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Noise-correlation spectrum for a pair of spin qubits in silicon

Abstract

Semiconductor qubits have a small footprint and so are appealing for building densely integrated quantum processors. However, fabricating them at high densities raises the issue of noise correlated across different qubits, which is of practical concern for scalability and fault tolerance. Here, we analyse and quantify the degree of noise correlation in a pair of neighbouring silicon spin qubits around 100 nm apart. We observe strong interqubit noise correlations with a correlation strength as large as 0.7 at around 1 Hz, even in the regime where the spin–spin exchange interaction contributes negligibly. We find that fluctuations of single-spin precession rates are strongly correlated with exchange noise, showing that they have an electrical origin. Noise cross-correlations have thus enabled us to pinpoint the most influential noise in our device. Our work presents a powerful tool set to assess and identify the noise acting on multiple qubits and highlights the importance of long-range electric noise in densely packed silicon spin qubits.

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Fig. 1: Qubit device and power spectral densities.
Fig. 2: Normalized cross-PSD between bare precession rates.
Fig. 3: Corrected auto-PSDs of the sum (Σ) and the difference (Δ) of the bare precession rates.
Fig. 4: Normalized cross-PSD between a bare precession rate and the exchange.

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Data availability

All data in this study are available from the Zenodo repository at https://doi.org/10.5281/zenodo.7467057. Source data are provided with this paper.

References

  1. de Leon, N. P. et al. Materials challenges and opportunities for quantum computing hardware. Science 372, eabb2823 (2021).

    Article  ADS  Google Scholar 

  2. Barends, R. et al. Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature 508, 500–503 (2014).

    Article  ADS  Google Scholar 

  3. Ballance, C. J., Harty, T. P., Linke, N. M., Sepiol, M. A. & Lucas, D. M. High-fidelity quantum logic gates using trapped-ion hyperfine qubits. Phys. Rev. Lett. 117, 060504 (2016).

    Article  ADS  Google Scholar 

  4. Rong, X. et al. Experimental fault-tolerant universal quantum gates with solid-state spins under ambient conditions. Nat. Commun. 6, 8748 (2015).

    Article  ADS  Google Scholar 

  5. 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).

    Article  ADS  Google Scholar 

  6. Noiri, A. et al. Fast universal quantum gate above the fault-tolerance threshold in silicon. Nature 601, 338–342 (2022).

    Article  ADS  Google Scholar 

  7. Xue, X. et al. Quantum logic with spin qubits crossing the surface code threshold. Nature 601, 343–347 (2022).

    Article  ADS  Google Scholar 

  8. Klesse, R. & Frank, S. Quantum error correction in spatially correlated quantum noise. Phys. Rev. Lett. 95, 230503 (2005).

    Article  ADS  Google Scholar 

  9. Google Quantum AI. Exponential suppression of bit or phase errors with cyclic error correction. Nature 595, 383–387 (2021).

    Article  Google Scholar 

  10. Wilen, C. D. et al. Correlated charge noise and relaxation errors in superconducting qubits. Nature 594, 369–373 (2021).

    Article  ADS  Google Scholar 

  11. von Lüpke, U. et al. Two-qubit spectroscopy of spatiotemporally correlated quantum noise in superconducting qubits. PRX Quantum 1, 010305 (2020).

    Article  Google Scholar 

  12. Szańkowski, P., Trippenbach, M., & Cywiński, Ł. Spectroscopy of cross correlations of environmental noises with two qubits. Phys. Rev. A 94, 012109 (2016).

    Article  ADS  Google Scholar 

  13. Paz-Silva, G. A., Norris, L. M. & Viola, L. Multiqubit spectroscopy of Gaussian quantum noise. Phys. Rev. A 95, 022121 (2017).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. Struck, T. et al. Low-frequency spin qubit energy splitting noise in highly purified 28Si/SiGe. npj Quantum Inf. 6, 40 (2020).

    Article  ADS  Google Scholar 

  16. Boter, J. M. et al. Spatial noise correlations in a Si/SiGe two-qubit device from Bell state coherences. Phys. Rev. B 101, 235133 (2020).

