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Self-consistent measurement and state tomography of an exchange-only spin qubit

Nature Nanotechnology volume 8, pages 654–659 (2013)Cite this article

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Abstract

Quantum-dot spin qubits characteristically use oscillating magnetic or electric fields, or quasi-static Zeeman field gradients, to realize full qubit control. For the case of three confined electrons, exchange interaction between two pairs allows qubit rotation around two axes, hence full control, using only electrostatic gates. Here, we report initialization, full control, and single-shot readout of a three-electron exchange-driven spin qubit. Control via the exchange interaction is fast, yielding a demonstrated 75 qubit rotations in less than 2 ns. Measurement and state tomography are performed using a maximum-likelihood estimator method, allowing decoherence, leakage out of the qubit state space, and measurement fidelity to be quantified. The methods developed here are generally applicable to systems with state leakage, noisy measurements and non-orthogonal control axes.

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Figure 1: Device, qubit Bloch sphere and spectrum.
Figure 2: Charge stability diagram and rotations around two axes.
Figure 3: Fast rotation and visibility model.
Figure 4: Effects of electrical and nuclear noise.
Figure 5: Dynamical decoupling.
Figure 6: Measurement and state tomography.

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References

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

    Article  CAS  Google Scholar 

  2. 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 

  3. 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 

  4. Gaudreau, L. et al. Coherent control of three-spin states in a triple quantum dot. Nature Phys. 8, 54–58 (2011).

    Article  Google Scholar 

  5. Nadj-Perge, S., Frolov, S., Bakkers, E. & Kouwenhoven, L. P. Spin–orbit qubit in a semiconductor nanowire. Nature 468, 1084–1087 (2010).

    Article  CAS  Google Scholar 

  6. Laird, E. A. et al. Hyperfine-mediated gate-driven electron spin resonance. Phys. Rev. Lett. 99, 246601 (2007).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  8. 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  CAS  Google Scholar 

  9. Petta, J. R., Lu, H. & Gossard, A. C. A coherent beam splitter for electronic spin states. Science 327, 669–672 (2010).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  12. Hawrylak, P. & Korkusinski, M. Voltage-controlled coded quit based on electron spin. Solid State Commun. 136, 508–512 (2005).

    Article  CAS  Google Scholar 

  13. Rogge, M. C. & Haug, R. J. The three dimensionality of triple quantum dot stability diagrams. New J. Phys. 11, 113037 (2009).

    Article  Google Scholar 

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

    Article  Google Scholar 

  15. Takakura, T. et al. Triple quantum dot device designed for three spin quits. Appl. Phys. Lett. 97, 212104 (2010).

    Article  Google Scholar 

  16. Hsieh, C., Shim, Y., Korkusinski, M. & Hawrylak, P. Physics of lateral triple quantum-dot molecules with controlled electron numbers. Rep. Prog. Phys. 75, 114501 (2012).

    Article  Google Scholar 

  17. Mehl, S. & DiVincenzo, D. P. Noise analysis of qubits implemented in triple quantum dot systems in a davies master equation approach. Preprint at http://lanl.arxiv.org/abs/1211.0417 (2012).

  18. West, J. R. & Fong, B. H. Exchange-only dynamical decoupling in the 3-qubit decoherence free subsystem. Preprint at http://lanl.arxiv.org/abs/1203.4296 (2012).

  19. Lundeen, J. et al. Tomography of quantum detectors. Nature Phys. 5, 27–30 (2008).

    Article  Google Scholar 

  20. Brida, G. et al. Quantum characterization of superconducting photon counters. New J. Phys. 14, 085001 (2012).

    Article  Google Scholar 

  21. Merkel, S. T. et al. Self-consistent quantum process tomography. Phys. Rev. A 87, 062119 (2013).

    Article  Google Scholar 

  22. Buchachenko, A. L. & Berdinsky, V. L. Electron spin catalysis. Chem. Rev. 102, 603–612 (2002).

    Article  CAS  Google Scholar 

  23. Reilly, D. J., Marcus, C. M., Hanson, M. P. & Gossard, A. C. Fast single-charge sensing with a rf quantum point contact. Appl. Phys. Lett. 91, 162101 (2007).

