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

Characterization and comparison of energy relaxation in fluxonium qubits

Kate Azar1,2,3,*, Lamia Ateshian2,3,†, Mallika T. Randeria1, Renée DePencier Piñero1, Jeffrey M. Gertler1, Junyoung An2,3, Felipe Contipelli1, Leon Ding2,4,‡, Michael Gingras1 et al.

Kevin Grossklaus1, Max Hays2, Thomas M. Hazard1, Junghyun Kim2,3, Bethany M. Niedzielski1, Hannah Stickler1, Kunal L. Tiwari1, Helin Zhang2, Jeffrey A. Grover2, Jonilyn L. Yoder1, Mollie E. Schwartz1, William D. Oliver2,4,3, and Kyle Serniak1,2,§

  • *Contact author: kazar@mit.edu
  • †Present address: Google Quantum AI, Santa Barbara, California, USA.
  • ‡Present address: Google Quantum AI, Cambridge, Massachusetts, USA.
  • §Contact author: kyle.serniak@ll.mit.edu

Phys. Rev. Research 8, 043013 – Published 5 October, 2026

DOI: https://doi.org/10.1103/3n9q-lg8m

Abstract

Fluxonium superconducting qubits have demonstrated long coherence times and high single- and two-qubit gate fidelities, making them a favorable building block for superconducting quantum processors. We investigate the dominant limitations to fluxonium qubit energy relaxation time T1 using a set of eight planar, aluminum-on-silicon qubits. We find that a circuit-based model for capacitive dielectric loss best captures the frequency dependence of T1, which we analyze within both a two-level and a six-level energy relaxation model. We convert the measured T1 into an effective capacitive quality factor QCeff to compare qubits on equal footing, accounting for independently estimated contributions from 1/f flux noise and radiative loss to the control and readout circuitry. We apply this methodology to compare qubits from two fabrication processes: a baseline process and one that applies a fluorine-based wet treatment prior to Josephson junction deposition. We resolve a small improvement of 13.8% ± 8.4% in the process mean QCeff, indicating that the fluorine treatment may have reduced loss from the metal-substrate interface, but did not address the primary source of loss in these fluxonium qubits.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (66)

  1. M. Kjaergaard, M. E. Schwartz, J. Braumüller, P. Krantz, J. I.-J. Wang, S. Gustavsson, and W. D. Oliver, Superconducting qubits: Current state of play, Annu. Rev. Condens. Matter Phys. 11, 369 (2020).
  2. A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
  3. 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).
  4. F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. S. L. Brandao, D. A. Buell, et al., Quantum supremacy using a programmable superconducting processor, Nature (London) 574, 505 (2019).
  5. Google Quantum AI, