Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Quantum computing with realistically noisy devices


In theory, quantum computers offer a means of solving problems that would be intractable on conventional computers. Assuming that a quantum computer could be constructed, it would in practice be required to function with noisy devices called ‘gates’. These gates cause decoherence of the fragile quantum states that are central to the computer's operation. The goal of so-called ‘fault-tolerant quantum computing’ is therefore to compute accurately even when the error probability per gate (EPG) is high. Here we report a simple architecture for fault-tolerant quantum computing, providing evidence that accurate quantum computing is possible for EPGs as high as three per cent. Such EPGs have been experimentally demonstrated, but to avoid excessive resource overheads required by the necessary architecture, lower EPGs are needed. Assuming the availability of quantum resources comparable to the digital resources available in today's computers, we show that non-trivial quantum computations at EPGs of as high as one per cent could be implemented.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it


Prices may be subject to local taxes which are calculated during checkout

Figure 1: Block structure of C4/C6 concatenated codes.
Figure 2: Conditional logical errors with postselection.
Figure 3: Conditional and detected logical errors with error correction.
Figure 4: Estimating C4/C6 resource requirements.


  1. Shor, P. W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484–1509 (1997)

    Article  MathSciNet  Google Scholar 

  2. Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982)

    Article  MathSciNet  Google Scholar 

  3. Abrams, D. S. & Williams, C. P. Fast quantum algorithms for numerical integrals and stochastic processes. Preprint at (1999).

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. Kitaev, A. Y. Quantum computations: Algorithms and error correction. Russ. Math. Surv. 52, 1191–1249 (1997)

    Article  MathSciNet  Google Scholar 

  7. Aharonov, D. & Ben-Or, M. Fault-tolerant quantum computation with constant error. Preprint at (1999).

  8. Knill, E., Laflamme, R. & Zurek, W. H. Resilient quantum computation. Science 279, 342–345 (1998)

    Article  ADS  CAS  Google Scholar 

  9. Steane, A. M. Overhead and noise threshold of fault-tolerant quantum error correction. Phys. Rev. A 68, 042322 (2003)

    Article  ADS  Google Scholar 

  10. Gottesman, D. Stabilizer Codes and Quantum Error Correction. PhD thesis, California Institute of Technology, Pasadena (1997)

    Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  12. Roos, C. F. et al. Bell states of atoms with ultralong lifetimes and their tomographic state analysis. Phys. Rev. Lett. 220402 (2004)

  13. Knill, E., Laflamme, R., Martinez, R. & Tseng, C.-H. An algorithmic benchmark for quantum information processing. Nature 404, 368–370 (2000)

    Article  ADS  CAS  Google Scholar 

  14. Childs, A. M., Chuang, I. L. & Leung, D. W. Realization of quantum process tomography in NMR. Phys. Rev. A 64, 012314 (2001)

    Article  ADS  Google Scholar 

  15. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge, UK, 2001)

    MATH  Google Scholar 

  16. Knill, E. Scalable quantum computation in the presence of large detected-error rates. Preprint at (2003).

  17. Gottesman, D. & Chuang, I. L. Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature 402, 390–393 (1999)

    Article  ADS  CAS  Google Scholar 

  18. Zhou, X., Leung, D. W. & Chuang, I. L. Methodology for quantum logic gate construction. Phys. Rev. A 62, 052316 (2000)

    Article  ADS  Google Scholar 

  19. Bollinger, J. J., Heinzen, D. J., Itano, W. M., Gilbert, S. L. & Wineland, D. J. A 303 MHz frequency standard based on trapped Be+ ions. IEEE Trans. Instrum. Meas. 40, 126–128 (1991)

    Article  CAS  Google Scholar 

  20. Steane, A. M. Quantum computer architecture for fast entropy extraction. Quant. Inf. Comput. 4, 297–306 (2002)

    MATH  Google Scholar 

  21. Svore, K. M., Terhal, B. M. & DiVincenzo, D. P. Local fault-tolerant quantum computation. Preprint at (2004).

  22. Steane, A. Space, time, parallelism and noise requirements for reliable quantum computing. Fort. Phys. 46, 443–457 (1998)

    Article  MathSciNet  Google Scholar 

  23. Knill, E. Fault-tolerant postselected quantum computation: Threshold analysis. Preprint at (2004).

  24. Knill, E. Quantum computing with very noisy devices. Preprint at (2004).

  25. Raussendorf, R. & Briegel, H. J. A one-way quantum computer. Phys. Rev. Lett. 86, 5188–5191 (2001)

    Article  ADS  CAS  Google Scholar 

  26. Bennett, C. H. et al. Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895–1899 (1993)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  27. Bennett, C. H. et al. Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722–725 (1996)

    Article  ADS  CAS  Google Scholar 

  28. Shor, P. W. In Proc. 37th Symp. Foundations of Computer Science (FOCS) 56–65 (IEEE Press, Los Alamitos, California, 1996)

    Google Scholar 

  29. Knill, E., Laflamme, R. & Zurek, W. Resilient quantum computation: Error models and thresholds. Proc. R. Soc. Lond. A 454, 365–384 (1998)

    Article  ADS  Google Scholar 

  30. Knil, E. Fault-tolerant postselected quantum computation: Schemes. Preprint at (2004).

  31. Bravyi, S. & Kitaev, A. Universal quantum computation based on a magic states distillation. Preprint at (2004).

  32. DiVincenzo, D. P., Shor, P. W. & Smolin, J. A. Quantum-channel capacity of very noisy channels. Phys. Rev. A 57, 830–839 (1998)

    Article  ADS  CAS  Google Scholar 

  33. Intel Cooperation. Microprocessor quick reference guide. (2004).

  34. Reichardt, B. W. Improved ancilla preparation scheme increases fault tolerant threshold. Preprint at (2004).

Download references


This work is a contribution of NIST, an agency of the US government, and is not subject to US copyright. Partial support from the DARPA QuIST programme is acknowledged.

Author information

Authors and Affiliations


Corresponding author

Correspondence to E. Knill.

Ethics declarations

Competing interests

The author declares that he has no competing financial interests.

Supplementary information

Supplementary Methods

Contains Supplementary Figures 1 to 10 and references. (A) Graphical networks useful for implementing the architecture presented. (B) A discussion of how the architecture was simulated. (C) The details underlying the resource graph computations. (PDF 210 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Knill, E. Quantum computing with realistically noisy devices. Nature 434, 39–44 (2005).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing