Coherent spin-state transfer via Heisenberg exchange

Abstract

Quantum information science has the potential to revolutionize modern technology by providing resource-efficient approaches to computing1, communication2 and sensing3. Although the physical qubits in a realistic quantum device will inevitably suffer errors, quantum error correction creates a path to fault-tolerant quantum information processing4. Quantum error correction, however, requires that individual qubits can interact with many other qubits in the processor. Engineering such high connectivity can pose a challenge for platforms such as electron spin qubits5, which naturally favour linear arrays. Here we present an experimental demonstration of the transmission of electron spin states via the Heisenberg exchange interaction in an array of spin qubits. Heisenberg exchange coupling—a direct manifestation of the Pauli exclusion principle, which prevents any two electrons with the same spin state from occupying the same orbital—tends to swap the spin states of neighbouring electrons. By precisely controlling the wavefunction overlap between electrons in a semiconductor quadruple quantum dot array, we generate a series of coherent SWAP operations to transfer both single-spin and entangled states back and forth in the array without moving any electrons. Because the process is scalable to large numbers of qubits, state transfer through Heisenberg exchange will be useful for multi-qubit gates and error correction in spin-based quantum computers.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Experimental setup.
Fig. 2: Coherent exchange oscillations between all nearest-neighbour pairs of spins.
Fig. 3: Spin-state transfer via Heisenberg exchange.
Fig. 4: Transfer of entangled states via Heisenberg exchange.

References

  1. 1.

    Ekert, A. & Jozsa, R. Quantum computation and Shor’s factoring algorithm. Rev. Mod. Phys. 68, 733–753 (1996).

    CAS  Article  ADS  MathSciNet  Google Scholar 

  2. 2.

    Kimble, H. J. The quantum internet. Nature 453, 1023–1030 (2008).

    CAS  Article  ADS  PubMed  PubMed Central  Google Scholar 

  3. 3.

    Degen, C. L., Reinhard, F. & Cappellaro, P. Quantum sensing. Rev. Mod. Phys. 89, 035002 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  4. 4.

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

    CAS  Article  ADS  PubMed  PubMed Central  Google Scholar 

  5. 5.

    Ladd, T. D. et al. Quantum computers. Nature 464, 45–53 (2010).

    CAS  Article  ADS  PubMed  PubMed Central  Google Scholar 

  6. 6.

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

    CAS  Article  ADS  Google Scholar 

  7. 7.

    Kane, B. E. A silicon-based nuclear spin quantum computer. Nature 393, 133–137 (1998).

    CAS  Article  ADS  Google Scholar 

  8. 8.

    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 (2018).

    CAS  Article  ADS  PubMed  PubMed Central  Google Scholar 

  9. 9.

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

    CAS  Article  ADS  Google Scholar 

  10. 10.

    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).

    CAS  Article  ADS  PubMed  PubMed Central  Google Scholar 

  11. 11.

    Huang, W. et al. Fidelity benchmarks for two-qubit gates in silicon. Nature 569, 532–536 (2019).

    CAS  Article  ADS  PubMed  PubMed Central  Google Scholar 

  12. 12.

    Zajac, D. M., Hazard, T. M., Mi, X., Nielsen, E. & Petta, J. R. Scalable gate architecture for densely packed semiconductor spin qubits. Phys. Rev. Appl. 6, 054013 (2016).

    Article  ADS  CAS  Google Scholar 

  13. 13.

    Mortemousque, P.-A. et al. Coherent control of individual electron spins in a two dimensional array of quantum dots. Preprint at https://arxiv.org/abs/1808.06180 (2018).

  14. 14.

    Mukhopadhyay, U., Dehollain, J. P., Reichl, C., Wegscheider, W. & Vandersypen, L. M. K. A 2 × 2 quantum dot array with controllable inter-dot tunnel couplings. Appl. Phys. Lett. 112, 183505 (2018).

    Article  ADS  CAS  Google Scholar 

  15. 15.

    Volk, C. et al. Loading a quantum-dot based “Qubyte” register. npj Quantum Inf. 5, 29 (2019).

    Article  ADS  Google Scholar 

  16. 16.

    Mi, X. et al. A coherent spin–photon interface in silicon. Nature 555, 599–603 (2018).

    CAS  Article  ADS  PubMed  PubMed Central  Google Scholar 

  17. 17.

    Samkharadze, N. et al. Strong spin-photon coupling in silicon. Science 359, 1123–1127 (2018).

    CAS  Article  ADS  PubMed  PubMed Central  Google Scholar 

  18. 18.

    Landig, A. J. et al. Coherent spin–photon coupling using a resonant exchange qubit. Nature 560, 179–184 (2018).

    CAS  Article  ADS  PubMed  PubMed Central  Google Scholar 

  19. 19.

    Mills, A. R. et al. Shuttling a single charge across a one-dimensional array of silicon quantum dots. Nat. Commun. 10, 1063 (2019).

    CAS  Article  ADS  PubMed  PubMed Central  Google Scholar 

  20. 20.

    Fujita, T., Baart, T. A., Reichl, C., Wegscheider, W. & Vandersypen, L. M. K. Coherent shuttle of electron-spin states. npj Quantum Inf. 3, 22 (2017).

    Article  ADS  Google Scholar 

  21. 21.

    Flentje, H. et al. Coherent long-distance displacement of individual electron spins. Nat. Commun. 8, 501 (2017).

    CAS  Article  ADS  PubMed  PubMed Central  Google Scholar 

  22. 22.

    Nakajima, T. et al. Coherent transfer of electron spin correlations assisted by dephasing noise. Nat. Commun. 9, 2133 (2018).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  23. 23.

    Baart, T. A. et al. Single-spin CCD. Nat. Nanotechnol. 11, 330–334 (2016).

    CAS  Article  ADS  PubMed  PubMed Central  Google Scholar 

  24. 24.

    Greentree, A. D., Cole, J. H., Hamilton, A. R. & Hollenberg, L. C. L. Coherent electronic transfer in quantum dot systems using adiabatic passage. Phys. Rev. B 70, 235317 (2004).

    Article  ADS  CAS  Google Scholar 

  25. 25.

    Shilton, J. M. et al. High-frequency single-electron transport in a quasi-one-dimensional GaAs channel induced by surface acoustic waves. J. Phys. Condens. Matter 8, 531–539 (1996).

    Article  Google Scholar 

  26. 26.

    Bertrand, B. et al. Fast spin information transfer between distant quantum dots using individual electrons. Nat. Nanotechnol. 11, 672–676 (2016).

    CAS  Article  ADS  PubMed  PubMed Central  Google Scholar 

  27. 27.

    Baart, T. A., Fujita, T., Reichl, C., Wegscheider, W. & Vandersypen, L. M. K. Coherent spin-exchange via a quantum mediator. Nat. Nanotechnol. 12, 26–30 (2017).

    CAS  Article  ADS  PubMed  PubMed Central  Google Scholar 

  28. 28.

    Malinowski, F. K. et al. Fast spin exchange across a multielectron mediator. Nat. Commun. 10, 1196 (2019).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  29. 29.

    Aharonov, D. & Ben-Or, M. Fault-tolerant quantum computation with constant error. In Proc. Twenty-ninth Annual ACM Symposium on Theory of Computing 176–188 (ACM Press, 1997).

  30. 30.

    Gottesman, D. Fault-tolerant quantum computation with local gates. J. Mod. Opt. 47, 333–345 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  31. 31.

    Fowler, A. G., Hill, C. D. & Hollenberg, L. C. L. Quantum-error correction on linear-nearest-neighbor qubit arrays. Phys. Rev. A 69, 042314 (2004).

    Article  ADS  CAS  Google Scholar 

  32. 32.

    Friesen, M., Biswas, A., Hu, X. & Lidar, D. Efficient multiqubit entanglement via a spin bus. Phys. Rev. Lett. 98, 230503 (2007).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  33. 33.

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

    CAS  Article  ADS  PubMed  PubMed Central  Google Scholar 

  34. 34.

    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).

    CAS  Article  ADS  PubMed  PubMed Central  Google Scholar 

  35. 35.

    Zajac, D. M., Hazard, T. M., Mi, X., Wang, K. & Petta, J. R. A reconfigurable gate architecture for Si/SiGe quantum dots. Appl. Phys. Lett. 106, 223507 (2015).

    Article  ADS  CAS  Google Scholar 

  36. 36.

    Nichol, J. M. et al. Quenching of dynamic nuclear polarization by spin–orbit coupling in GaAs quantum dots. Nat. Commun. 6, 7682 (2015).

    CAS  Article  ADS  PubMed  PubMed Central  Google Scholar 

  37. 37.

