- Physical Review Journals
All JournalsPhysics Magazine

PRX Quantum

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

Efficient Chromatic-Number-Based Multiqubit Decoherence and Crosstalk Suppression

Amy F. Brown1,2,* and Daniel A. Lidar1,2,3,4,5

  • *Contact author: afbrown@usc.edu
PDF

PRX Quantum 6, 020354 – Published 18 June, 2025

DOI: https://doi.org/10.1103/1d4l-73x6

Abstract

The performance of quantum computers is hindered by decoherence and crosstalk, which cause errors and limit the ability to perform long computations. Dynamical decoupling is a technique that alleviates these issues by applying carefully timed pulses to individual qubits, effectively suppressing unwanted interactions. However, as quantum devices grow in size, it becomes increasingly important to minimize the time required to implement dynamical decoupling across the entire system. Here, we present “chromatic Hadamard dynamical decoupling” (CHaDD), an approach that efficiently schedules dynamical decoupling pulses for quantum devices with arbitrary qubit connectivity. By leveraging Hadamard matrices, CHaDD achieves a circuit depth that scales linearly with the chromatic number of the connectivity graph for general two-qubit interactions, assuming instantaneous pulses. This includes ZZ crosstalk, which is prevalent in superconducting quantum processing units (QPUs). The scaling of CHaDD represents an exponential improvement over all previous multiqubit decoupling schemes for devices with connectivity graphs the chromatic number of which grows at most polylogarithmically with the number of qubits. For graphs with a constant chromatic number, the scaling of CHaDD is independent of the number of qubits. We report on experiments we have conducted using IBM QPUs that confirm the advantage conferred by CHaDD. Our results suggest that CHaDD can become a useful tool for enhancing the performance and scalability of quantum computers by efficiently suppressing decoherence and crosstalk across large qubit arrays.

View figure in article

Physics Subject Headings (PhySH)

Popular Summary

As the number of qubits in quantum computers increases, managing the network or graph of qubits becomes an increasingly complex task. Dynamical decoupling (DD) is a time-tested method of suppressing noise arising from interactions between qubits and the environment. However, applying DD to one qubit has implications for its neighbors, and applying this technique to an arbitrary graph has, until now, required a number of operations that grows in proportion to the number of qubits. We provide a method we call chromatic Hadamard dynamical decoupling (CHaDD) that, instead, scales in proportion to the chromatic number of the graph, i.e., the smallest number of colors needed to color the nodes of a graph so that no two neighboring nodes have the same color. This results in an exponential improvement in the cost of applying DD for the typical case of relatively sparsely connected graphs.

We achieve this by combining graph coloring with multiqubit DD methods based on orthogonal arrays designed to efficiently average out the noise terms corresponding to qubits and pairs of qubits. We leverage graph coloring to average out only those noise terms corresponding to nodes and pairs of qubits that are colored differently, thereby substantially decreasing the number of operations required to achieve decoupling compared with all previous methods.

This is a timely improvement as qubit counts increase and reasoning about their interactions in graph-theoretic terms becomes more pertinent. We hope that combining CHaDD with quantum error correction techniques will speed up the arrival of fully fault-tolerant quantum computation.

Article Text

References (84)

