Possible realization of an ideal quantum computer in Josephson junction array

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.

RexTeX4, 8 pages, 3 EPS figures. Significantly longer version with more detailed estimates of decoherence times and many new relevant references

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• Fractionalization in an Easy-axis Kagome Antiferromagnet
• Quantum dimer model on the kagome lattice: solvable dimer liquid and Ising gauge theory
• Topologically protected quantum bits from Josephson junction arrays
• Pairing of Cooper Pairs in a Fully Frustrated Josephson Junction Chain
• Ground-state properties of the Rokhsar-Kivelson dimer model on the triangular lattice

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