- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

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
  • Editors' Suggestion
  • Open Access

Josephson Junction Tuning Described by Depinning Physics

Oscar W. Kennedy1,*, Jared H. Cole2,†, and Connor D. Shelly1,‡

  • 1Oxford Quantum Circuits, Thames Valley Science Park, Shinfield, Reading, RG2 9LH, United Kingdom
  • 2Theoretical, Computational, and Quantum Physics, School of Science, RMIT University, Melbourne, Australia

  • *Contact author: okennedy@oqc.tech
  • †Contact author: jared.cole@rmit.edu.au
  • ‡Contact author: cshelly@oqc.tech
PDF

Phys. Rev. Lett. 135, 196202 – Published 4 November, 2025

DOI: https://doi.org/10.1103/xkqs-grnd

Abstract

Superconducting quantum computers leverage superconducting qubits, systems with well-defined energy levels, the spacing of which is determined by the properties of embedded Josephson junctions. Indeterminacy of Josephson junction manufacturing limits large-scale superconducting circuits; however, junction-by-junction tuning affords the possibility of an order of magnitude improvement of determinacy—although the origin of this tuning effect is uncertain. Understanding how tuning techniques may physically modify the tunnel barrier of a Josephson junction is important and will enable these techniques to be optimized. We develop a model of junction tuning based on depinning theory to interpret a phase diagram of the tuning rate. We extract the dependence on temperature, time-varying voltages, and oscillation frequency. Comparing the effect of junction tuning on room-temperature I−V’s, electrical breakdown, and frequency of higher-energy levels of transmon qubits indicates that the tuning process leaves the barrier thickness unchanged but modifies its composition.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (57)

