Possible realization of an ideal quantum computer in Josephson junction array

TL;DR

This paper proposes a Josephson junction array with topological order that can serve as an ideal quantum computer with built-in error correction, long coherence times, and unique superconducting properties.

Contribution

It introduces a new class of Josephson arrays with topological order, demonstrating their potential for robust quantum computation and error correction.

Findings

Arrays exhibit long-range order and topological degeneracy.

Degeneracy is protected from external perturbations in ideal conditions.

Small arrays show superconductivity with double charge (4e) and long decoherence times.

Abstract

We introduce a new class of Josephson arrays which have non-trivial topology and exhibit a novel state at low temperatures. This state is characterized by long range order in a two Cooper pair condensate and by a discrete topological order parameter. These arrays have degenerate ground states with this degeneracy 'protected' from the external perturbations (and noise) by the topological order parameter. We show that in ideal conditions the low order effect of the external perturbations on this degeneracy is exactly zero and that deviations from ideality lead to only exponentially small effects of perturbations. We argue that this system provides a physical implementation of an ideal quantum computer with a built in error correction and show that even a small array exhibits interesting physical properties such as superconductivity with double charge, 4e, and extremely long decoherence times.