  1. J. Preskill, Quantum computing in the NISQ era and beyond, Quantum 2, 79 (2018).
  2. L. Viola and S. Lloyd, Dynamical suppression of decoherence in two-state quantum systems, Phys. Rev. A 58, 2733 (1998).
  3. L. Viola, E. Knill, and S. Lloyd, Dynamical decoupling of open quantum systems, Phys. Rev. Lett. 82, 2417 (1999).
  4. P. Zanardi, Symmetrizing evolutions, Phys. Lett. A 258, 77 (1999).
  5. D. Vitali and P. Tombesi, Using parity kicks for decoherence control, Phys. Rev. A 59, 4178 (1999).
  6. L. Viola and E. Knill, Random decoupling schemes for quantum dynamical control and error suppression, Phys. Rev. Lett. 94, 060502 (2005).
  7. L. F. Santos and L. Viola, Enhanced convergence and robust performance of randomized dynamical decoupling, Phys. Rev. Lett. 97, 150501 (2006).
  8. E. L. Hahn, Spin echoes, Phys. Rev. 80, 580 (1950).
  9. H. Carr and E. Purcell, Effects of diffusion on free precession in nuclear magnetic resonance experiments, Phys. Rev. 94, 630 (1954).
  10. S. Meiboom and D. Gill, Modified spin echo method for measuring nuclear relaxation times, Rev. Sci. Instrum. 29, 688 (1958).
  11. A. A. Maudsley, Modified Carr-Purcell-Meiboom-Gill sequence for NMR Fourier imaging applications, Journal of Magnetic Resonance 69, 488 (1986).
  12. D. Suter and G. A. Álvarez, Colloquium: Protecting quantum information against environmental noise, Rev. Mod. Phys. 88, 041001 (2016).
  13. 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).
  14. 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).
  15. G. Ravi, K. N. Smith, P. Gokhale, A. Mari, N. Earnest, A. Javadi-Abhari, and F. T. Chong, in 2022 IEEE International Symposium on High-Performance Computer Architecture (HPCA) (IEEE, Seoul, South Korea, 2022), p. 288.
  16. C. Tong, H. Zhang, and B. Pokharel, Empirical learning of dynamical decoupling on quantum processors, PRX Quantum (2025).
  17. J. Jones and E. Knill, Efficient refocusing of one-spin and two-spin interactions for NMR quantum computation, J. Magn. Reson. 141, 322 (1999).
  18. T. Tsunoda, G. Bhole, S. A. Jones, J. A. Jones, and P. J. Leek, Efficient Hamiltonian programming in qubit arrays with nearest-neighbor couplings, Phys. Rev. A 102, 032405 (2020).
  19. 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).
  20. Z. Zhou, R. Sitler, Y. Oda, K. Schultz, and G. Quiroz, Quantum crosstalk robust quantum control, Phys. Rev. Lett. 131, 210802 (2023).
  21. S. Niu, A. Todri-Sanial, and N. T. Bronn, Multi-qubit dynamical decoupling for enhanced crosstalk suppression, Quantum Sci. Technol. 9, 045003 (2024).
  22. B. Evert, Z. G. Izquierdo, J. Sud, H.-Y. Hu, S. Grabbe, E. G. Rieffel, M. J. Reagor, and Z. Wang, Syncopated dynamical decoupling for suppressing crosstalk in quantum circuits, arXiv:2403.07836 [quant-ph].
  23. J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. Cory, Y. Nakamura, J. Tsai, and W. Oliver, Noise spectroscopy through dynamical decoupling with a superconducting flux qubit, Nat. Phys. 7, 565 (2011).
  24. G. A. Álvarez and D. Suter, Measuring the spectrum of colored noise by dynamical decoupling, Phys. Rev. Lett. 107, 230501 (2011).
  25. 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).
  26. L. M. Norris, G. A. Paz-Silva, and L. Viola, Qubit noise spectroscopy for non-Gaussian dephasing environments, Phys. Rev. Lett. 116, 150503 (2016).
  27. V. Tripathi, H. Chen, E. Levenson-Falk, and D. A. Lidar, Modeling low- and high-frequency noise in transmon qubits with resource-efficient measurement, PRX Quantum 5, 010320 (2024).
  28. J. A. Gross, É. Genois, D. M. Debroy, Y. Zhang, W. Mruczkiewicz, Z.-P. Cian, and Z. Jiang, Characterizing coherent errors using matrix-element amplification, npj Quantum Inf. 10, 123 (2024).
  29. V. Tripathi, D. Kowsari, K. Saurav, H. Zhang, E. M. Levenson-Falk, and D. A. Lidar, Benchmarking quantum gates and circuits, Chem. Rev. (2025).
