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Simple trapped-ion architecture for high-fidelity Toffoli gates

Massimo Borrelli, Laura Mazzola, Mauro Paternostro, and Sabrina Maniscalco
Phys. Rev. A 84, 012314 – Published 13 July 2011
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  • INTRODUCTION
  • THE PROTOCOL
  • ANLLYSIS OF IMPERFECTIONS
  • CONCLUSIONS
  • ACKNOWLEDGEMENTS
  • APPENDICES
    • References

    Abstract

    We discuss a simple architecture for a quantum toffoli gate implemented using three trapped ions. The gate, which, in principle, can be implemented with a single laser-induced operation, is effective under rather general conditions and is strikingly robust (within any experimentally realistic range of values) against dephasing, heating, and random fluctuations of the Hamiltonian parameters. We provide a full characterization of the unitary and noise-affected gate using three-qubit quantum process tomography.

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    • Received 15 December 2010

    DOI:https://doi.org/10.1103/PhysRevA.84.012314

    © 2011 American Physical Society

    Authors & Affiliations

    Massimo Borrelli1, Laura Mazzola2,3, Mauro Paternostro3, and Sabrina Maniscalco1,2

    • 1CM-DTC, SUPA, EPS/School of Engineering & Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
    • 2Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turun yliopisto, Finland
    • 3School of Mathematics and Physics, Queen’s University, BT7 1NN Belfast, United Kingdom

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    Issue

    Vol. 84, Iss. 1 — July 2011

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    • Figure 1
      Figure 1
      Reconstructed process matrix for U∧T. The matrix is expressed in the three-qubit operator basis formed by {I≡∧1,X≡σ̂x,Y≡−iσ̂y,Z≡σ̂z}. We show the moduli of the matrix entries. The differences with respect to the elements of an ideal gate are O(10−4).Reuse & Permissions
    • Figure 2
      Figure 2
      We take the largest entry per row in the discrepancy matrix |χ̃(tG)−χT| for n̲=5,γ/Ω=10−3. We have highlighted the bars corresponding to some of the operator-basis elements.Reuse & Permissions
    • Figure 3
      Figure 3
      Bottom horizontal axis and circular points: Average state fidelity for U∧T vs γ/Ω. At γ=0, it is F̲s=0.999 988, while for the larger dephasing rate that we have considered we have F̲s>0.93. Top horizontal axis and squared points: Average gate fidelity for U∧T vs the variance Δ of the distribution taken for the amplitudes of lasers. The lines are guides for the eye.Reuse & Permissions
    • Figure 4
      Figure 4
      (a) Moduli of the real part of the process matrix associated with the unitary gate U∧T. The top-left corner of the matrix corresponds to the operator-basis element I⊗I⊗I. (b) Same as in panel (a) but for the imaginary parts of the χ matrix.Reuse & Permissions
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