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Realization of quantum error correction


Scalable quantum computation1 and communication require error control to protect quantum information against unavoidable noise. Quantum error correction2,3 protects information stored in two-level quantum systems (qubits) by rectifying errors with operations conditioned on the measurement outcomes. Error-correction protocols have been implemented in nuclear magnetic resonance experiments4,5,6, but the inherent limitations of this technique7 prevent its application to quantum information processing. Here we experimentally demonstrate quantum error correction using three beryllium atomic-ion qubits confined to a linear, multi-zone trap. An encoded one-qubit state is protected against spin-flip errors by means of a three-qubit quantum error-correcting code. A primary ion qubit is prepared in an initial state, which is then encoded into an entangled state of three physical qubits (the primary and two ancilla qubits). Errors are induced simultaneously in all qubits at various rates. The encoded state is decoded back to the primary ion one-qubit state, making error information available on the ancilla ions, which are separated from the primary ion and measured. Finally, the primary qubit state is corrected on the basis of the ancillae measurement outcome. We verify error correction by comparing the corrected final state to the uncorrected state and to the initial state. In principle, the approach enables a quantum state to be maintained by means of repeated error correction, an important step towards scalable fault-tolerant quantum computation using trapped ions.

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Figure 1: Quantum circuit for the quantum error-correction protocol described and implemented in this work as one would compose it of single-bit rotations, Hadamard gates, and controlled-not gates15.
Figure 2: Schematic representation of experimental techniques.
Figure 3: Results of quantum error correction protocol.


  1. 1

    Preskill, J. Reliable quantum computers. Proc. R. Soc. Lond. A 454, 385–410 (1998)

    ADS  Article  Google Scholar 

  2. 2

    Calderbank, A. R. & Shor, P. W. Good quantum error-correcting codes exist. Phys. Rev. A 54, 1098–1105 (1996)

    ADS  CAS  Article  Google Scholar 

  3. 3

    Steane, A. Multiple particle interference and quantum error correction. Proc. R. Soc. Lond. A 452, 2551–2577 (1996)

    ADS  MathSciNet  Article  Google Scholar 

  4. 4

    Cory, D. G. et al. Experimental quantum error correction. Phys. Rev. Lett. 81, 2152–2155 (1998)

    ADS  CAS  Article  Google Scholar 

  5. 5

    Leung, D. et al. Experimental realization of a two-bit phase damping quantum code. Phys. Rev. A 60, 1924–1943 (1999)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Knill, E., Laflamme, R., Martinez, R. & Negrevergne, C. Benchmarking quantum computers: The five-qubit error correcting code. Phys. Rev. Lett. 86, 5811–5814 (2001)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Cory, D. G. et al. NMR based quantum information processing: Achievements and prospects. Fortschr. Phys. 48, 875–907 (2000)

    CAS  Article  Google Scholar 

  8. 8

    Lo, H.-K. & Chau, H. F. Unconditional security of quantum key distribution over arbitrarily long distances. Science 283, 2050–2056 (1999)

    ADS  CAS  Article  Google Scholar 

  9. 9

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

    Book  Google Scholar 

  10. 10

    Wineland, D. J. et al. Experimental issues in coherent quantum-state manipulation of trapped atomic ions. J. Res. Natl Inst. Stand. Technol. 103(3), 259–328 (1998)

    CAS  Article  Google Scholar 

  11. 11

    Barrett, M. D. et al. Deterministic quantum teleportation of atomic qubits. Nature 429, 737–739 (2004)

    ADS  CAS  Article  Google Scholar 

  12. 12

    Leibfried, D. et al. Toward Heisenberg-limited spectroscopy with multiparticle entangled states. Science 304, 1476–1478 (2004)

    ADS  CAS  Article  Google Scholar 

  13. 13

    Riebe, M. et al. Deterministic quantum teleportation with atoms. Nature 429, 734–737 (2004)

    ADS  CAS  Article  Google Scholar 

  14. 14

    Blinov, B. B., Moehring, D. L., Duan, L.-M. & Monroe, C. Observation of entanglement between a single trapped atom and a single photon. Nature 428, 153–157 (2004)

    ADS  CAS  Article  Google Scholar 

  15. 15

    Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge, UK, 2000)

    MATH  Google Scholar 

  16. 16

    Rowe, M. A. et al. Transport of quantum states and separation of ions in a dual rf ion trap. Quant. Inf. Comput. 2, 257–271 (2002)

    CAS  MATH  Google Scholar 

  17. 17

    Leibfried, D. et al. Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate. Nature 422, 412–415 (2003)

    ADS  CAS  Article  Google Scholar 

  18. 18

    Wineland, D. J. et al. Quantum information processing with trapped ions. Phil. Trans. R. Soc. Lond. A 361, 1349–1361 (2003)

    ADS  CAS  Article  Google Scholar 

  19. 19

    Schaetz, T. et al. Quantum dense coding with atomic qubits. Phys. Rev. Lett. 93, 040505 (2004)

    ADS  CAS  Article  Google Scholar 

  20. 20

    King, B. E. et al. Cooling the collective motion of trapped ions to initialize a quantum register. Phys. Rev. Lett. 81, 1525–1528 (1998)

    ADS  CAS  Article  Google Scholar 

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We thank T. Rosenband and D. Rosenberg for comments on the manuscript. This work was supported by the US National Security Agency (NSA) and the Advanced Research and Development Activity (ARDA). This manuscript is a publication of NIST.

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Correspondence to J. Chiaverini.

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Chiaverini, J., Leibfried, D., Schaetz, T. et al. Realization of quantum error correction. Nature 432, 602–605 (2004).

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