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.

Silicon qubit fidelities approaching incoherent noise limits via pulse engineering


Spin qubits created from gate-defined silicon metal–oxide–semiconductor quantum dots are a promising architecture for quantum computation. The high single qubit fidelities possible in these systems, combined with quantum error correcting codes, could potentially offer a route to fault-tolerant quantum computing. To achieve fault tolerance, however, gate error rates must be reduced to below a certain threshold and, in general, correlated errors must be removed. Here we show that pulse engineering techniques can be used to reduce the average Clifford gate error rates for silicon quantum dot spin qubits down to 0.043%. This represents a factor of three improvement over state-of-the-art silicon quantum dot devices and extends the randomized benchmarking coherence time to 9.4 ms. By including tomographically complete measurements in our randomized benchmarking, we infer a higher-order feature of the noise called the unitarity, which measures the coherence of noise. This, in turn, allows us to theoretically predict that average gate error rates as low as 0.026% may be achievable with further pulse improvements. These spin qubit fidelities are ultimately limited by incoherent noise, which we attribute to charge noise from the silicon device structure or the environment.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Device image, experimental set-up and GRAPE-optimized Clifford gates.
Fig. 2: Density matrix reconstruction through tomographic readout.
Fig. 3: Feedback control and calibration for randomized benchmarking over 35 h.
Fig. 4: Randomized benchmarking result and noise profile.
Fig. 5: Randomized benchmarking experimental data.

Data availability

The data sets generated during and/or analysed during the current study are available from the corresponding authors on reasonable request.

Code availability

The analysis code that support the findings during the current study are available from the corresponding authors on reasonable request.


  1. 1.

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

    Article  Google Scholar 

  2. 2.

    Fowler, A. G., Mariantoni, M., Martinis, J. M. & Cleland, A. N. Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86, 032324 (2012).

    Article  Google Scholar 

  3. 3.

    Veldhorst, M. et al. An addressable quantum dot qubit with fault-tolerant control-fidelity. Nat. Nanotechnol. 9, 981–985 (2014).

    Article  Google Scholar 

  4. 4.

    Kawakami, E. et al. Gate fidelity and coherence of an electron spin in an Si/SiGe quantum dot with micromagnet. Proc. Natl Acad. Sci. USA 113, 11738–11743 (2016).

    Article  Google Scholar 

  5. 5.

    Watson, T. F. et al. A programmable two-qubit quantum processor in silicon. Nature 555, 633–637 (2018).

    Article  Google Scholar 

  6. 6.

    Zajac, D. M. et al. Resonantly driven CNOT gate for electron spins. Science 359, 439–442 (2017).

    MathSciNet  Article  Google Scholar 

  7. 7.

    Yoneda, J. et al. A quantum-dot spin qubit with coherence limited by charge noise and fidelity higher than 99.9%. Nat. Nanotechnol. 13, 102–106 (2017).

    Article  Google Scholar 

  8. 8.

    Emerson, J., Alicki, R. & Życzkowski, K. Scalable noise estimation with random unitary operators. J. Opt. B 7, S347–S352 (2005).

    MathSciNet  Article  Google Scholar 

  9. 9.

    Knill, E. et al. Randomized benchmarking of quantum gates. Phys. Rev. A 77, 012307 (2008).

    Article  Google Scholar 

  10. 10.

    Dankert, C., Cleve, R., Emerson, J. & Livine, E. Exact and approximate unitary 2-designs and their application to fidelity estimation. Phys. Rev. A 80, 012304 (2009).

    Article  Google Scholar 

  11. 11.

    Magesan, E., Gambetta, J. M. & Emerson, J. Scalable and robust randomized benchmarking of quantum processes. Phys. Rev. Lett. 106, 180504 (2011).

    Article  Google Scholar 

  12. 12.

    Magesan, E., Gambetta, J. M. & Emerson, J. Characterizing quantum gates via randomized benchmarking. Phys. Rev. A 85, 042311 (2012).

    Article  Google Scholar 

  13. 13.

    Wallman, J. J. Randomized benchmarking with gate-dependent noise. Quantum 2, 47 (2018).

    Article  Google Scholar 

  14. 14.

    Wallman, J. J., Granade, C., Harper, R. & Flammia, S. T. Estimating the coherence of noise. New J. Phys. 17, 113020 (2015).

  15. 15.

    Kimmel, S., da Silva, M. P., Ryan, Ca, Johnson, B. R. & Ohki, T. Robust extraction of tomographic information via randomized benchmarking. Phys. Rev. X 4, 011050 (2014).

    Google Scholar 

  16. 16.

    Feng, G. et al. Estimating the coherence of noise in quantum control of a solid-state qubit. Phys. Rev. Lett. 117, 260501 (2016).

    Article  Google Scholar 

  17. 17.

    Fogarty, M. A. et al. Nonexponential fidelity decay in randomized benchmarking with low-frequency noise. Phys. Rev. A 92, 022326 (2015).

    Article  Google Scholar 

  18. 18.

