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arXiv · 1109.4561

Non-Abelian Braiding of Lattice Bosons

Eliot Kapit·Paul Ginsparg·Erich Mueller
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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 $ν$, 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 $ν$ near $1$ and $3/2$, with Berry matrices respectively consistent with Ising and Fibonacci anyons. Near $ν=1/2$, the braids commute.

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Eliot Kapit, Paul Ginsparg, Erich Mueller. 2011-09-21. Non-Abelian Braiding of Lattice Bosons. https://doi.org/10.1103/physrevlett.108.066802

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