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

    CAS  Article  Google Scholar 

  38. 38.

    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  CAS  Google Scholar 

  39. 39.

    Shulman, M. D. et al. Suppressing qubit dephasing using real-time Hamiltonian estimation. Nat. Commun. 5, 5156 (2014).

    CAS  Article  ADS  PubMed  PubMed Central  Google Scholar 

  40. 40.

    Bluhm, H., Foletti, S., Mahalu, D., Umansky, V. & Yacoby, A. Enhancing the coherence of a spin qubit by operating it as a feedback loop that controls its nuclear spin bath. Phys. Rev. Lett. 105, 216803 (2010).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  41. 41.

    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).

    CAS  Article  ADS  PubMed  PubMed Central  Google Scholar 

  42. 42.

    Studenikin, S. et al. Enhanced charge detection of spin qubit readout via an intermediate state. Appl. Phys. Lett. 101, 233101 (2012).

    Article  ADS  CAS  Google Scholar 

  43. 43.

    Reed, M. D. et al. Reduced sensitivity to charge noise in semiconductor spin qubits via symmetric operation. Phys. Rev. Lett. 116, 110402 (2016).

    CAS  Article  ADS  PubMed  PubMed Central  Google Scholar 

  44. 44.

    Martins, F. et al. Noise suppression using symmetric exchange gates in spin qubits. Phys. Rev. Lett. 116, 116801 (2016).

    Article  ADS  MathSciNet  CAS  PubMed  PubMed Central  Google Scholar 

  45. 45.

    Orona, L. A. et al. Readout of singlet–triplet qubits at large magnetic field gradients. Phys. Rev. B 98, 125404 (2018).

    CAS  Article  ADS  Google Scholar 

  46. 46.

    Wang, X. et al. Composite pulses for robust universal control of singlet–triplet qubits. Nat. Commun. 3, 997 (2012).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  47. 47.

    Nichol, J. M., Orona, L. A., Harvey, S. P., Fallahi, S., Gardner, G. C., Manfra, M. J. & Yacoby, A. High-fidelity entangling gate for double-quantum-dot spin qubits. npj Quantum Inf. 3, 3 (2017).

    Article  ADS  Google Scholar 

  48. 48.

    Sigillito, A. J., Gullans, M. J., Edge, L. F., Borselli, M. & Petta, J. R. Coherent transfer of quantum information in silicon using resonant SWAP gates. Preprint at https://arxiv.org/abs/1906.04512 (2019).

Download references

Acknowledgements

This work was sponsored the Defense Advanced Research Projects Agency under grant number D18AC00025 and the Army Research Office under grant numbers W911NF-16-1-0260 and W911NF-19-1-0167. 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. The US Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.

Author information

Affiliations

Authors

Contributions

Y.P.K., H.Q. and J.M.N. fabricated the device and performed the experiments. S.F., G.C.G. and M.J.M. grew and characterized the AlGaAs/GaAs heterostructure. All authors discussed and analysed the data and wrote the manuscript.

Corresponding author

Correspondence to John M. Nichol.

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.

Peer review information Nature thanks Andrew Dzurak and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Extended data figures and tables

Extended Data Fig. 1 Experimental data showing four-dot transfer of entangled states.

a, Schematic of the four-dot entangled-state transfer process. b, Interleaved data showing (I, ΔB, I), (S23, ΔB, S23) and (S23, S12, ΔB, S12, S23) measurements. c, Data from repetition 2, plotted on the same horizontal axis. d, Time evolution of the different magnetic gradients. Because the gradients result from different nuclear-spin configurations, they have different values and time evolutions. Error bars are fitting errors.

Extended Data Fig. 2 Results of the three-dot state transfer simulation.

The simulation results show good agreement with the data in Fig. 2 (see Methods). a, Simulated right-side measurements for the S34, S34, S23, S23, S34, S34 sequence. b, Simulated left-side measurements for the same sequence. c, Simulated right-side measurements for the three-dot state transfer control sequence with I in place of S34. d, Simulated left-side measurements for the same sequence. e, Simulated right-side measurements for the three-dot control sequence with I in place of S23. f, Simulated left-side measurements for the same sequence.

Extended Data Fig. 3 Results of the four-dot state transfer simulation.

