Statistical dynamics of a non-Abelian anyonic quantum walk

Abstract

We study the single particle dynamics of a mobile non-Abelian anyon hopping around many pinned anyons on a surface. The dynamics is modelled by a discrete time quantum walk and the spatial degree of freedom of the mobile anyon becomes entangled with the fusion degrees of freedom of the collective system. Each quantum trajectory makes a closed braid on the world lines of the particles establishing a direct connection between statistical dynamics and quantum link invariants. We find that asymptotically a mobile Ising anyon becomes so entangled with its environment that its statistical dynamics reduces to a classical random walk with linear dispersion in contrast to particles with Abelian statistics which have quadratic dispersion.

7 pages, 5 figures

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• Review on Quantum Walk Computing: Theory, Implementation, and Application
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• Matrix product states for anyonic systems and efficient simulation of dynamics
• Discrete time quantum walk with nitrogen-vacancy centers in diamond coupled to a superconducting flux qubit
• Transport properties of anyons in random topological environments
• Phase transitions on a ladder of braided non-Abelian anyons
• Environment-induced mixing processes in quantum walks
• Quantum walk on a square lattice with identical particles
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