Non-Abelian Braiding of Lattice Bosons

TL;DR

This paper demonstrates through numerical simulations that braiding non-abelian quasiparticles in lattice bosons under magnetic fields can produce non-commuting operations, with potential implications for topological quantum computing.

Contribution

It introduces a method to simulate braiding of non-abelian quasiparticles in lattice bosons, revealing non-commutative braids at certain filling factors and their connection to anyon models.

Findings

Braids do not commute near ν=1 and 3/2, consistent with Ising and Fibonacci anyons.

Braids commute near ν=1/2, indicating different topological properties.

Numerical experiments simulate braiding operations relevant for quantum computation.

Abstract

We report on a numerical experiment in which we use time-dependent potentials to braid non-abelian quasiparticles. We consider lattice bosons in a uniform magnetic field within the fractional quantum Hall regime, where $\nu$, the ratio of particles to flux quanta, is near 1/2, 1 or 3/2. We introduce time-dependent potentials which move quasiparticle excitations around one another, explicitly simulating a braiding operation which could implement part of a gate in a quantum computation. We find that different braids do not commute for $\nu$ near $1$ and $3/2$, with Berry matrices respectively consistent with Ising and Fibonacci anyons. Near $\nu=1/2$, the braids commute.