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Microwave-driven coherent operation of a semiconductor quantum dot charge qubit


An intuitive realization of a qubit is an electron charge at two well-defined positions of a double quantum dot. This qubit is simple and has the potential for high-speed operation because of its strong coupling to electric fields. However, charge noise also couples strongly to this qubit, resulting in rapid dephasing at all but one special operating point called the ‘sweet spot’. In previous studies d.c. voltage pulses have been used to manipulate semiconductor charge qubits1,2,3,4,5,6,7,8 but did not achieve high-fidelity control, because d.c. gating requires excursions away from the sweet spot. Here, by using resonant a.c. microwave driving we achieve fast (greater than gigahertz) and universal single qubit rotations of a semiconductor charge qubit. The Z-axis rotations of the qubit are well protected at the sweet spot, and we demonstrate the same protection for rotations about arbitrary axes in the XY plane of the qubit Bloch sphere. We characterize the qubit operation using two tomographic approaches: standard process tomography9,10 and gate set tomography11. Both methods consistently yield process fidelities greater than 86% with respect to a universal set of unitary single-qubit operations.

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Figure 1: Si/SiGe quantum dot device, qubit spectroscopy and coherent Rabi oscillation measurements.
Figure 2: Ramsey fringes and demonstration of three-axis control of the a.c.-gated charge qubit.
Figure 3: Hahn echo measurement.
Figure 4: QPT and GST of the a.c.-gated charge qubit.


  1. Cao, G. et al. Ultrafast universal quantum control of a quantum-dot charge qubit using Landau–Zener–Stückelberg interference. Nature Commun. 4, 1401 (2013).

    Article  Google Scholar 

  2. Shinkai, G., Hayashi, T., Ota, T. & Fujisawa, T. Correlated coherent oscillations in coupled semiconductor charge qubits. Phys. Rev. Lett. 103, 056802 (2009).

    Article  Google Scholar 

  3. 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  CAS  Google Scholar 

  4. Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999).

    Article  CAS  Google Scholar 

  5. 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  CAS  Google Scholar 

  6. Dovzhenko, Y. et al. Nonadiabatic quantum control of a semiconductor charge qubit. Phys. Rev. B 84, 161302 (2011).

    Article  Google Scholar 

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

    Article  Google Scholar 

  8. Gorman, J., Hasko, D. G. & Williams, D. A. Charge-qubit operation of an isolated double quantum dot. Phys. Rev. Lett. 95, 090502 (2005).

    Article  CAS  Google Scholar 

  9. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000).

  10. 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  CAS  Google Scholar 

  11. Blume-Kohout, R. et al. (2013). Robust, self-consistent closed-form tomography of quantum logic gates on a trapped ion qubit. Preprint

  12. Vion, D. et al. Manipulating the quantum state of an electrical circuit. Science 296, 886–889 (2002).

    Article  CAS  Google Scholar 

  13. Chow, J. M. et al. Optimized driving of superconducting artificial atoms for improved single-qubit gates. Phys. Rev. A 82, 040305 (2010).

    Article  Google Scholar 

  14. Fedorov, A., Steffen, L., Baur, M., da Silva, M. P. & Wallraff, A. Implementation of a Toffoli gate with superconducting circuits. Nature 481, 170–172 (2012).

    Article  CAS  Google Scholar 

  15. DiVincenzo, D. P. The physical implementation of quantum computation. Fortschr. Phys. 48, 771–783 (2000).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  17. Koppens, F. H. L., Nowack, K. C. & Vandersypen, L. M. K. Spin echo of a single electron spin in a quantum dot. Phys. Rev. Lett. 100, 236802 (2008).

    Article  CAS  Google Scholar 

  18. Pla, J. J. et al. A single-atom electron spin qubit in silicon. Nature 489, 541–545 (2012).

    Article  CAS  Google Scholar 

  19. Nowack, K. C., Koppens, F. H. L., Nazarov, Y. V. & Vandersypen, L. M. K. Coherent control of a single electron spin with electric fields. Science 318, 1430–1433 (2007).

    Article  CAS  Google Scholar 

  20. van den Berg, J. W. G. et al. Fast spin–orbit qubit in an indium antimonide nanowire. Phys. Rev. Lett. 110, 066806 (2013).

    Article  CAS  Google Scholar 

  21. Petersson, K. D. et al. Circuit quantum electrodynamics with a spin qubit. Nature 490, 380–383 (2012).

    Article  CAS  Google Scholar 

  22. Kawakami, E. et al. Electrical control of a long-lived spin qubit in a Si/SiGe quantum dot. Nature Nanotech. 9, 666–670 (2014).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  25. Kim, D. et al. Quantum control and process tomography of a semiconductor quantum dot hybrid qubit. Nature 511, 70–74 (2014).

    Article  CAS  Google Scholar 

  26. Shore, B. W. The Theory of Coherent Atomic Excitation (Wiley, 1990).

  27. Vandersypen, L. M. K. & Chuang, I. L. NMR techniques for quantum control and computation. Rev. Mod. Phys. 76, 1037–1069 (2005).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  29. Magesan, E., Blume-Kohout, R. & Emerson, J. Gate fidelity fluctuations and quantum process invariants. Phys. Rev. A 84, 012309 (2011).

    Article  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  CAS  Google Scholar 

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This work was supported in part by the Army Research Office (W911NF-12-0607), the National Science Foundation (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 United States Department of Energy's National Nuclear Security Administration (contract DE-AC04-94AL85000). Development and maintenance of the growth facilities used for fabricating samples is supported by the Department of Energy (DE-FG02-03ER46028). This research utilized National Science Foundation-supported shared facilities at the University of Wisconsin–Madison.

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D.K. performed electrical measurements, state and process tomography, and analysed the data with M.A.E., M.F. and S.N.C. D.R.W. developed the hardware and software for measurements. C.B.S. fabricated the quantum dot device. J.K.G., R.B-K. and E.N. performed gate-set tomography. D.E.S. and M.G.L. prepared the Si/SiGe heterostructure. All authors contributed to the preparation of the manuscript.

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Correspondence to M. A. Eriksson.

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The authors declare no competing financial interests.

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Kim, D., Ward, D., Simmons, C. et al. Microwave-driven coherent operation of a semiconductor quantum dot charge qubit. Nature Nanotech 10, 243–247 (2015).

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