal to the classical unbiased random walk distribution.

UR - http://www.scopus.com/inward/record.url?scp=84879611590&partnerID=8YFLogxK

U2 - 10.1166/jctn.2013.3102

DO - 10.1166/jctn.2013.3102

M3 - Article

AN - SCOPUS:84879611590

SN - 1546-1955

VL - 10

SP - 1634

EP - 1643

JO - Journal of Computational and Theoretical Nanoscience

JF - Journal of Computational and Theoretical Nanoscience

IS - 7

ER -