  30. P. Jurcevic et al., Demonstration of quantum volume 64 on a superconducting quantum computing system, Quantum Sci. Technol. 6, 025020 (2021).
  31. B. Pokharel and D. A. Lidar, Demonstration of algorithmic quantum speedup, Phys. Rev. Lett. 130, 210602 (2023).
  32. B. Pokharel and D. A. Lidar, Better-than-classical Grover search via quantum error detection and suppression, npj Quantum Inf. 10, 23 (2024).
  33. P. Singkanipa, V. Kasatkin, Z. Zhou, G. Quiroz, and D. A. Lidar, Demonstration of algorithmic quantum speedup for an Abelian hidden subgroup problem, arXiv:2401.07934 [quant-ph].
  34. E. Bäumer, V. Tripathi, D. S. Wang, P. Rall, E. H. Chen, S. Majumder, A. Seif, and Z. K. Minev, Efficient long-range entanglement using dynamic circuits, PRX Quantum 5, 030339 (2024).
  35. E. Bäumer, V. Tripathi, A. Seif, D. Lidar, and D. S. Wang, Quantum Fourier transform using dynamic circuits, arXiv:2403.09514 [quant-ph].
  36. K. Khodjasteh and D. A. Lidar, Fault-tolerant quantum dynamical decoupling, Phys. Rev. Lett. 95, 180501 (2005).
  37. K. Khodjasteh and D. A. Lidar, Performance of deterministic dynamical decoupling schemes: Concatenated and periodic pulse sequences, Phys. Rev. A 75, 062310 (2007).
  38. G. S. Uhrig, Keeping a quantum bit alive by optimized π-pulse sequences, Phys. Rev. Lett. 98, 100504 (2007).
  39. 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 458, 996 (2009).
  40. G. S. Uhrig and D. A. Lidar, Rigorous bounds for optimal dynamical decoupling, Phys. Rev. A 82, 012301 (2010).
  41. 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).
  42. Z.-Y. Wang and R.-B. Liu, Protection of quantum systems by nested dynamical decoupling, Phys. Rev. A 83, 022306 (2011).
  43. J. R. West, B. H. Fong, and D. A. Lidar, Near-optimal dynamical decoupling of a qubit, Phys. Rev. Lett. 104, 130501 (2010).
  44. Y. Xia, G. S. Uhrig, and D. A. Lidar, Rigorous performance bounds for quadratic and nested dynamical decoupling, Phys. Rev. A 84, 062332 (2011).
  45. W.-J. Kuo, G. Quiroz, G. A. Paz-Silva, and D. A. Lidar, Universality proof and analysis of generalized nested Uhrig dynamical decoupling, J. Math. Phys. 53, 122207 (2012).
  46. 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).
  47. G. Quiroz and D. A. Lidar, Optimized dynamical decoupling via genetic algorithms, Phys. Rev. A 88, 052306 (2013).
  48. 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).
  49. G. T. Genov, N. Aharon, F. Jelezko, and A. Retzker, Mixed dynamical decoupling, Quantum Sci. Technol. 4, 035010 (2019).
  50. K. Khodjasteh and D. A. Lidar, Quantum computing in the presence of spontaneous emission by a combined dynamical decoupling and quantum-error-correction strategy, Phys. Rev. A 68, 022322 (2003), erratum: ibid, Phys. Rev. A 72, 029905 (2005).
  51. H. K. Ng, D. A. Lidar, and J. Preskill, Combining dynamical decoupling with fault-tolerant quantum computation, Phys. Rev. A 84, 012305 (2011).
  52. G. A. Paz-Silva and D. A. Lidar, Optimally combining dynamical decoupling and quantum error correction, Sci. Rep. 3, 1530 (2013).
  53. 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).
  54. J. Conrad, Twirling and Hamiltonian engineering via dynamical decoupling for Gottesman-Kitaev-Preskill quantum computing, Phys. Rev. A 103, 022404 (2021).
  55. A. Mena López and L.-A. Wu, Protectability of IBMQ qubits by dynamical decoupling technique, Symmetry 15, 62 (2023).
  56. G. Quiroz, B. Pokharel, J. Boen, L. Tewala, V. Tripathi, D. Williams, L.-A. Wu, P. Titum, K. Schultz, and D. Lidar, Dynamically generated decoherence-free subspaces and subsystems on superconducting qubits, Rep. Prog. Phys. 87, 097601 (2024).
  57. J.-X. Han, J. Zhang, G.-M. Xue, H. Yu, and G. Long, Protecting logical qubits with dynamical decoupling, arXiv:2402.05604.
  58. D. Leung, Simulation and reversal of n-qubit Hamiltonians using Hadamard matrices, J. Mod. Opt. 49, 1199 (2002).
  59. M. Stollsteimer and G. Mahler, Suppression of arbitrary internal coupling in a quantum register, Phys. Rev. A 64, 052301 (2001).