  1. F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. Brandao, D. A. Buell et al., Quantum supremacy using a programmable superconducting processor, Nature (London) 574, 505 (2019).
  2. J. Robledo-Moreno et al., Chemistry beyond the scale of exact diagonalization on a quantum-centric supercomputer, Sci. Adv. 11, eadu9991 (2025).
  3. Google Quantum AI, Suppressing quantum errors by scaling a surface code logical qubit, Nature (London) 614, 676 (2023).
  4. J. Kreikebaum, K. O’Brien, A. Morvan, and I. Siddiqi, Improving wafer-scale Josephson junction resistance variation in superconducting quantum coherent circuits, Supercond. Sci. Technol. 33, 06LT02 (2020).
  5. J. B. Hertzberg, E. J. Zhang, S. Rosenblatt, E. Magesan, J. A. Smolin, J.-B. Yau, V. P. Adiga, M. Sandberg, M. Brink, J. M. Chow et al., Laser-annealing Josephson junctions for yielding scaled-up superconducting quantum processors, npj Quantum Inf. 7, 129 (2021).
  6. X. Wang, J. Howard, E. A. Sete, G. Stiehl, C. Kopas, S. Poletto, X. Wu, M. Field, N. Sharac, C. Eckberg et al., Precision frequency tuning of tunable transmon qubits using alternating-bias assisted annealing, in Proceedings of the 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) (IEEE, New York, 2024), Vol. 1, pp. 1315–1323.
  7. N. Muthusubramanian, M. Finkel, P. Duivestein, C. Zachariadis, S. L. van der Meer, H. M. Veen, M. W. Beekman, T. Stavenga, A. Bruno, and L. DiCarlo, Wafer-scale uniformity of dolan-bridge and bridgeless manhattan-style Josephson junctions for superconducting quantum processors, Quantum Sci. Technol. 9, 025006 (2024).
  8. A. Osman, J. Fernández-Pendás, C. Warren, S. Kosen, M. Scigliuzzo, A. Frisk Kockum, G. Tancredi, A. Fadavi Roudsari, and J. Bylander, Mitigation of frequency collisions in superconducting quantum processors, Phys. Rev. Res. 5, 043001 (2023).
  9. E. J. Zhang, S. Srinivasan, N. Sundaresan, D. F. Bogorin, Y. Martin, J. B. Hertzberg, J. Timmerwilke, E. J. Pritchett, J.-B. Yau, C. Wang et al., High-performance superconducting quantum processors via laser annealing of transmon qubits, Sci. Adv. 8, eabi6690 (2022).
  10. A. Morvan, L. Chen, J. M. Larson, D. I. Santiago, and I. Siddiqi, Optimizing frequency allocation for fixed-frequency superconducting quantum processors, Phys. Rev. Res. 4, 023079 (2022).
  11. Z. Du, S. Kan, S. Stein, Z. Liang, A. Li, and Y. Mao, Hardware-aware compilation for chip-to-chip coupler-connected modular quantum systems, arXiv:2505.09036.
  12. P. Koppinen, L. Väistö, and I. Maasilta, Complete stabilization and improvement of the characteristics of tunnel junctions by thermal annealing, Appl. Phys. Lett. 90, 053503 (2007).
  13. H. Kim, C. Jünger, A. Morvan, E. S. Barnard, W. P. Livingston, M. Altoé, Y. Kim, C. Song, L. Chen, J. M. Kreikebaum et al., Effects of laser-annealing on fixed-frequency superconducting qubits, Appl. Phys. Lett. 121, 142601 (2022).
  14. Y. Balaji, N. Acharya, R. Armstrong, K. G. Crawford, S. Danilin, T. Dixon, O. W. Kennedy, R. D. Pothuraju, K. Shahbazi, and C. D. Shelly, Electron-beam annealing of Josephson junctions for frequency tuning of quantum processors, arXiv:2402.17395.
  15. D. P. Pappas, M. Field, C. J. Kopas, J. A. Howard, X. Wang, E. Lachman, J. Oh, L. Zhou, A. Gold, G. M. Stiehl et al., Alternating-bias assisted annealing of amorphous oxide tunnel junctions, Commun. Mater. 5, 150 (2024).
  16. K. J. Wiese, Theory and experiments for disordered elastic manifolds, depinning, avalanches, and sandpiles, Rep. Prog. Phys. 85, 086502 (2022).
  17. S. Brazovskii and T. Nattermann, Pinning and sliding of driven elastic systems: From domain walls to charge density waves, Adv. Phys. 53, 177 (2004).
  18. N. Vogt, R. Schäfer, H. Rotzinger, W. Cui, A. Fiebig, A. Shnirman, and A. V. Ustinov, One-dimensional Josephson junction arrays: Lifting the Coulomb blockade by depinning, Phys. Rev. B 92, 045435 (2014).
