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Volume thresholds for quantum fault tolerance

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Abstract

We introduce finite-level concatenation threshold regions for quantum fault tolerance. These volume thresholds are regions in an error probability manifold that allow for the implemented system dynamics to satisfy a prescribed implementation inaccuracy bound at a given level of quantum error correction concatenation. Satisfying this condition constitutes our fundamental definition of fault tolerance. The prescribed bound provides a halting condition identifying the attainment of fault tolerance that allows for the determination of the optimum choice of quantum error correction code(s) and number of concatenation levels. Our method is constructed to apply to finite levels of concatenation, does not require that error proabilities consistently decrease from one concatenation level to the next, and allows for analysis, without approximations, of physical systems characterized by non-equiprobable distributions of qubit error probabilities. We demonstrate the utility of this method via a general error model.

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References

  1. Shor, P.W.: Proceedings of the 37th Annual Symposium on Foundation of Computer Science, 56. IEEE Press, Los Alamitos, CA (1996)

  2. Nielsen M., Chuang I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  3. Calderbank A.R., Shor P.W.: Phys. Rev. A 54, 1098 (1996)

    Article  CAS  ADS  PubMed  Google Scholar 

  4. Calderbank A.R., Rains E.M., Shor P.M., Sloane N.J.A.: IEEE Trans. Inf. Th. 44, 1369 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  5. Calderbank A.R., Rains E.M., Shor P.W., Sloane N.J.A.: Phys. Rev. Lett. 78, 405 (1997)

    Article  CAS  MathSciNet  ADS  MATH  Google Scholar 

  6. Knill, E., Laflamme, R.: arXiv:quant-ph/9608012, (1996)

  7. Aharonov, D., Ben-Or, M.: Proc. 29th Ann. ACM Symp. on Th. Comp., 176 (1997)

  8. Kitaev A.Y.: Russ. Math. Surv. 52, 1191 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  9. Knill, E., Laflamme, R., Zurek, W.H.: Proceedings of the Royal Society of London A, 365 (1998)

  10. Aliferis P., Gottesman D., Preskill J.: Quant. Inf. Comp. 6, 97 (2006)

    MathSciNet  MATH  Google Scholar 

  11. Rahn B., Doherty A.C., Mabuchi H.: Phys. Rev. A 66, 032304 (2002)

    Article  ADS  Google Scholar 

  12. Svore K.M., Cross A.W., Chuang I.L., Aho A.V.: Quant. Inf. Comp. 6, 193 (2006)

    MathSciNet  MATH  Google Scholar 

  13. Stephens A.M., Fowler A.G., Hollenberg L.C.L.: Quant. Inf. Comp. 8, 330 (2008)

    MathSciNet  MATH  Google Scholar 

  14. Cross A.W., DiVincenzo D.P., Terhal B.M.: Quant. Inf. Comp. 9, 541 (2009)

    MathSciNet  MATH  Google Scholar 

  15. Gilbert G., Hamrick M., Weinstein Y.S.: Quant. Inf. Proc. 7, 263 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Aliferis P., Preskill J.: Phys. Rev. A 78, 052331 (2008)

    Article  ADS  Google Scholar 

  17. Gilbert, G., Weinstein, Y.S., Aggarwal, V., Calderbank, A.R.: To appear

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Authors and Affiliations

  1. Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA

    Vaneet Aggarwal & A. Robert Calderbank

  2. Quantum Information Science Group, Mitre, 260 Industrial Way West, Eatontown, NJ, 07224, USA

    Gerald Gilbert & Yaakov S. Weinstein

Authors
  1. Vaneet Aggarwal
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  2. A. Robert Calderbank
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  3. Gerald Gilbert
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  4. Yaakov S. Weinstein
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Corresponding author

Correspondence to Gerald Gilbert.

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Aggarwal, V., Calderbank, A.R., Gilbert, G. et al. Volume thresholds for quantum fault tolerance. Quantum Inf Process 9, 541–549 (2010). https://doi.org/10.1007/s11128-010-0181-2

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  • DOI: https://doi.org/10.1007/s11128-010-0181-2

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