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Acknowledgements

The authors acknowledge the financial support from MEXT Q-LEAP (No.

JPMXS0118067395), KAKENHI (No. 15H05868, 16H06326) and the Collaborative

Research Program of ICR, Kyoto University (2019-103). They also thank Prof H. Kosaka

for helpful discussions.

Author contributions

E.D.H. designed the algorithm, performed the experiments/simulations/analyses and

conceived the supplementary; H.K. grew the phosphorus-doped diamond, assisted by

T.M. and S.Y.; N.M. supervised the work; E.D.H. and N.M. wrote the manuscript, and all

authors discussed it.

Competing interests

The authors declare no competing interests.

Additional information

Supplementary information is available for this paper at https://doi.org/10.1038/s41467020-20561-x.

Correspondence and requests for materials should be addressed to E.D.H. or N.M.

Peer review information Nature Communications thanks the anonymous reviewer(s) for

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