The simulation results show good agreement with the data in Fig. 2 (see Methods). a, Simulated right-side measurements for the S23, S12, S12, S23, S34, S34 sequence. b, Simulated left-side measurements for the same sequence.

Extended Data Fig. 4 Calibration of SWAP operations by pulse concatenation.

Each panel shows the results of concatenating specific operations. Each SWAP operation is implemented by a separate voltage pulse to a barrier gate. a, Right-side measurements for repeated S12 operations. Prior to the first step, the array was initialized in the \(\left|\downarrow \uparrow \downarrow \uparrow \right\rangle \) state. b, Left-side measurements for repeated S12 operations. c, Right-side measurements for repeated S34 operations. Prior to the first step, the array was initialized in the \(\left|\downarrow \uparrow \downarrow \uparrow \right\rangle \) state. d, Left-side measurements for repeated S34 operations. e, Right-side measurements for repeated S23 operations. The array was initialized in the \(\left|\uparrow \uparrow \downarrow \uparrow \right\rangle \) state. We did not record left-side measurements for this sequence. In all panels, vertical black lines indicate error bars, which represent the standard deviation of 64 repetitions of the average of 64 single-shot measurements of each pulse configuration.

Extended Data Fig. 5 Simulated fidelity of SWAP pulses for entangled states.

a, Simulated ensemble-averaged state fidelity after applying a simulated realistic S23 operation to the initial state \(\left|{\psi }_{0}\right\rangle =\frac{1}{\sqrt{2}}\left(\left|\uparrow \uparrow \uparrow \downarrow \right\rangle -\left|\uparrow \uparrow \downarrow \uparrow \right\rangle \right)\). The target state is \(\left|{\psi }_{t}\right\rangle =\frac{1}{\sqrt{2}}\left(\left|\uparrow \uparrow \uparrow \downarrow \right\rangle -\left|\uparrow \downarrow \uparrow \uparrow \right\rangle \right)\). The horizontal axis represents the free-evolution time of the state under the influence of the magnetic gradient after the exchange operation. The fidelity is averaged over 2,000 different simulations of magnetic and electrical noise. The state fidelity has a maximum of about 0.65, and it quickly decays to 0.5. The decay results from the fluctuating magnetic gradient. b, Calculated characteristic single-shot state fidelity for one simulation of the noise. For specific times, the state fidelity returns to about 0.9. The magnetic gradient is assumed to be stable in each realization of the sequence.

Extended Data Fig. 6 Preparation of quadruple quantum dot state.

a, Verification of exchange oscillations on the left side. Initializing the left side in the \(\left|\uparrow \uparrow \right\rangle \) state before a T12 pulse yields no exchange oscillations. Initialization in the \(\left|\downarrow \uparrow \right\rangle \) state shows exchange oscillations. b, Initializing the right side in the \(\left|\uparrow \uparrow \right\rangle \) state before a T34 pulse yields no exchange oscillations. Initialization in the \(\left|\downarrow \uparrow \right\rangle \) state shows exchange oscillations. c, Verification of the ground-state orientation of the right side. We load the left side in the \(\left|\uparrow \uparrow \right\rangle \) state and the right side by adiabatic separation of the singlet state, which gives either \(\left|\uparrow \downarrow \right\rangle \) or \(\left|\downarrow \uparrow \right\rangle \), depending on the sign of the gradient. We pulse T23 to induce exchange between the middle two spins. Dynamic nuclear polarization with singlets yields no oscillations, whereas pumping with triplets yields oscillations. These data confirm that the separated singlet state evolves to the \(\left|\downarrow \uparrow \right\rangle \) state under triplet pumping for the right side. d, Verification of the ground state of the left side. We initialize the array by separating singlets on both sides. In the case of triplet pumping on the right side, the third spin is \(\left|\downarrow \right\rangle \), so the second spin must be \(\left|\uparrow \right\rangle \) in order to generate exchange oscillations with a T23 pulse, as measured on the left side. Singlet pumping on the left side yields no exchange oscillations. e, The same initialization and pulses as in e, but measured on the right side. In all cases, \({P}_{{\rm{S}}}^{{\rm{L}}\left({\rm{R}}\right)}\) indicates the singlet return probability measured on the left (right) side.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kandel, Y.P., Qiao, H., Fallahi, S. et al. Coherent spin-state transfer via Heisenberg exchange. Nature 573, 553–557 (2019). https://doi.org/10.1038/s41586-019-1566-8

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

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