    Article  ADS  Google Scholar 

  17. Gutiérrez-Rubio, Á. et al. Bayesian estimation of correlation functions. Phys. Rev. Res. 4, 043166 (2022).

    Article  Google Scholar 

  18. Kerckhoff, J. et al. Magnetic gradient fluctuations from quadrupolar 73Ge in Si/SiGe exchange-only qubits. PRX Quantum 2, 010347 (2021).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  20. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Rev. Mod. Phys. 86, 361–418 (2014).

    Article  ADS  Google Scholar 

  21. Stano, P. & Loss, D. Review of performance metrics of spin qubits in gated semiconducting nanostructures. Nat. Rev. Phys. 4, 672–688 (2022).

    Article  Google Scholar 

  22. Burkard, G., Ladd, T. D., Nichol, J. M., Pan, A. & Petta, J. R. Semiconductor spin qubits. Rev. Mod. Phys. 95, 025003 (2023).

  23. Xue, X. et al. Benchmarking gate fidelities in a Si/SiGe two-qubit device. Phys. Rev. 9, 021011 (2019).

    Article  Google Scholar 

  24. Mills, A. et al. Two-qubit silicon quantum processor with operation fidelity exceeding 99%. Sci. Adv. 8, eabn5130 (2021).

    Article  Google Scholar 

  25. Gonzalez-Zalba, M. F. et al. Scaling silicon-based quantum computing using CMOS technology. Nat. Electron. 4, 872–884 (2021).

    Article  Google Scholar 

  26. Yoneda, J. et al. Quantum non-demolition readout of an electron spin in silicon. Nat. Commun. 11, 1144 (2020).

    Article  ADS  Google Scholar 

  27. Noiri, A. et al. Radio-frequency-detected fast charge sensing in undoped silicon quantum dots. Nano Lett. 20, 947–952 (2020).

    Article  ADS  Google Scholar 

  28. Eshraghi, M. J., Sasada, I., Kim, J. M. & Lee, Y. H. Characterization of a low frequency magnetic noise from a two-stage pulse tube cryocooler. Cryogenics 49, 334–339 (2009).

    Article  ADS  Google Scholar 

  29. Kalra, R. et al. Vibration-induced electrical noise in a cryogen- free dilution refrigerator: characterization, mitigation, and impact on qubit coherence. Rev. Sci. Instrum. 87, 073905 (2016).

    Article  ADS  Google Scholar 

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Acknowledgements

We are grateful to Á. Gutiérrez-Rubio for fruitful discussions. Part of this work was financially supported by MEXT Quantum Leap Flagship Programme (MEXT Q-LEAP) grant no. JPMXS0118069228 (S.T.), JST PRESTO grant nos. JPMJPR21BA (J.Y.) and JPMJPR2017 (T.N.), JST Moonshot R&D grant nos. JPMJMS2065 (J.Y., T.N.) and JPMJMS226B (S.T., T.N.), JST CREST grant no. JPMJCR1675 (S.T., D.L.), JSPS KAKENHI grant nos. JP21K14485 (J.Y.), JP23H01790 (J.Y., A.N.) and JP23H05455 (J.Y., K.T.), Swiss National Science Foundation and NCCR SPIN grant no. 51NF40-180604 (D.L.), The Precise Measurement Technology Promotion Foundation (J.Y.), Suematsu Fund (J.Y.) and Advanced Technology Institute Research Grants (J.Y.).

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J.Y. conceived and performed the experiment. J.S.R.-A. and P.S. assisted J.Y. with data analysis and performed device modelling. K.T. fabricated the device. A.N. and T.N. contributed to the measurement setup. D.L. and S.T. supervised the project.

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Correspondence to J. Yoneda or S. Tarucha.

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The authors declare no competing interests.

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Nature Physics thanks Natalia Ares, Łukasz Cywiński and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Sections I–VI and Figs. 1–12.

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Yoneda, J., Rojas-Arias, J.S., Stano, P. et al. Noise-correlation spectrum for a pair of spin qubits in silicon. Nat. Phys. 19, 1793–1798 (2023). https://doi.org/10.1038/s41567-023-02238-6

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