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Quantum control and process tomography of a semiconductor quantum dot hybrid qubit

Nature volume 511, pages 70–74 (2014)Cite this article

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Abstract

The similarities between gated quantum dots and the transistors in modern microelectronics1,2—in fabrication methods, physical structure and voltage scales for manipulation—have led to great interest in the development of quantum bits (qubits) in semiconductor quantum dots3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18. Although quantum dot spin qubits have demonstrated long coherence times, their manipulation is often slower than desired for important future applications, such as factoring19. Furthermore, scalability and manufacturability are enhanced when qubits are as simple as possible. Previous work has increased the speed of spin qubit rotations by making use of integrated micromagnets11, dynamic pumping of nuclear spins12 or the addition of a third quantum dot17. Here we demonstrate a qubit that is a hybrid of spin and charge. It is simple, requiring neither nuclear-state preparation nor micromagnets. Unlike previous double-dot qubits, the hybrid qubit enables fast rotations about two axes of the Bloch sphere. We demonstrate full control on the Bloch sphere with π-rotation times of less than 100 picoseconds in two orthogonal directions, which is more than an order of magnitude faster than any other double-dot qubit. The speed arises from the qubit’s charge-like characteristics, and its spin-like features result in resistance to decoherence over a wide range of gate voltages. We achieve full process tomography in our electrically controlled semiconductor quantum dot qubit, extracting high fidelities of 85 per cent for X rotations (transitions between qubit states) and 94 per cent for Z rotations (phase accumulation between qubit states).

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Figure 1: Si/SiGe hybrid qubit device, energy levels and measurement of quantum oscillations.
Figure 2: State tomography and universal gate control of the hybrid qubit.
Figure 3: Quantum process tomography of the hybrid qubit.

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References

  1. Hanson, R., Kouwenhoven, L. P., Petta, J. R., Tarucha, S. & Vandersypen, L. M. K. Spins in few-electron quantum dots. Rev. Mod. Phys. 79, 1217–1265 (2007)

    Article  ADS  CAS  Google Scholar 

  2. Zwanenburg, F. A. et al. Silicon quantum electronics. Rev. Mod. Phys. 85, 961–1019 (2013)

    Article  ADS  CAS  Google Scholar 

  3. Loss, D. & DiVincenzo, D. P. Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998)

    Article  ADS  CAS  Google Scholar 

  4. Hayashi, T., Fujisawa, T., Cheong, H. D., Jeong, Y. H. & Hirayama, Y. Coherent manipulation of electronic states in a double quantum dot. Phys. Rev. Lett. 91, 226804 (2003)

    Article  ADS  CAS  Google Scholar 

  5. Petta, J. R., Johnson, A. C., Marcus, C. M., Hanson, M. P. & Gossard, A. C. Manipulation of a single charge in a double quantum dot. Phys. Rev. Lett. 93, 186802 (2004)

    Article  ADS  CAS  Google Scholar 

  6. Elzerman, J. M. et al. Single-shot read-out of an individual electron spin in a quantum dot. Nature 430, 431–435 (2004)

    Article  ADS  CAS  Google Scholar 

  7. Petta, J. R. et al. Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180–2184 (2005)

    Article  ADS  CAS  Google Scholar 

  8. Koppens, F. H. L. et al. Driven coherent oscillations of a single electron spin in a quantum dot. Nature 442, 766–771 (2006)

    Article  ADS  CAS  Google Scholar 

  9. Kouwenhoven, L. P., Elzerman, J. M., Hanson, R., van Beveren, L. H. W. & Vandersypen, L. M. K. Control and measurement of electron spins in semiconductor quantum dots. Phys. Stat. Solidi B 243, 3682–3691 (2006)

    Article  ADS  CAS  Google Scholar 

  10. Taylor, J. M. et al. Relaxation, dephasing, and quantum control of electron spins in double quantum dots. Phys. Rev. B 76, 035315 (2007)

    Article  ADS  Google Scholar 

  11. Pioro-Ladrière, M. et al. Electrically driven single-electron spin resonance in a slanting Zeeman field. Nature Phys. 4, 776–779 (2008)

    Article  ADS  Google Scholar 

  12. Foletti, S., Bluhm, H., Mahalu, D., Umansky, V. & Yacoby, A. Universal quantum control of two-electron spin quantum bits using dynamic nuclear polarization. Nature Phys. 5, 903–908 (2009)

    Article  ADS  CAS  Google Scholar 

  13. Laird, E. A. et al. Coherent spin manipulation in an exchange-only qubit. Phys. Rev. B 82, 075403 (2010)

    Article  ADS  Google Scholar 

  14. Gaudreau, L. et al. Coherent control of three-spin states in a triple quantum dot. Nature Phys. 8, 54–58 (2012)

    Article  ADS  CAS  Google Scholar 

  15. Maune, B. M. et al. Coherent singlet-triplet oscillations in a silicon-based double quantum dot. Nature 481, 344–347 (2012)

    Article  ADS  CAS  Google Scholar 

  16. Medford, J. et al. Quantum-dot-based resonant exchange qubit. Phys. Rev. Lett. 111, 050501 (2013)

    Article  ADS  CAS  Google Scholar 

  17. Medford, J. et al. Self-consistent measurement and state tomography of an exchange-only spin qubit. Nature Nanotechnol. 8, 654–659 (2013)

