- 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

Crosstalk dispersion and spatial scaling in superconducting qubit arrays

Mohammed Alghadeer1,*, Simon Pettersson Fors2, Shuxiang Cao1, Simone D. Fasciati1, Haru Ishizaka1, Anton Frisk Kockum2, Peter Leek1, and Mustafa Bakr1,†

  • *Contact author: mohammed.alghadeer@physics.ox.ac.uk
  • †Contact author: mustafa.bakr@physics.ox.ac.uk
PDF

Phys. Rev. Research 8, 033193 – Published 17 August, 2026

DOI: https://doi.org/10.1103/2zb3-4vwq

Abstract

Crosstalk between qubits fundamentally limits the scalability of quantum processors, necessitating physics-based models that can handle the complexity of large qubit arrays. Here, we develop a comprehensive theoretical and experimental framework that captures residual interactions between both adjacent and nonadjacent qubits in fixed-frequency transmon lattices. The model integrates the combined effects of exponential localization in banded capacitance matrices, suppression of virtual couplings through detuning products across intermediate modes, and evanescent decay of below-cutoff electromagnetic fields, yielding predictive scaling relations for coupling strength as a function of spatial separation and spectral detuning. Experimental characterization of a 4×4 superconducting qubit lattice with inductive shunt pillars reveals exponential spatial decay and frequency-dependent suppression consistent with theoretical predictions, achieving quantitative agreement for all nearest-neighbor couplings across the 4–6GHz operating range. Our results show that standard dispersive Hamiltonian approximations systematically overestimate long-range coupling when spatial and spectral dependencies are neglected; these errors propagate into circuit simulation and design strategies. Our framework provides design guidance for crosstalk mitigation in larger-scale quantum processors under realistic fabrication constraints, addressing a bottleneck in scalability.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (59)