    Article  Google Scholar 

  24. Cywiński, Ł., Lutchyn, R. M., Nave, C. P. & Das Sarma, S. How to enhance dephasing time in superconducting qubits. Phys. Rev. B 77, 174509 (2008).

    Article  Google Scholar 

  25. Ladd, T. D. Hyperfine-induced decay in triple quantum dots. Phys. Rev. B 86, 125408 (2012).

    Article  Google Scholar 

  26. Reilly, D. J. et al. Measurement of temporal correlations of the Overhauser field in a double quantum dot. Phys. Rev. Lett. 101, 236803 (2008).

    Article  CAS  Google Scholar 

  27. Koppens, F. H. L. et al. Universal phase shift and nonexponential decay of driven single-spin oscillations. Phys. Rev. Lett. 99, 106803 (2007).

    Article  CAS  Google Scholar 

  28. Bluhm, H. et al. Dephasing time of gaas electron-spin qubits coupled to a nuclear bath exceeding 200 µs. Nature Phys. 7, 109–113 (2010).

    Article  Google Scholar 

  29. Medford, J. et al. Scaling of dynamical decoupling for spin qubits. Phys. Rev. Lett. 108, 086802 (2012).

    Article  CAS  Google Scholar 

  30. Barthel, C., Reilly, D. J., Marcus, C. M., Hanson, M. P. & Gossard, A. C. Rapid single-shot measurement of a singlet–triplet qubit. Phys. Rev. Lett. 103, 160503 (2009).

    Article  CAS  Google Scholar 

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Acknowledgements

The authors acknowledge support from the Intelligence Advanced Research Projects Agency (IARPA) through the Multi-Qubit Coherent Operation (MQCO) programme, the Danish National Research Foundation and the Villum Foundation. S.B. and A.D. acknowledge support from the Australian Research Council (ARC) via the Centre of Excellence in Engineered Quantum Systems (EQuS), project number CE110001013. The authors thank O. Dial, B. Halperin, F. Kuemmeth, T. Ladd and A. Yacoby for useful discussions, and B. Armstrong for technical contributions.

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Authors and Affiliations

  1. Department of Physics, Harvard University, Cambridge, 02138, Massachusetts, USA

    J. Medford, J. Beil, E. I. Rashba & C. M. Marcus

  2. Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, Copenhagen, DK-2100, Denmark

    J. Beil & C. M. Marcus

  3. Joint Quantum Institute/NIST, College Park, Maryland, USA

    J. M. Taylor

  4. Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, NSW 2006, Australia

    S. D. Bartlett & A. C. Doherty

  5. Institute for Quantum Information, RWTH Aachen University, Aachen, 52056, Germany

    D. P. DiVincenzo

  6. Department of Theoretical Nanoelectronics, PGI, Forschungszentrum Juelich, Juelich, 52425, Germany

    D. P. DiVincenzo

  7. Materials Department, University of California, Santa Barbara, 93106, California, USA

    H. Lu & A. C. Gossard

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  1. J. Medford
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  10. C. M. Marcus
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Contributions

H.L. and A.G. grew the heterostructure. J.M. fabricated the device and built the measurement set-up. J.M. and J.B. measured the device. J.T., S.B., A.D., D.V. and E.R. provided the theoretical framework for the results. J.M., J.B. and C.M. analysed the data. J.M., J.B., S.B., A.D., E.R. and C.M. wrote the paper. All authors contributed to the design of the experiment.

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Correspondence to C. M. Marcus.

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The authors declare no competing financial interests.

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Medford, J., Beil, J., Taylor, J. et al. Self-consistent measurement and state tomography of an exchange-only spin qubit. Nature Nanotech 8, 654–659 (2013). https://doi.org/10.1038/nnano.2013.168

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