    Article  ADS  CAS  Google Scholar 

  18. Dial, O. E. et al. Charge noise spectroscopy using coherent exchange oscillations in a singlet-triplet qubit. Phys. Rev. Lett. 110, 146804 (2013)

    Article  ADS  CAS  Google Scholar 

  19. Van Meter, R., Itoh, K. M. & Ladd, T. D. in Controllable Quantum States: Mesoscopic Superconductivity & Spintronics (MS+S2006), Proc. Int. Symp. (eds Takayanagi, H., Nitta, J. & Nakano, H. ) 183–188 (World Scientific, 2008); preprint at http://arxiv.org/abs/quant-ph/0507023 (2006)

  20. Shi, Z. et al. Fast hybrid silicon double quantum dot qubit. Phys. Rev. Lett. 108, 140503 (2012)

    Article  ADS  Google Scholar 

  21. Koh, T. S., Gamble, J. K., Friesen, M., Eriksson, M. A. & Coppersmith, S. N. Pulse-gated quantum dot hybrid qubit. Phys. Rev. Lett. 109, 250503 (2012)

    Article  ADS  Google Scholar 

  22. Thalakulam, M. et al. Fast tunnel rates in Si/SiGe one-electron single and double quantum dots. Appl. Phys. Lett. 96, 183104 (2010)

    Article  ADS  Google Scholar 

  23. DiVincenzo, D. P., Bacon, D., Kempe, J., Burkard, G. & Whaley, K. B. Universal quantum computation with the exchange interaction. Nature 408, 339–342 (2000)

    Article  ADS  CAS  Google Scholar 

  24. Petersson, K. D., Petta, J. R., Lu, H. & Gossard, A. C. Quantum coherence in a one-electron semiconductor charge qubit. Phys. Rev. Lett. 105, 246804 (2010)

    Article  ADS  CAS  Google Scholar 

  25. Shi, Z. et al. Coherent quantum oscillations and echo measurements of a Si charge qubit. Phys. Rev. B 88, 075416 (2013)

    Article  ADS  Google Scholar 

  26. Shi, Z. et al. Fast coherent manipulation of three-electron states in a double quantum dot. Nature Commun. 5, 3020 (2014)

    Article  ADS  Google Scholar 

  27. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information 389–393 (Cambridge Univ. Press, 2000)

    MATH  Google Scholar 

  28. Chow, J. M. et al. Randomized benchmarking and process tomography for gate errors in a solid-state qubit. Phys. Rev. Lett. 102, 090502 (2009)

    Article  ADS  CAS  Google Scholar 

  29. Koh, T. S., Coppersmith, S. N. & Friesen, M. High-fidelity gates in quantum dot spin qubits. Proc. Natl Acad. Sci. USA 110, 19695–19700 (2013)

    Article  ADS  CAS  Google Scholar 

  30. Simmons, C. B. et al. Tunable spin loading and T1 of a silicon spin qubit measured by single-shot readout. Phys. Rev. Lett. 106, 156804 (2011)

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

This work was supported in part by ARO (W911NF-12-0607), the NSF (PHY-1104660) and by the Laboratory Directed Research and Development programme at Sandia National Laboratories. Sandia National Laboratories is a multi-programme laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. Development and maintenance of the growth facilities used for fabricating samples is supported by the US Department of Energy (DE-FG02-03ER46028). This research used US National Science Foundation-supported shared facilities at the University of Wisconsin-Madison. D.K. acknowledges conversations with X. Wu and K. Rudinger.

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Authors and Affiliations

  1. Department of Physics, University of Wisconsin-Madison, Madison, 53706, Wisconsin, USA

    Dohun Kim, Zhan Shi, C. B. Simmons, D. R. Ward, J. R. Prance, Teck Seng Koh, Mark Friesen, S. N. Coppersmith & Mark A. Eriksson

  2. Sandia National Laboratories, Albuquerque, 87185, New Mexico, USA

    John King Gamble

  3. Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, 53706, Wisconsin, USA

    D. E. Savage & M. G. Lagally

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  1. Dohun Kim
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Contributions

M.A.E. and S.N.C. had the idea for the experiment. D.K. developed pulse sequences for qubit operation and tomography, performed electrical measurements and numerical simulations with the aid of Z.S., and analysed the data with M.A.E. and S.N.C. C.B.S. fabricated the quantum dot device. J.R.P. and D.R.W. developed hardware and software for the measurements. T.S.K., J.K.G. and M.F. helped with the theoretical analysis. D.E.S. and M.G.L. prepared the Si/SiGe heterostructure. D.K., S.N.C. and M.A.E. wrote the manuscript with the contributions of all authors.

Corresponding author

Correspondence to Mark A. Eriksson.

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The authors declare no competing financial interests.

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This file contains Supplementary Text and Data 1-6, Supplementary Figures 1-6 and additional references. (PDF 5562 kb)

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Kim, D., Shi, Z., Simmons, C. et al. Quantum control and process tomography of a semiconductor quantum dot hybrid qubit. Nature 511, 70–74 (2014). https://doi.org/10.1038/nature13407

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