Braiding interactions in anyonic quantum walks

L. J. Lehman, V. Zatloukal, J. K. Pachos, G. K. Brennen

Research output: Contribution to journalArticlepeer-review

Abstract

The anyonic quantum walk is a dynamical model describing a single anyon propagating along a chain of stationary anyons and interacting via mutual braiding statistics. We review the recent results on the eects of braiding statistics in anyonic quantum walks in quasi-one dimensional ladder geometries. For anyons which correspond to spin-1/2 irreps of the quantum groups SU(2)k, the non-Abelian species (1 <k <∞) gives rise to entanglement between the walker and topological degrees of freedom which is quantied by quantum link invariants over the trajectories of the walk. The decoherence is strong enough to reduce the walk on the innite ladder to classical like behaviour. We also present numerical results on mixing times of SU(2)₂ or Ising model anyon walks on cyclic graphs. Finally, the possible experimental simulation of the anyonic quantum walk in Fractional Quantum Hall systems is discussed.
Original languageEnglish
Pages (from-to)51-62
Number of pages12
JournalQuantum computers and computing
Volume12
Issue number1
Publication statusPublished - 2012

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