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  • Open Access

Qubit sensing by optimal narrowband pulses: Demonstration for Rabi frequency sensing

Meri Harutyunyan1, Bruno Peaudecerf2, Dominique Sugny1, and Stéphane Guérin1,*

  • *Contact author: sguerin@u-bourgogne.fr
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Phys. Rev. Research 7, 043255 – Published 8 December, 2025

DOI: https://doi.org/10.1103/gt51-g34c

Abstract

Narrowband optimal control is proposed as a protocol of optimal quantum sensing, providing maximum accuracy for given resources. The procedure is demonstrated on the IBM quantum computer to estimate the amplitude of the qubit Rabi frequency. It is based on optimizing the quantum Fisher information (QFI) when it becomes equal to the classical Fisher information. This scenario offers a practical quantum sensing because it only involves population transfer to the excited state as the target without dynamical phases, which would otherwise be difficult to control and measure. The protocol uses the single-shot-shaped pulse method and an inverse optimization, to design a pulse that results in the optimal QFI in terms of energy or equivalently operating time, referred to in short as local narrowband inverse optimization (NIO). Multiple π pulses are shown to be particular cases of this protocol. An alternative semiglobal optimal NIO procedure producing a partially nonoscillatory profile is also demonstrated. Our approach also offers application to optimal atomic selective excitation in an array of atoms for quantum technology.

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References (51)