  60. M. Rotteler and P. Wocjan, Equivalence of decoupling schemes and orthogonal arrays, IEEE Trans. Inf. Theory 52, 4171 (2006).
  61. P. Wocjan, Efficient decoupling schemes with bounded controls based on Eulerian orthogonal arrays, Phys. Rev. A 73, 062317 (2006).
  62. M. Rötteler and P. Wocjan, in Quantum Error Correction, edited by D. A. Lidar and T. A. Brun (Cambridge University Press, Cambridge, 2013), Chap. 15, p. 376.
  63. A. D. Bookatz, M. Roetteler, and P. Wocjan, Improved bounded-strength decoupling schemes for local Hamiltonians, IEEE Trans. Inf. Theory 62, 2881 (2016).
  64. D. Hayes, K. Khodjasteh, L. Viola, and M. J. Biercuk, Reducing sequencing complexity in dynamical quantum error suppression by Walsh modulation, Phys. Rev. A 84, 062323 (2011).
  65. 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).
  66. L. Shirizly, G. Misguich, and H. Landa, Dissipative dynamics of graph-state stabilizers with superconducting qubits, Phys. Rev. Lett. 132, 010601 (2024).
  67. N. M. Linke, D. Maslov, M. Roetteler, S. Debnath, C. Figgatt, K. A. Landsman, K. Wright, and C. Monroe, Experimental comparison of two quantum computing architectures, Proc. Natl. Acad. Sci. 114, 3305 (2017).
  68. K. Boothby, P. Bunyk, J. Raymond, and A. Roy, Next-generation topology of D-wave quantum processors, arXiv:2003.00133 [quant-ph].
  69. M. Sarovar, T. Proctor, K. Rudinger, K. Young, E. Nielsen, and R. Blume-Kohout, Detecting crosstalk errors in quantum information processors, Quantum 4, 321 (2020).
  70. D. Bluvstein, H. Levine, G. Semeghini, T. T. Wang, S. Ebadi, M. Kalinowski, A. Keesling, N. Maskara, H. Pichler, M. Greiner, V. Vuletić, and M. D. Lukin, A quantum processor based on coherent transport of entangled atom arrays, Nature 604, 451 (2022).
  71. R. L. Brooks, On colouring the nodes of a network, Math. Proc. Camb. Phil. Soc. 37, 194 (1941).
  72. L. Lovász, Three short proofs in graph theory, J. Comb. Theory, Series B 19, 269 (1975).
  73. R. Diestel, Graph Theory (Springer, Berlin, 2017), 5th ed.
  74. P. Wocjan and C. Elphick, New spectral bounds on the chromatic number encompassing all eigenvalues of the adjacency matrix, Electron. J. Combin. 20, P39 (2013).
  75. T. Ando and M. Lin, Proof of a conjectured lower bound on the chromatic number of a graph, Linear Algebra Appl. 485, 480 (2015).
  76. R. Karp, in Complexity of Computer Computations, The IBM Research Symposia Series, edited by R. E. Miller and J. W. Thatcher (Plenum, New York, 1972), Chap. 9, p. 85.
  77. Rigetti Computing, Rigetti systems, https://qcs.rigetti.com/qpus (2024).
  78. P. Nation, H. Paik, A. Cross, and Z. Nazario, The IBM Quantum heavy hex lattice, https://www.ibm.com/quantum/blog/heavy-hex-lattice (2021).
  79. A. Beutelspacher, Partial spreads in finite projective spaces and partial designs, Math Z 145, 211 (1975).
  80. D. C. McKay, C. J. Wood, S. Sheldon, J. M. Chow, and J. M. Gambetta, Efficient Z gates for quantum computing, Phys. Rev. A 96, 022330 (2017).
  81. A. Vezvaee, V. Tripathi, D. Kowsari, E. Levenson-Falk, and D. A. Lidar, Virtual Z gates and symmetric gate compilation, arXiv:2407.14782 [quant-ph].
  82. M. A. Nielsen, M. J. Bremner, J. L. Dodd, A. M. Childs, and C. M. Dawson, Universal simulation of Hamiltonian dynamics for quantum systems with finite-dimensional state spaces, Phys. Rev. A 66, 022317 (2002).
  83. Y. Wang, Z. Hu, B. C. Sanders, and S. Kais, Qudits and high-dimensional quantum computing, Front. Phys. 8, 589504 (2020).
  84. A. F. Brown and D. A. Lidar, Data Repository for “Efficient Chromatic-Number-Based Multi-Qubit Decoherence and Crosstalk Suppression,” https://doi.org/10.5281/zenodo.15572005 (2025).

Outline

Information

PRX Quantum 6, 020354– Published 18 June, 2025
  • Received 4 February 2025
  • Revised 29 April 2025
  • Accepted 22 May 2025
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