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Realization of the Cirac–Zoller controlled-NOT quantum gate


Quantum computers have the potential to perform certain computational tasks more efficiently than their classical counterparts. The Cirac–Zoller proposal1 for a scalable quantum computer is based on a string of trapped ions whose electronic states represent the quantum bits of information (or qubits). In this scheme, quantum logical gates involving any subset of ions are realized by coupling the ions through their collective quantized motion. The main experimental step towards realizing the scheme is to implement the controlled-NOT (CNOT) gate operation between two individual ions. The CNOT quantum logical gate corresponds to the XOR gate operation of classical logic that flips the state of a target bit conditioned on the state of a control bit. Here we implement a CNOT quantum gate according to the Cirac–Zoller proposal1. In our experiment, two 40Ca+ ions are held in a linear Paul trap and are individually addressed using focused laser beams2; the qubits3 are represented by superpositions of two long-lived electronic states. Our work relies on recently developed precise control of atomic phases4 and the application of composite pulse sequences adapted from nuclear magnetic resonance techniques5,6.

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Figure 1: State evolution of both qubits under the CNOT operation.
Figure 2: Joint probabilities for the ions prepared in |DD〉.
Figure 3: Cirac-Zoller CNOT gate operation.


  1. 1

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

    ADS  CAS  Article  Google Scholar 

  2. 2

    Nägerl, H. C. et al. Laser addressing of individual ions in a linear ion trap. Phys. Rev. A 60, 145–148 (1999)

    ADS  Article  Google Scholar 

  3. 3

    Nägerl, H. C. et al. Investigating a qubit candidate: Spectroscopy on the S1/2 to D5/2 transition of a trapped calcium ion in a linear Paul trap. Phys. Rev. A 61, 023405 (2000)

    ADS  Article  Google Scholar 

  4. 4

    Häffner, H. et al. Precision measurement and compensation of optical Stark shifts for an ion-trap quantum processor. Phys. Rev. Lett. (in the press); preprint available at 〈〉 (2002)

  5. 5

    Childs, A. M. & Chuang, I. M. Universal quantum computation with two-level trapped ions. Phys. Rev. A 63, 012306 (2001)

    ADS  Article  Google Scholar 

  6. 6

    Levitt, M. H. Composite pulses (NMR spectroscopy). Prog. Nucl. Magn. Reson. Spectrosc. 18, 61–122 (1986)

    ADS  CAS  Article  Google Scholar 

  7. 7

    DiVincenzo, D. P. The physical implementation of quantum computation. Fortschr. Phys. 48, 771–783 (2000)

    Article  Google Scholar 

  8. 8

    Sleator, T. & Weinfurter, H. Realizable universal quantum logic gates. Phys. Rev. Lett. 74, 4087–4090 (1995)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  9. 9

    DiVincenzo, D. P. Two-bit gates are universal for quantum computation. Phys. Rev. A 51, 1015–1022 (1995)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Shor, P. W. in Proc. 35th Annu. Symp. Foundations of Computer Science (ed. Goldwasser, S.) 124–133 (IEEE Computer Society Press, Los Alamitos, California, 1994)

    Google Scholar 

  11. 11

    Vandersypen, L. M. K. et al. Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance. Nature 414, 883–887 (2001)

    ADS  CAS  Article  Google Scholar 

  12. 12

    Šašura, M. & Bužek, V. Cold trapped ions as quantum information processors. J. Mod. Opt. 49, 1593–1647 (2002)

    ADS  MathSciNet  Article  Google Scholar 

  13. 13

    Roos, Ch. et al. Quantum state engineering on an optical transition and decoherence in a Paul trap. Phys. Rev. Lett. 83, 4713–4716 (1999)

    ADS  CAS  Article  Google Scholar 

  14. 14

    Meekhof, D. M., Monroe, C., King, B. E., Itano, W. M. & Wineland, D. J. Generation of nonclassical motional states of a trapped atom. Phys. Rev. Lett. 76, 1796–1799 (1996)

    ADS  CAS  Article  Google Scholar 

  15. 15

    Dehmelt, H. Proposed 1014Δν > ν laser fluorescence spectroscopy on Tl+ mono-ion oscillator. Bull. Am. Phys. Soc. 20, 60 (1975)

    Google Scholar 

  16. 16

    Turchette, Q. A. et al. Deterministic entanglement of two trapped ions. Phys. Rev. Lett. 81, 3631–3634 (1998)

    ADS  CAS  Article  Google Scholar 

  17. 17

    Sackett, C. A. et al. Experimental entanglement of four particles. Nature 404, 256–259 (2000)

    ADS  CAS  Article  Google Scholar 

  18. 18

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

    ADS  MathSciNet  CAS  Article  Google Scholar 

  19. 19

    Gulde, S. et al. Implementation of the Deutsch–Jozsa algorithm on an ion-trap quantum computer. Nature 421, 48–50 (2003)

    ADS  CAS  Article  Google Scholar 

  20. 20

    Rohde, H. et al. Sympathetic ground state cooling and coherent manipulation with two-ion crystals. J. Opt. B 3, S34–S41 (2001)

    CAS  Article  Google Scholar 

  21. 21

    Jones, J. A. Robust Ising gates for practical quantum computation. Phys. Rev. A 67, 012317 (2003)

    ADS  Article  Google Scholar 

  22. 22

    de Vivie-Riedle, R., Rabitz, H. & Kompa, K. (eds) Chem. Phys., 267, Issues 1–3 (2001). Special issue on coherent control.

  23. 23

    Pan, J.-W., Bouwmeester, D., Daniell, M., Weinfurter, H. & Zeilinger, A. Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement. Nature 403, 515–519 (2000)

    ADS  CAS  Article  Google Scholar 

  24. 24

    Steane, A. M. Efficient fault-tolerant quantum computing. Nature 399, 124–126 (1999)

    ADS  CAS  Article  Google Scholar 

  25. 25

    Duan, L. M., Lukin, M., Cirac, J. I. & Zoller, P. Long-distance quantum communication with atomic ensembles and linear optics. Nature 414, 413–418 (2001)

    ADS  CAS  Article  Google Scholar 

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We thank P. Zoller for discussions and we gratefully acknowledge support by the European Commission (QUEST and QUBITS networks), by the Austrian Science Fund (FWF), and by the Institut für Quanteninformation GmbH. H.H. is supported by the Marie-Curie programme of the European Commission.

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Correspondence to Rainer Blatt.

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Schmidt-Kaler, F., Häffner, H., Riebe, M. et al. Realization of the Cirac–Zoller controlled-NOT quantum gate. Nature 422, 408–411 (2003).

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