  19. N. Vogt, J. H. Cole, and A. Shnirman, De-pinning of disordered bosonic chains, New J. Phys. 18, 053026 (2016).
  20. K. Cedergren, R. Ackroyd, S. Kafanov, N. Vogt, A. Shnirman, and T. Duty, Insulating Josephson junction chains as pinned Luttinger liquids, Phys. Rev. Lett. 119, 167701 (2017).
  21. D. Willsch, D. Rieger, P. Winkel, M. Willsch, C. Dickel, J. Krause, Y. Ando, R. Lescanne, Z. Leghtas, N. T. Bronn et al., Observation of Josephson harmonics in tunnel junctions, Nat. Phys. 20, 815 (2024).
  22. N. Acharya, R. Armstrong, Y. Balaji, K. G. Crawford, J. C. Gates, P. C. Gow, O. W. Kennedy, R. D. Pothuraju, K. Shahbazi, and C. D. Shelly, Integration of through-sapphire substrate machining with superconducting quantum processors, Adv. Mater. 37, 2411780 (2024).
  23. See Supplemental Material at http://link.aps.org/supplemental/10.1103/xkqs-grnd for extended data (AFM of junction, room temperature tuning curve) and analysis of the date from the main text (alternate fits to tuning curves, replot phase diagram data, analysis of self-heating in junctions and an estimate of parameters from the depinning equations).
  24. E. R. Dobrovinskaya, L. A. Lytvynov, and V. Pishchik, Sapphire. Micro- and Opto-Electronic Materials, Structures, and Systems (Springer, Boston, MA, 2009).
  25. A. A. Middleton and D. S. Fisher, Critical behavior of pinned charge-density waves below the threshold for sliding, Phys. Rev. Lett. 66, 92 (1991).
  26. T. Nattermann, V. Pokrovsky, and V. M. Vinokur, Hysteretic dynamics of domain walls at finite temperatures, Phys. Rev. Lett. 87, 197005 (2001).
  27. C. Müller, J. H. Cole, and J. Lisenfeld, Towards understanding two-level-systems in amorphous solids: Insights from quantum circuits, Rep. Prog. Phys. 82, 124501 (2019).
  28. T. Nattermann and V. Pokrovsky, Hysteresis mediated by a domain wall motion, Physica (Amsterdam) 340A, 625 (2004).
  29. F. Schütze and T. Nattermann, Mean-field theory for driven domain walls in disordered environments, Phys. Rev. B 83, 024412 (2011).
  30. T. Imamura, T. Shiota, and S. Hasuo, Fabrication of high quality Nb/AlO/sub x/-Al/Nb Josephson junctions. I. Sputtered nb films for junction electrodes, IEEE Trans. Appl. Supercond. 2, 1 (1992).
  31. A. Oliva and R. Monaco, Annealing properties of high quality Nb/Al-AlO/sub x//Nb tunnel junctions, IEEE Trans. Appl. Supercond. 4, 25 (1994).
  32. J. Migacz and M. Huber, Thermal annealing of Nb/Al-AlO/sub x//Nb Josephson junctions, IEEE Trans. Appl. Supercond. 13, 123 (2003).
  33. I. M. Pop, T. Fournier, T. Crozes, F. Lecocq, I. Matei, B. Pannetier, O. Buisson, and W. Guichard, Fabrication of stable and reproducible submicron tunnel junctions, J. Vac. Sci. Technol. B 30, 010607 (2012).
  34. J. K. Julin, P. J. Koppinen, and I. J. Maasilta, Reduction of low-frequency 1/f noise in Al-AlOx-Al tunnel junctions by thermal annealing, Appl. Phys. Lett. 97, 152501 (2010).
  35. P. J. Koppinen, L. M. Väistö, and I. J. Maasilta, Complete stabilization and improvement of the characteristics of tunnel junctions by thermal annealing, Appl. Phys. Lett. 90, 053503 (2007).
  36. N. D. Korshakov, D. O. Moskalev, A. A. Soloviova, D. A. Moskaleva, E. S. Lotkov, A. R. Ibragimov, M. V. Androschuk, I. A. Ryzhikov, Y. V. Panfilov, and I. A. Rodionov, Aluminum Josephson junction microstructure and electrical properties modification with thermal annealing, Sci. Rep. 14, 26066 (2024).
  37. J. W. McPherson, Time dependent dielectric breakdown physics–models revisited, Microelectron. Reliab. 52, 1753 (2012).
  38. S. J. Moxim, F. V. Sharov, D. R. Hughart, G. S. Haase, C. G. McKay, and P. M. Lenahan, Atomic-scale defects generated in the early/intermediate stages of dielectric breakdown in Si/SiO2 transistors, Appl. Phys. Lett. 120, 063502 (2022).