  1. F. Arute et al., Quantum supremacy using a programmable superconducting processor, Nature (London) 574, 505 (2019).
  2. A. Megrant and Y. Chen, Scaling up superconducting quantum computers, Nat. Electron. 8, 549 (2025).
  3. R. P. Acharya et al., Suppressing quantum errors by scaling a surface code logical qubit, Nature (London) 614, 676 (2023).
  4. R. P. Acharya et al., Quantum error correction below the surface code threshold, Nature (London) 638, 920 (2025).
  5. M. Mohseni et al., How to build a quantum supercomputer: Scaling challenges and opportunities, arXiv:2411.10406.
  6. S. Krinner et al., Benchmarking coherent errors in controlled-phase gates due to spectator qubits, Phys. Rev. Appl. 14, 024042 (2020).
  7. P. W. Shor, Scheme for reducing decoherence in quantum computer memory, Phys. Rev. A 52, R2493 (1995).
  8. N. Lacroix et al., Scaling and logic in the color code on a superconducting quantum processor, Nature (London) 645, 614 (2025).
  9. A. Eickbusch et al., Demonstration of dynamic surface codes, Nat. Phys. 21, 1994 (2025).
  10. N. H. Le, M. Cykiert, and E. Ginossar, Scalable and robust quantum computing on qubit arrays with fixed coupling, npj Quantum Inf. 9, 1 (2023).
  11. J. Koch et al., Charge-insensitive qubit design derived from the Cooper pair box, Phys. Rev. A 76, 042319 (2007).
  12. M. Alghadeer et al., Characterization of nanostructural imperfections in superconducting quantum circuits, Mater. Quantum Technol. 5, 035201 (2025).
  13. F. Yan et al., Tunable coupling scheme for implementing high-fidelity two-qubit gates, Phys. Rev. Appl. 10, 054062 (2018).
  14. A. Ketterer and T. Wellens, Characterizing crosstalk of superconducting transmon processors, Phys. Rev. Appl. 20, 034065 (2023).
  15. V. Tripathi et al., Suppression of crosstalk in superconducting qubits using dynamical decoupling, Phys. Rev. Appl. 18, 024068 (2022).
  16. P. Murali, D. C. McKay, M. Martonosi, and A. Javadi-Abhari, Software mitigation of crosstalk on noisy intermediate-scale quantum computers, in Proceedings of the 25th International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS) (ACM Press, New York, 2020), p. 1001.
  17. P. Zhao et al., Quantum crosstalk analysis for simultaneous gate operations on superconducting qubits, PRX Quantum 3, 020301 (2022).
  18. S. Pettersson Fors, J. Fernández-Pendás, and A. F. Kockum, Comprehensive explanation of ZZ coupling in superconducting qubits, arXiv:2408.15402.
  19. J. M. Chow et al., Simple all-microwave entangling gate for fixed-frequency superconducting qubits, Phys. Rev. Lett. 107, 080502 (2011).
  20. M. C. Collodo et al., Implementation of conditional phase gates based on tunable ZZ interactions, Phys. Rev. Lett. 125, 240502 (2020).
  21. Y. Sung et al., Realization of high-fidelity CZ and ZZ-free iSWAP gates with a tunable coupler, Phys. Rev. X 11, 021058 (2021).
  22. J. Stehlik et al., Tunable coupling architecture for fixed-frequency transmon superconducting qubits, Phys. Rev. Lett. 127, 080505 (2021).
  23. J. Long et al., A universal quantum gate set for transmon qubits with strong ZZ interactions, arXiv:2103.12305.
  24. J. Chu and F. Yan, Coupler-assisted controlled-phase gate with enhanced adiabaticity, Phys. Rev. Appl. 16, 054020 (2021).
  25. M. Alghadeer, K. U. Giang, S. Cao, S. D. Fasciati, M. Piscitelli, N. Ng, P. J. Leek, M. Gluza, and M. Bakr, Double-bracket algorithmic cooling, arXiv:2510.00302.
  26. Y. Chen, K. N. Nesterov, H. Churchill, J. Shabani, V. E. Manucharyan, and M. G. Vavilov, Voltage-activated parametric entangling gates based on gatemon qubits, Phys. Rev. Appl. 20, 044012 (2023).
  27. M. Ganzhorn et al., Benchmarking the noise sensitivity of different parametric two-qubit gates in a single superconducting quantum computing platform, Phys. Rev. Res. 2, 033447 (2020).
  28. D. C. McKay, S. Sheldon, J. A. Smolin, J. M. Chow, and J. M. Gambetta, Three-qubit randomized benchmarking, Phys. Rev. Lett. 122, 200502 (2019).
  29. K. Bharti et al., Noisy intermediate-scale quantum algorithms, Rev. Mod. Phys. 94, 015004 (2022).
  30. M. Bakr, Dynamic Josephson-junction metasurfaces for multiplexed control of superconducting qubits, Phys. Rev. Appl. 24, 054069 (2025).
  31. M. Bakr, Long-range entangling operations via Josephson junction metasurfaces, in Proceedings of the IEEE International Conference on Quantum Computing and Engineering (QCE) (IEEE, New York, 2025), Vol. 2, p. 458.
