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

TL;DR

This paper proposes a topologically protected qubit using minimal Josephson junction arrays with non-trivial boundary conditions, analyzing their ground states and stability for quantum computing applications.

Contribution

It introduces a novel qubit design based on topological order in fully frustrated Josephson junction arrays with specific boundary conditions.

Findings

Ground states exhibit topological protection against decoherence

Magnetic flux changes can manipulate the qubit states

Minimal configurations support the necessary properties for qubit implementation

Abstract

Recently a one-dimensional closed ladder of Josephson junctions has been studied (G. Cristofano et al., Phys. Lett. A 372 (2008) 2464) within a twisted conformal field theory (CFT) approach (G. Cristofano et al., Mod. Phys. Lett. A 15 (2000) 1679; Nucl. Phys. B 641 (2002) 547) and shown to develop the phenomenon of flux fractionalization (G. Cristofano et al., Eur. Phys. J. B 49 (2006) 83). That led us to predict the emergence of a topological order in such a system (G. Cristofano et al., JSTAT (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.