- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

High-fidelity single-qubit quantum state tomography of electron-N14 nuclear hybrid spin register in diamond using Rabi oscillations

Abhishek Shukla1,2,*,†, Boo Carmans1,*, Michael Petrov1,*, Daan Vrancken1,‡, and Milos Nesladek1,2,3,§

  • 1Q-Lab, Hasselt University, Wetenschapspark 1, 3590 Diepenbeek, Belgium
  • 2IMOMEC Division IMEC, Wetenschapspark 1, 3590 Diepenbeek, Belgium
  • 3FBMI-CVUT, Sitna 3105, 27201 Kladno, Czech Republic

  • *These authors contributed equally to this work.
  • †Contact author: abhishek.shukla@uhasselt.be
  • ‡Present address: Center for Molecular Modeling (CMM), Ghent University, Technologiepark 46, 9052 Zwijnaarde, Belgium.
  • §Contact author: milos.nesladek@uhasselt.be
PDF

Phys. Rev. Research 8, 023151 – Published 11 May, 2026

DOI: https://doi.org/10.1103/j1s1-w37c

Abstract

We report on a quantum state characterization method, which we call Rabi-based quantum state tomography (RQST), that we have validated on single-qubit quantum states, in particular on the electron and nuclear spins of a single nitrogen-vacancy (NV) center in diamond, demonstrating high fidelities. The difference of RQST with conventional tomography methods is in the implementation of rotation operators and construction of the density matrix from the measured datasets. We demonstrate efficient quantum state control of the electron spin at room temperature with an average fidelity of 0.995 over more than 40 measurements on different states on the Bloch sphere. Also, we apply the methodology to the dark NV nuclear spin state. The state is read via the electron spin using the C-NOT two-qubit entanglement gate and demonstrates fidelities of the same order.

View figure in article

Physics Subject Headings (PhySH)

Corrections

15 June, 2026

Correction: The omission of a support statement in the Acknowledgments has been fixed.

Article Text

Supplemental Material

References (27)