  32. M. Bakr et al., Multiplexed readout of superconducting qubits using a three-dimensional reentrant-cavity filter, Phys. Rev. Appl. 23, 054089 (2025).
  33. S. D. Fasciati et al., Complementing the transmon by integrating a geometric shunt inductor, arXiv:2410.10416.
  34. S. Kosen et al., Signal crosstalk in a flip-chip quantum processor, PRX Quantum 5, 030350 (2024).
  35. R. N. Das et al., Reworkable superconducting qubit package for quantum computing, in Proceedings of the IEEE 74th Electronic Components and Technology Conference (ECTC) (IEEE, New York, 2024), p. 427.
  36. S. Huang et al., Microwave package design for superconducting quantum processors, PRX Quantum 2, 020306 (2021).
  37. P. A. Spring, T. Tsunoda, B. Vlastakis, and P. J. Leek, Modeling enclosures for large-scale superconducting quantum circuits, Phys. Rev. Appl. 14, 024061 (2020).
  38. P. A. Spring et al., High coherence and low cross-talk in a tileable 3D integrated superconducting circuit architecture, Sci. Adv. 8, eabl6698 (2022).
  39. M. Mathews et al., Placing and routing quantum LDPC codes in multilayer superconducting hardware, npj Quantum Inf. 12, 114 (2026).
  40. A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
  41. Y. Yao, M. S. Bakr, and I. C. Hunter, Modal analysis and same-bandedge response optimization of 3-D lumped networks, in Proceedings of the 49th European Microwave Conference (EuMC) (European Microwave Association, Louvain-la-Neuve, Wallonia, 2019), pp. 9–12.
  42. E. Musonda and M. S. Bakr, The singlet: Direct synthesis of pseudo-elliptic inline filters with frequency-variant couplings, IEEE Trans. Microwave Theory Techn. 71, 4969 (2023).
  43. S. Bravyi, D. P. DiVincenzo, and D. Loss, Schrieffer–Wolff transformation for quantum many-body systems, Ann. Phys. 326, 2793 (2011).
  44. C. W. Gardiner and P. Zoller, Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics, 3rd ed. (Springer, Berlin, 2004).
  45. M. Boissonneault, J. M. Gambetta, and A. Blais, Dispersive regime of circuit QED: Photon-dependent qubit dephasing and relaxation rates, Phys. Rev. A 79, 013819 (2009).
  46. D. Finkelstein-Shapiro, D. Viennot, I. Saideh, T. Hansen, T. Pullerits, and A. Keller, Adiabatic elimination and subspace evolution of open quantum systems, Phys. Rev. A 101, 042102 (2020).
  47. M. Bakr et al., Intrinsic multi-mode interference for passive suppression of Purcell decay in superconducting circuits, arXiv:2507.09715.
  48. F. Solgun, Microwave engineer’s guide to the design of superconducting qubit circuits, in Proceedings of the IEEE MTT-S International Microwave Symposium (IMS) (IEEE, New York, 2019), pp. 263–266.
  49. M. Bakr and R. Wopalenski, Exact multimode quantization of superconducting circuits via boundary admittance and continued fractions, arXiv:2601.04407.
  50. M. Bakr, A boundary condition perspective on circuit QED dispersive readout, arXiv:2512.24466.
  51. G. B. Arfken, H. J. Weber, and F. E. Harris, Mathematical Methods for Physicists, 7th ed. (Academic Press, New York, 2012), Chap. 10.
  52. F. Solgun, D. P. DiVincenzo, and J. M. Gambetta, Simple impedance response formulas for the dispersive interaction rates in the effective Hamiltonians of low anharmonicity superconducting qubits, IEEE Trans. Microwave Theory Techn. 67, 928 (2019).
  53. F. Solgun and S. Srinivasan, Direct calculation of ZZ interaction rates in multimode circuit quantum electrodynamics, Phys. Rev. Appl. 18, 044025 (2022).
  54. M. Alghadeer et al., Low crosstalk in a scalable superconducting quantum lattice, EPJ Quantum Technol. 13, 19 (2026).
  55. P. Mundada, G. Zhang, T. Hazard, and A. A. Houck, Suppression of qubit crosstalk in a tunable coupling superconducting circuit, Phys. Rev. Appl. 12, 054023 (2019).
  56. S. Cao et al., Automating quantum computing laboratory experiments with an agent-based AI framework, Patterns 6, 101372 (2025).
  57. A. Petrescu et al., Accurate methods for the analysis of strong-drive effects in parametric gates, Phys. Rev. Appl. 19, 044003 (2023).
  58. M. Leib, F. Deppe, A. Marx, R. Gross, and M. J. Hartmann, Networks of nonlinear superconducting transmission line resonators, New J. Phys. 14, 075024 (2012).
  59. V. V. Mikhailov, Ordering of some boson operator functions, J. Phys. A: Math. Gen. 16, 3817 (1983).

Outline

Information

Phys. Rev. Research 8, 033193– Published 17 August, 2026
  • Received 25 December 2025
  • Accepted 21 July 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