Steve Simon

Abstract:

We describe a method for engineering local kbody interactions (k=1,2,3) from two-body couplings in spin-12 systems. When implemented in certain systems with a flat single-particle band with a unit Chern number, the resulting many-body ground states are fractional Chern insulators which exhibit Abelian and non-Abelian anyon excitations. The most complex of these, with k=3, has Fibonacci anyon excitations; our system is thus capable of universal topological quantum computation. We then demonstrate that an appropriately tuned circuit of qubits could faithfully replicate this model up to small corrections, and further, we describe the process by which one might create and manipulate non-Abelian vortices in these circuits, allowing for direct control of the system's quantum information content. © 2013 American Physical Society.