Tilted Interferometry Realizes Universal Quantum Computation in the Ising TQFT without Overpasses

Abstract

We show how a universal gate set for topological quantum computation in the Ising TQFT, the non-Abelian sector of the putative effective field theory of the $ν=5/2$ fractional quantum Hall state, can be implemented. This implementation does not require overpasses or surgery, unlike the construction of Bravyi and Kitaev, which we take as a starting point. However, it requires measurements of the topological charge around time-like loops encircling moving quasiaparticles, which require the ability to perform `tilted' interferometry measurements.

This manuscript has substantial overlap with cond-mat/0512066 which contains more physics and less emphasis on the topology. The present manuscript is posted as a possibly useful companion to the former