Topologically protected qubits as minimal Josephson junction arrays with non-trivial boundary conditions: A proposal

Recently a one-dimensional closed ladder of Josephson junctions has been studied [G. Cristofano, V. Marotta, A. Naddeo, G. Niccoli, Phys. Lett. A 372 (2008) 2464] within a twisted conformal field theory (CFT) approach [G. Cristofano, G. Maiella, V. Marotta, Mod. Phys. Lett. A 15 (2000) 1679; G. Cristofano, G. Maiella, V. Marotta, G. Niccoli, Nucl. Phys. B 641 (2002) 547] and shown to develop the phenomenon of flux fractionalization [G. Cristofano, V. Marotta, A. Naddeo, G. Niccoli, Eur. Phys. J. B 49 (2006) 83]. That led us to predict the emergence of a topological order in such a system [G. Cristofano, V. Marotta, A. Naddeo, J. Stat. Mech.: Theory Exp. (2005) P03006]. In this Letter we analyze the ground states and the topological properties of fully frustrated Josephson junction arrays (JJA) arranged in a Corbino disk geometry for a variety of boundary conditions. In particular minimal configurations of fully frustrated JJA are considered and shown to exhibit the properties needed in order to build up a solid state qubit, protected from decoherence. The stability and transformation properties of the ground states of the JJA under adiabatic magnetic flux changes are analyzed in detail in order to provide a tool for the manipulation of the proposed qubit.