  1. V. Giovannetti, S. Lloyd, and L. Maccone, Quantum-enhanced measurements: Beating the standard quantum limit, Science 306, 1330 (2004).
  2. V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nat. Photon. 5, 222 (2011).
  3. D. Ma, V. Gulani, N. Seiberlich, K. Liu, J. L. Sunshine, J. L. Duerk, and M. A. Griswold, Magnetic resonance fingerprinting, Nature (London) 495, 187 (2013).
  4. J. Liu and H. Yuan, Control-enhanced multiparameter quantum estimation, Phys. Rev. A 96, 042114 (2017).
  5. J. Yang, S. Pang, and A. N. Jordan, Quantum parameter estimation with the Landau-Zener transition, Phys. Rev. A 96, 020301 (2017).
  6. C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys. 89, 035002 (2017).
  7. T. Gefen, F. Jelezko, and A. Retzker, Control methods for improved Fisher information with quantum sensing, Phys. Rev. A 96, 032310 (2017).
  8. F. Poggiali, P. Cappellaro, and N. Fabbri, Optimal control for one-qubit quantum sensing, Phys. Rev. X 8, 021059 (2018).
  9. Z. Hou, R.-J. Wang, J.-F. Tang, H. Yuan, G.-Y. Xiang, C.-F. Li, and G.-C. Guo, Control enhanced sequential scheme for general quantum parameter estimation at the Heisenberg limit, Phys. Rev. Lett. 123, 040501 (2019).
  10. L. Liu and H. Yuan, Achieving higher precision in quantum parameter estimation with feedback controls, Phys. Rev. A 102, 012208 (2020).
  11. D. Basilewitsch, H. Yuan, and C. P. Koch, Optimally controlled quantum discrimination and estimation, Phys. Rev. Res. 2, 033396 (2020).
  12. P. Rembold, N. Oshnik, M. M. Müller, S. Montangero, T. Calarco, and E. Neu, Introduction to quantum optimal control for quantum sensing with nitrogen-vacancy centers in diamond, AVS Quantum Sci. 2, 024701 (2020).
  13. S. A. Haine and J. J. Hope, Machine-designed sensor to make optimal use of entanglement generating dynamics for quantum sensing, Phys. Rev. Lett. 124, 060402 (2020).
  14. H. Xu, L. Wang, H. Yuan, and X. Wang, Generalizable control for multiparameter quantum metrology, Phys. Rev. A 103, 042615 (2021).
  15. J. Liu, M. Zhang, H. Chen, L. Wang, and H. Yuan, Optimal scheme for quantum metrology, Adv. Quantum Tech. 5, 2100080 (2022).
  16. J. Yang, S. Pang, Z. Chen, A. N. Jordan, and A. del Campo, Variational principle for optimal quantum controls in quantum metrology, Phys. Rev. Lett. 128, 160505 (2022).
  17. C. Lin, Y. Ma, and D. Sels, Application of Pontryagin’s maximum principle to quantum metrology in dissipative systems, Phys. Rev. A 105, 042621 (2022).
  18. M. Zhang, H.-M. Yu, H. Yuan, X. Wang, R. Demkowicz-Dobrzanski, and J. Liu, QuanEstimation: An open-source toolkit for quantum parameter estimation, Phys. Rev. Res. 4, 043057 (2022).
  19. Y. Zhai, X. Yang, K. Tang, X. Long, X. Nie, T. Xin, D. Lu, and J. Li, Control enhanced quantum metrology under Markovian noise, Phys. Rev. A 107, 022602 (2023).
  20. J. T. Reilly, J. D. Wilson, S. B. Jäger, C. Wilson, and M. J. Holland, Optimal generators for quantum sensing, Phys. Rev. Lett. 131, 150802 (2023).
  21. J. C. Pelayo, K. Gietka, and T. Busch, Distributed quantum sensing with optical lattices, Phys. Rev. A 107, 033318 (2023).
  22. K. Herb and C. L. Degen, Quantum speed limit in quantum sensing, Phys. Rev. Lett. 133, 210802 (2024).
  23. D. Louzon, G. T. Genov, N. Staudenmaier, F. Frank, J. Lang, M. L. Markham, A. Retzker, and F. Jelezko, Robust noise suppression and quantum sensing by continuous phased dynamical decoupling, Phys. Rev. Lett. 134, 120802 (2025).
  24. S. Pang and A. N. Jordan, Optimal adaptive control for quantum metrology with time-dependent Hamiltonians, Nat. Commun. 8, 14695 (2017).
  25. M. Naghiloo, A. N. Jordan, and K. W. Murch, Achieving optimal quantum acceleration of frequency estimation using adaptive coherent control, Phys. Rev. Lett. 119, 180801 (2017).
  26. J. Liu and H. Yuan, Quantum parameter estimation with optimal control, Phys. Rev. A 96, 012117 (2017).
  27. D. Guéry-Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez-Garaot, and J. G. Muga, Shortcuts to adiabaticity: Concepts, methods, and applications, Rev. Mod. Phys. 91, 045001 (2019).
  28. U. Boscain, M. Sigalotti, and D. Sugny, Introduction to the Pontryagin maximum principle for quantum optimal control, PRX Quantum 2, 030203 (2021).
  29. D. Stefanatos and E. Paspalakis, A shortcut tour of quantum control methods for modern quantum technologies, Europhys. Lett. 132, 60001 (2020).
  30. C. P. Koch, U. Boscain, T. Calarco, G. Dirr, S. Filipp, S. Glaser, R. Kosloff, S. Montangero, T. Schulte-Herbruggen, D. Sugny, and F. K. Wilhelm, Quantum optimal control in quantum technologies, strategic report on current status, visions and goals for research in Europe, EPJ Quantum Technol. 9, 19 (2022).
  31. Q. Ansel, E. Dionis, F. Arrouas, B. Peaudecerf, S. Guérin, D. Guéry-Odelin, and D. Sugny, Introduction to the theoretical and experimental aspects of quantum optimal control, J. Phys. B 57, 133001 (2024).
  32. M. Cabedo-Olaya, J. G. Muga, and S. Martínez-Garaot, Shortcut-to-adiabaticity-like techniques for parameter estimation in quantum metrology, Entropy 22, 1251 (2020).
  33. C. Lin, Y. Ma, and D. Sels, Optimal control for quantum metrology via Pontryagin’s principle, Phys. Rev. A 103, 052607 (2021).
  34. Q. Ansel, E. Dionis, and D. Sugny, Optimal control strategies for parameter estimation of quantum systems, SciPost Phys. 16, 013 (2024).
  35. J. Liu et al., Quantum Fisher information matrix and multiparameter estimation, J. Phys. A: Math. Theor. 53, 023001 (2020).
  36. Q. Ansel, M. Tesch, S. J. Glaser, and D. Sugny, Optimizing fingerprinting experiments for parameter identification: Application to spin systems, Phys. Rev. A 96, 053419 (2017).
  37. S. L. Braunstein and C. M. Caves, Statistical distance and the geometry of quantum states, Phys. Rev. Lett. 72, 3439 (1994).
  38. IBM Quantum, https://quantum.cloud.ibm.com/.
  39. G. Aleksandrowicz et al., Qiskit: An open-source framework for quantum computing, Zenodo (2019), https://doi.org/10.5281/zenodo.2562111.
  40. T. Alexander, N. Kanazawa, D. J. Egger, L. Capelluto, C. J. Wood, A. Javadi-Abhari, and D. McKay, Qiskit pulse: Programming quantum computers through the cloud with pulses, Quantum Sci. Technol. 5, 044006 (2020).
  41. N. V. Vitanov, Arbitrarily accurate narrowband composite pulse sequences, Phys. Rev. A 84, 065404 (2011).
  42. D. Daems, A. Ruschhaupt, D. Sugny, and S. Guérin, Robust quantum control by a single-shot shaped pulse, Phys. Rev. Lett. 111, 050404 (2013).
  43. G. Dridi, K. Liu, and S. Guérin, Optimal robust quantum control by inverse geometric optimization, Phys. Rev. Lett. 125, 250403 (2020).
  44. M. Harutyunyan, F. Holweck, D. Sugny, and S. Guérin, Digital optimal robust control, Phys. Rev. Lett. 131, 200801 (2023).
  45. O. Fresse-Colson, S. Guérin, X. Chen, and D. Sugny, Application of the Pontryagin maximum principle to the robust time-optimal control of two-level quantum systems, Phys. Rev. A 112, 022618 (2025).
  46. U. Boscain, G. Charlot, J.-P. Gauthier, S. Guérin, and H. R. Jauslin, Optimal control in laser-induced population transfer for two- and three-level quantum systems, J. Math. Phys. 43, 2107 (2002).
  47. B. T. Torosov and N. V. Vitanov, Experimental demonstration of composite pulses on IBM’s quantum computer, Phys. Rev. Appl. 18, 034062 (2022).
  48. T. Monz, K. Kim, W. Hänsel, M. Riebe, A. S. Villar, P. Schindler, M. Chwalla, M. Hennrich, and R. Blatt, Realization of the quantum Toffoli gate with trapped ions, Phys. Rev. Lett. 102, 040501 (2009).
  49. C. Weitenberg, M. Endres, J. F. Sherson, M. Cheneau, P. Schauss, T. Fukuhara, I. Bloch, and S. Kuhr, Single-spin addressing in an atomic mott insulator, Nature (London) 471, 319 (2011).
  50. S. S. Ivanov and N. V. Vitanov, High-fidelity local addressing of trapped ions and atoms by composite sequences of laser pulses, Opt. Lett. 36, 1275 (2011).
  51. E. Kyoseva and N. V. Vitanov, Arbitrarily accurate passband composite pulses for dynamical suppression of amplitude noise, Phys. Rev. A 88, 063410 (2013).

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Information

Phys. Rev. Research 7, 043255– Published 8 December, 2025
  • Received 3 May 2025
  • Accepted 28 October 2025
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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.

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