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Topologically protected quantum bits using Josephson junction arrays

Nature volume 415, pages 503–506 (2002)Cite this article

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.

References

  1. Cirac, J. I. & Zoller, P. Quantum computations with cold trapped ions. Phys. Rev. Lett. 74, 4091–4094 (1995).

    Article  ADS  CAS  Google Scholar 

  2. Monroe, C., Meekhof, D., King, B., Itano, W. & Wineland, D. Demonstration of a fundamental quantum logic gate. Phys. Rev. Lett. 75, 4714–4717 (1995).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  3. Turchette, Q., Hood, C., Lange, W., Mabushi, H. & Kimble, H. J. Measurement of conditional phase shifts for quantum logics. Phys. Rev. Lett. 75, 4710–4713 (1995).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  4. Loss, D. & DiVincenzo, D. P. Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998).

    Article  ADS  CAS  Google Scholar 

  5. Shnirman, A., Schön, G. & Hermon, Z. Quantum manipulations of small Josephson junctions. Phys. Rev. Lett. 79, 2371–2374 (1997).

    Article  ADS  CAS  Google Scholar 

  6. Averin, D. V. Adiabatic quantum computation with Cooper pairs. Solid State Commun. 105, 659–664 (1998).

    Article  ADS  CAS  Google Scholar 

  7. Mooij, J. E. et al. Josephson persistent-current qubit. Science 285, 1036–1039 (1999).

    Article  CAS  Google Scholar 

  8. Ioffe, L., Geshkenbein, V. B., Feigel'man, M. V., Fauchère, A. L. & Blatter, G. Environmentally decoupled s-wave–d-wave–s-wave Josephson junctions for quantum computing. Nature 398, 678–681 (1999).

    Article  ADS  Google Scholar 

  9. Nakamura, Y., Pashkin, Yu. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999).

    Article  ADS  CAS  Google Scholar 

  10. Friedman, J. R., Patel, V., Chen, W., Tolpygo, S. K. & Lukens, J. E. Quantum superposition of distinct macroscopic states. Nature 406, 43–46 (2000).

    Article  ADS  CAS  Google Scholar 

  11. van der Wal, C. H. et al. Quantum superposition of macroscopic persistent-current states. Science 290, 773–777 (2000).

    Article  ADS  CAS  Google Scholar 

  12. Kitaev, A. Yu. Fault-tolerant quantum computation by anyons. Preprint quant-ph/9707021 at 〈http://xxx.lanl.gov/〉 (1997).

  13. Preskill, J. in Introduction to Quantum Computation and Information (eds Lo, H.-K., Popescu, S. & Spiller, T.) 213–269 (World Scientific, Singapore, 1998).

    Book  Google Scholar 

  14. Kivelson, S. A., Rokhsar, D. S. & Sethna, J. P. Topology of the resonating valence-bond state: solitons and high-Tc superconductivity. Phys. Rev. B 35, 8865–8868 (1987).

    Article  ADS  CAS  Google Scholar 

  15. Rokhwar, D. S. & Kivelson, S. A. Superconductivity and the quantum hard-core dimer gas. Phys. Rev. Lett. 61, 2376–2379 (1988).

    Article  ADS  Google Scholar 

  16. Wen, X. G. Mean-field theory of spin-liquid states with finite energy gap and topological orders. Phys. Rev. B 44, 2664–2672 (1991).

    Article  ADS  CAS  Google Scholar 

  17. Ioffe, L. B. & Larkin, A. I. Superconductivity in the liquid-dimer valence-bond state. Phys. Rev. B 40, 6941–6947 (1989).

    Article  ADS  CAS  Google Scholar 

  18. Anderson, P. W. The resonating valence bond state in La2CuO4 and superconductivity. Science 235, 1196–1198 (1987).

    Article  ADS  CAS  Google Scholar 

  19. Moessner, R. & Sondhi, S. L. Resonating valence bond phase in the triangular lattice quantum dimer model. Phys. Rev. Lett. 86, 1881–1884 (2001).

    Article  ADS  CAS  Google Scholar 

  20. Misguich, G., Lhuillier, C., Bernu, B. & Waldtmann, C. Spin-liquid phase of the multiple-spin exchange Hamiltonian on the triangular lattice. Phys. Rev. B 60, 1064–1074 (1999).

    Article  ADS  CAS  Google Scholar 

  21. Sachdev, S. Kagome-acute- and triangular-lattice Heisenberg antiferromagnets. Phys. Rev. B 45, 12377–12396 (1992).

    Article  ADS  CAS  Google Scholar 

  22. Grabert, H. & Devoret, M. H. Single Charge Tunneling: Coulomb Blockade Phenomena in Nanostructures (Plenum, New York, 1992).

    Book  Google Scholar 

  23. Fradkin, E. Field Theories of Condensed Matter Systems (Addison-Wesley, Redwood City, 1991).

    MATH  Google Scholar 

  24. Moessner, R., Sondhi, S. L. & Fradkin, E. Short-ranged RVB physics, quantum dimer models and Ising gauge theories. Preprint cond-mat/0103396 at 〈http://xxx.lanl.gov/〉 (2001).

  25. Fradkin, E. & Shenker, S. H. Phase diagrams of lattice gauge theories with Higgs fields. Phys. Rev. D 19, 3682 (1979).

    Article  ADS  CAS  Google Scholar 

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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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Authors and Affiliations

  1. Department of Physics and Astronomy, Rutgers University, Piscataway, 08854, New Jersey, USA

    L. B. Ioffe

  2. Landau Institute for Theoretical Physics, Moscow, 117940, Russia

    L. B. Ioffe, M. V. Feigel'man & A. Ioselevich

  3. Theoretische Physik, ETH-Hönggerberg, Zürich, CH-8093, Switzerland

    D. Ivanov, M. Troyer & G. Blatter

Authors
  1. L. B. Ioffe
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  2. M. V. Feigel'man
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  3. A. Ioselevich
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  4. D. Ivanov
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  5. M. Troyer
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  6. G. Blatter
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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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