    Khaneja, N., Reiss, T., Kehlet, C., Schulte-Herbrüggen, T. & Glaser, S. J. Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms. J. Magn. Reson. 172, 296–305 (2005).

    Article  Google Scholar 

  19. 19.

    Huang, W. et al. Fidelity benchmarks for two-qubit gates in silicon. Nature (in the press); preprint available at

  20. 20.

    Muhonen, J. T. et al. Quantifying the quantum gate fidelity of single-atom spin qubits in silicon by randomized benchmarking. J. Phys. Condens. Matter 27, 154205 (2015).

    Article  Google Scholar 

  21. 21.

    Wallman, J. J. Bounding experimental quantum error rates relative to fault-tolerant thresholds. Preprint at (2015).

  22. 22.

    Kueng, R., Long, D. M., Doherty, A. C. & Flammia, S. T. Comparing experiments to the fault-tolerance threshold. Phys. Rev. Lett. 117, 170502 (2016).

    Article  Google Scholar 

  23. 23.

    Dugas, A. C., Wallman, J. J. & Emerson, J. Efficiently characterizing the total error in quantum circuits. Preprint at (2018).

  24. 24.

    Barends, R. et al. Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature 508, 500–503 (2014).

    Article  Google Scholar 

  25. 25.

    Ballance, C. J., Harty, T. P., Linke, N. M., Sepiol, M. A. & Lucas, D. M. High-fidelity quantum logic gates using trapped-ion hyperfine qubits. Phys. Rev. Lett. 117, 060504 (2016).

    Article  Google Scholar 

  26. 26.

    Rong, X. et al. Experimental fault-tolerant universal quantum gates with solid-state spins under ambient conditions. Nat. Commun. 6, 8748 (2015).

    Article  Google Scholar 

  27. 27.

    Chan, K. W. et al. Assessment of a silicon quantum dot spin qubit environment via noise spectroscopy. Phys. Rev. Appl. 10, 044017 (2018).

    Article  Google Scholar 

  28. 28.

    Itoh, K. M. & Watanabe, H. Isotope engineering of silicon and diamond for quantum computing and sensing applications. MRS Commun. 4, 143–157 (2014).

    Article  Google Scholar 

  29. 29.

    Angus, S. J., Ferguson, A. J., Dzurak, A. S. & Clark, R. G. Gate-defined quantum dots in intrinsic silicon. Nano Lett. 7, 2051–2055 (2007).

    Article  Google Scholar 

  30. 30.

    Lim, W. H. et al. Observation of the single-electron regime in a highly tunable silicon quantum dot. Appl. Phys. Lett. 95, 242102 (2009).

    Article  Google Scholar 

  31. 31.

    Granade, C., Ferrie, C. & Cory, D. G. Accelerated randomized benchmarking. New J. Phys. 17, 013042 (2015).

    Article  Google Scholar 

  32. 32.

    Granade, C. et al. QInfer: statistical inference software for quantum applications. Quantum 1, 5 (2017).

    Article  Google Scholar 

  33. 33.

    Ball, H., Stace, T. M., Flammia, S. T. & Biercuk, M. J. Effect of noise correlations on randomize benchmarking. Phys. Rev. A 93, 022303 (2016).

    Article  Google Scholar 

  34. 34.

    Magesan, E. et al. Efficient measurement of quantum gate error by interleaved randomized benchmarking. Phys. Rev. Lett. 109, 080505 (2012).

    Article  Google Scholar 

Download references


The authors acknowledge support from the US Army Research Office (W911NF-13-1-0024, W911NF-14-1-0098, W911NF-14-1-0103 and W911NF-17-1-0198), the Australian Research Council (CE170100009 and CE170100012) and the NSW Node of the Australian National Fabrication Facility. B.H. acknowledges support from the Netherlands Organization for Scientific Research (NWO) through a Rubicon Grant. K.M.I. acknowledges support from a Grant-in-Aid for Scientific Research by MEXT, NanoQuine, FIRST and the JSPS Core-to-Core Program. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the US Government.

Author information




C.H.Y. conceived and designed the GRAPE pulse sequences and the feedback control systems for the experiments. C.H.Y. and K.W.C. performed the experiments. C.H.Y., R.H., T.E., S.T.F. and S.D.B. analysed the data. K.W.C. and F.E.H. fabricated the device. K.M.I. prepared and supplied the 28Si epilayer wafer. All authors contributed materials, analysis and/or tools. C.H.Y., R.H., S.T.F., S.D.B. and A.S.D. wrote the paper with input from all co-authors. A.S.D. supervised the project.

Corresponding authors

Correspondence to C. H. Yang or S. D. Bartlett or A. S. Dzurak.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–2, Supplementary equations 1–2, Supplementary Table 1

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Yang, C.H., Chan, K.W., Harper, R. et al. Silicon qubit fidelities approaching incoherent noise limits via pulse engineering. Nat Electron 2, 151–158 (2019).

Download citation

Further reading


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