Rutgers University

Title:A novel class of Josephson Junction arrays with topologically protected ground states and its application for quantum computing

Abstract
I discuss a new class of Josephson arrays which have non-trivial topology and exhibit a novel quantum state at low temperatures characterized by a topological order parameter. The low energy states of these systems are described by the lattice gauge theory with discrete group. I focus on two specific arrays designs that allow the easiest implementation: the one that can be described as a topological superconductor and the other that is a topological insulator. The ground state of the topological superconductor is characterized by long range order in a two Cooper pair condensate and by a discrete topological order parameter. The excited states are gapful and carry charge 2e. There are two types of vortices in this array: usual ones and the half-vortices, both have a large energy in the superconductive state. The ground state of the topological insulator has only topological order parameter, it can be viewed as a superfluid liquid of usual vortices in which the gap of half-vortices is preserved. The variation of the external magnetic field leads to a quantum phase transition between these two states.

Both these arrays have 2^K degenerate ground states, with K being the number of global holes in the array. This degeneracy is exact in the thermodynamic limit or in finite arrays it is 'protected' from the external perturbations (and noise) by the topological order parameter and a spectral gap. In the ideal conditions the low order effect of the external perturbations on this degeneracy is exactly zero; deviations from ideality lead to exponentially small effects of perturbations. I argue that this system provides a physical implementation of an ideal quantum computer with a built in error correction and discuss possible experiments to test these proposals.