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Topologically protected quantum bits using Josephson junction arrays

Abstract

All physical implementations of quantum bits (or qubits, the logical elements in a putative quantum computer) must overcome conflicting requirements: the qubits should be manipulable through external signals, while remaining isolated from their environment. Proposals based on quantum optics emphasize optimal isolation1,2,3, while those following the solid-state route exploit the variability and scalability of nanoscale fabrication techniques4,5,6,7,8. Recently, various designs using superconducting structures have been successfully tested for quantum coherent operation9,10,11, however, the ultimate goal of reaching coherent evolution over thousands of elementary operations remains a formidable task. Protecting qubits from decoherence by exploiting topological stability is a qualitatively new proposal12 that holds promise for long decoherence times, but its physical implementation has remained unclear. Here we show how strongly correlated systems developing an isolated twofold degenerate quantum dimer liquid ground state can be used in the construction of topologically stable qubits; we discuss their implementation using Josephson junction arrays. Although the complexity of their architecture challenges the technology base available today, such topological qubits greatly benefit from their built-in fault-tolerance.

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Figure 1: Dimers on a triangular lattice forming liquid (main panel), staggered, and columnar configurations.
Figure 2: Splitting Δd of the ground-state energies under the action of a disorder potential of strength d for a 6 * 5 torus and a 6 * 5 cylinder (top inset; periodicity is along x with Lx = 6) testing the susceptibility of the degenerate ground states to local perturbations.
Figure 3: Josephson junction arrays forming triangular (JJT) and Kagome (JJK) lattices and emulating dimer systems.
Figure 4: Topologically protected qubits.

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Acknowledgements

We thank V. Geshkenbein for discussions. We acknowledge financial support through the SCOPES programme (Swiss Federal Department of Foreign Affairs and Swiss National Foundation), the Dutch Organization for Fundamental Research (NWO), the Russian Foundation for Basic Research, the programme ‘Quantum Macrophysics’ of the Russian Academy of Science, and the Russian Ministry of Science. Computations were carried out on the Beowulfcluster Asgard at ETHZ.

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Correspondence to G. Blatter.

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Ioffe, L., Feigel'man, M., Ioselevich, A. et al. Topologically protected quantum bits using Josephson junction arrays. Nature 415, 503–506 (2002). https://doi.org/10.1038/415503a

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