  39. J. McPherson, J. Kim, A. Shanware, and H. Mogul, Thermochemical description of dielectric breakdown in high dielectric constant materials, Appl. Phys. Lett. 82, 2121 (2003).
  40. S. Amara-Dababi, H. Bea, R. Sousa, K. Mackay, and B. Dieny, Modelling of time-dependent dielectric barrier breakdown mechanisms in MgO-based magnetic tunnel junctions, J. Phys. D 45, 295002 (2012).
  41. J. P. Borja, T.-M. Lu, and J. Plawsky, Dielectric Breakdown in Gigascale Electronics: Time Dependent Failure Mechanisms (Springer, New York, 2016).
  42. J. Borja, J. L. Plawsky, T.-M. Lu, and W. N. Gill, Impact of frequency from a bipolar applied field on dielectric breakdown for low-k materials, IEEE Trans. Electron Devices 59, 1745 (2012).
  43. D. Schaefer, P. Fichtner, M. Carara, L. Schelp, and L. Dorneles, Dielectric breakdown in AlOx tunnelling barriers, J. Phys. D 44, 135403 (2011).
  44. J. Kolodzey, E. A. Chowdhury, T. N. Adam, G. Qui, I. Rau, J. O. Olowolafe, J. S. Suehle, and Y. Chen, Electrical conduction and dielectric breakdown in aluminum oxide insulators on silicon, IEEE Trans. Electron Devices 47, 121 (2000).
  45. S. K. Tolpygo and D. Amparo, Electrical stress effect on Josephson tunneling through ultrathin AlOx barrier in Nb/Al/AlOx/Nb junctions, J. Appl. Phys. 104, 063904 (2008).
  46. H. De Wit, C. Wijenberg, and C. Crevecoeur, The dielectric breakdown of anodic aluminum oxide, J. Electrochem. Soc. 123, 1479 (1976).
  47. O. W. Kennedy, K. G. Crawford, K. Shahbazi, and C. D. Shelly, Analysis of Josephson junction barrier variation: A combined electron microscopy, breakdown, and Monte Carlo approach, Phys. Rev. Mater. 9, 084803 (2025).
  48. J. G. Simmons, Generalized formula for the electric tunnel effect between similar electrodes separated by a thin insulating film, J. Appl. Phys. 34, 1793 (1963).
  49. M. J. Cyster, J. S. Smith, J. A. Vaitkus, N. Vogt, S. P. Russo, and J. H. Cole, Effect of atomic structure on the electrical response of aluminum oxide tunnel junctions, Phys. Rev. Res. 2, 013110 (2020).
  50. K. Bayros, M. Cyster, J. Smith, and J. Cole, Influence of pinholes and weak-points in aluminum-oxide Josephson junctions, Phys. Rev. Mater. 8, 046202 (2024).
  51. T. Greibe, M. P. V. Stenberg, C. M. Wilson, T. Bauch, V. S. Shumeiko, and P. Delsing, Are “pinholes” the cause of excess current in superconducting tunnel junctions? A study of Andreev current in highly resistive junctions, Phys. Rev. Lett. 106, 1657 (2011).
  52. J. Rahamim, T. Behrle, M. Peterer, A. Patterson, P. Spring, T. Tsunoda, R. Manenti, G. Tancredi, and P. Leek, Double-sided coaxial circuit QED with out-of-plane wiring, Appl. Phys. Lett. 110, 222602 (2017).
  53. Z. Wang, R. W. Parker, E. Champion, and M. S. Blok, Systematic study of high ej/ec transmon qudits up to d=12, Phys. Rev. Appl. 23, 034046 (2025).
  54. J. R. Johansson, P. D. Nation, and F. Nori, qutip: An open-source python framework for the dynamics of open quantum systems, Comput. Phys. Commun. 183, 1760 (2012).
  55. J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Charge-insensitive qubit design derived from the Cooper pair box, Phys. Rev. A 76, 042319 (2007).
  56. J. Strand and A. L. Shluger, On the structure of oxygen deficient amorphous oxide films, Adv. Sci. 11, 2306243 (2024).
  57. J.-S. Oh, C. J. Kopas, H. Cansizoglu, J. Y. Mutus, K. Yadavalli, T.-H. Kim, M. Kramer, A. H. King, and L. Zhou, Correlating aluminum layer deposition rates, Josephson junction microstructure, and superconducting qubits’ performance, Acta Mater. 284, 120631 (2025).

Outline

Information

Phys. Rev. Lett. 135, 196202– Published 4 November, 2025
  • Received 21 July 2025
  • Accepted 7 October 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