  1. F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. Brandao, D. A. Buell, et al., Quantum supremacy using a programmable superconducting processor, Nature (London) 574, 505 (2019).
  2. H.-S. Zhong, H. Wang, Y.-H. Deng, M.-C. Chen, L.-C. Peng, Y.-H. Luo, J. Qin, D. Wu, X. Ding, Y. Hu, et al., Quantum computational advantage using photons, Science 370, 1460 (2020).
  3. D. Ristè, M. P. Da Silva, C. A. Ryan, A. W. Cross, A. D. Córcoles, J. A. Smolin, J. M. Gambetta, J. M. Chow, and B. R. Johnson, Demonstration of quantum advantage in machine learning, npj Quantum Inf. 3, 16 (2017).
  4. A. Morvan, B. Villalonga, X. Mi, S. Mandra, A. Bengtsson, P. Klimov, Z. Chen, S. Hong, C. Erickson, I. Drozdov, et al., Phase transition in random circuit sampling, Nature 634, 328 (2024).
  5. B. Andreas, B. Guillaume, J. Binder, B. Thierry, H. Ehm, T. Ehmer, M. Erdmann, G. Norbert, H. Philipp, M. Hess, et al., Industry quantum computing applications, EPJ Quantum Technol. 8, 25 (2021).
  6. J. Zhang, S. S. Hegde, and D. Suter, Fast quantum state tomography in the nitrogen vacancy center of diamond, Phys. Rev. Lett. 130, 090801 (2023).
  7. B. D’Anjou and W. A. Coish, Optimal post-processing for a generic single-shot qubit readout, Phys. Rev. A 89, 012313 (2014).
  8. X. Rong, J. Geng, F. Shi, Y. Liu, K. Xu, W. Ma, F. Kong, Z. Jiang, Y. Wu, and J. Du, Experimental fault-tolerant universal quantum gates with solid-state spins under ambient conditions, Nat. Commun. 6, 8748 (2015).
  9. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, UK, 2010).
  10. E. Neu, C. Hepp, M. Hauschild, S. Gsell, M. Fischer, H. Sternschulte, D. Steinmüller-Nethl, M. Schreck, and C. Becher, Low-temperature investigations of single silicon vacancy colour centres in diamond, New J. Phys. 15, 043005 (2013).
  11. M. H. Metsch, K. Senkalla, B. Tratzmiller, J. Scheuer, M. Kern, J. Achard, A. Tallaire, M. B. Plenio, P. Siyushev, and F. Jelezko, Initialization and readout of nuclear spins via a negatively charged silicon-vacancy center in diamond, Phys. Rev. Lett. 122, 190503 (2019).
  12. V. Ivady, I. Abrikosov, and A. Gali, First principles calculation of spin-related quantities for point defect qubit research, npj Comput. Mater. 4, 76 (2018).
  13. J. Wrachtrup and F. Jelezko, Processing quantum information in diamond, J. Phys.: Condens. Matter 18, S807 (2006).
  14. G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. Hemmer, and F. Jelezko, Ultralong spin coherence time in isotopically engineered diamond, Nat. Mater. 8, 383 (2009).
  15. M. W. Doherty, N. B. Manson, P. Delaney, F. Jelezko, J. Wrachtrup, and L. C. Hollenberg, The nitrogen-vacancy colour centre in diamond, Phys. Rep. 528, 1 (2013) .
  16. J. Stolze and D. Suter, Quantum Computing: A Short Course from Theory to Experiment (Wiley‐VCH Verlag GmbH & Co., Weinheim, Germany, 2008).
  17. P. Siyushev, M. Nesladek, E. Bourgeois, M. Gulka, J. Hruby, T. Yamamoto, M. Trupke, T. Teraji, J. Isoya, and F. Jelezko, Photoelectrical imaging and coherent spin-state readout of single nitrogen-vacancy centers in diamond, Science 363, 728 (2019).
  18. M. Ruf, N. H. Wan, H. Choi, D. Englund, and R. Hanson, Quantum networks based on color centers in diamond, J. Appl. Phys. 130, 070901 (2021).
  19. R. Hanson, V. Dobrovitski, A. Feiguin, O. Gywat, and D. Awschalom, Coherent dynamics of a single spin interacting with an adjustable spin bath, Science 320, 352 (2008).
  20. K. G. Fehler, A. P. Ovvyan, N. Gruhler, W. H. P. Pernice, and A. Kubanek, Efficient coupling of an ensemble of nitrogen vacancy center to the mode of a high-Q, Si3N4 photonic crystal cavity, ACS Nano 13, 6891 (2019).
  21. I. L. Chuang and M. A. Nielsen, Prescription for experimental determination of the dynamics of a quantum black box, J. Mod. Opt. 44, 2455 (1997).
  22. S. Yang, Y. Wang, D. D. B. Rao, T. Hien Tran, A. S. Momenzadeh, M. Markham, D. J. Twitchen, P. Wang, W. Yang, R. Stöhr, P. Neumann, H. Kosaka, and J. Wrachtrup, High-fidelity transfer and storage of photon states in a single nuclear spin, Nat. Photon. 10, 507 (2016).
  23. See Supplemental Material at http://link.aps.org/supplemental/10.1103/j1s1-w37c for a detailed description of sample, hybrid register, Hamiltonian, experimental setup, simulation for the effect of decoherence and other errors on the quantum state, and detailed QST methodology and experimental implementation, including Ref. [24] as cited in the main text.
  24. T. Chakraborty, J. Zhang, and D. Suter, Polarizing the electronic and nuclear spin of the NV-center in diamond in arbitrary magnetic fields: Analysis of the optical pumping process, New J. Phys. 19, 073030 (2017).
  25. P. Neumann, J. Beck, M. Steiner, F. Rempp, H. Fedder, P. R. Hemmer, J. Wrachtrup, and F. Jelezko, Single-shot readout of a single nuclear spin, Science 329, 542 (2010).
  26. T. Joas, F. Ferlemann, R. Sailer, P. J. Vetter, J. Zhang, R. S. Said, T. Teraji, S. Onoda, T. Calarco, G. Genov, M. M. Müller, and F. Jelezko, High-fidelity electron spin gates for scaling diamond quantum registers, Phys. Rev. X 15, 021069 (2025).
  27. E. Bourgeois, M. Gulka, and M. Nesladek, Photoelectric detection and quantum readout of nitrogen-vacancy center spin states in diamond, Adv. Opt. Mater. 8, 1902132 (2020).

Outline

Information

Phys. Rev. Research 8, 023151– Published 11 May, 2026
  • Received 24 January 2024
  • Accepted 14 January 2026
  • Corrected 15 June 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation