Letter | Published:

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

Nature volume 511, pages 7074 (03 July 2014) | Download Citation

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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References

  1. 1.

    , , , & Spins in few-electron quantum dots. Rev. Mod. Phys. 79, 1217–1265 (2007)

  2. 2.

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

  3. 3.

    & Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998)

  4. 4.

    , , , & Coherent manipulation of electronic states in a double quantum dot. Phys. Rev. Lett. 91, 226804 (2003)

  5. 5.

    , , , & Manipulation of a single charge in a double quantum dot. Phys. Rev. Lett. 93, 186802 (2004)

  6. 6.

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

  7. 7.

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

  8. 8.

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

  9. 9.

    , , , & Control and measurement of electron spins in semiconductor quantum dots. Phys. Stat. Solidi B 243, 3682–3691 (2006)

  10. 10.

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

  11. 11.

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

  12. 12.

    , , , & Universal quantum control of two-electron spin quantum bits using dynamic nuclear polarization. Nature Phys. 5, 903–908 (2009)

  13. 13.

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

  14. 14.

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

  15. 15.

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

  16. 16.

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

  17. 17.

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

  18. 18.

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

  19. 19.

    , & in Controllable Quantum States: Mesoscopic Superconductivity & Spintronics (MS+S2006), Proc. Int. Symp. (eds , & ) 183–188 (World Scientific, 2008); preprint at (2006)

  20. 20.

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

  21. 21.

    , , , & Pulse-gated quantum dot hybrid qubit. Phys. Rev. Lett. 109, 250503 (2012)

  22. 22.

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

  23. 23.

    , , , & Universal quantum computation with the exchange interaction. Nature 408, 339–342 (2000)

  24. 24.

    , , & Quantum coherence in a one-electron semiconductor charge qubit. Phys. Rev. Lett. 105, 246804 (2010)

  25. 25.

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

  26. 26.

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

  27. 27.

    & Quantum Computation and Quantum Information 389–393 (Cambridge Univ. Press, 2000)

  28. 28.

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

  29. 29.

    , & High-fidelity gates in quantum dot spin qubits. Proc. Natl Acad. Sci. USA 110, 19695–19700 (2013)

  30. 30.

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

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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.

Author information

Affiliations

  1. Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, 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, New Mexico 87185, USA

    • John King Gamble
  3. Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA

    • D. E. Savage
    •  & M. G. Lagally

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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.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Mark A. Eriksson.

Supplementary information

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    Supplementary Information

    This file contains Supplementary Text and Data 1-6, Supplementary Figures 1-6 and additional references.

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DOI

https://doi.org/10.1038/nature13407

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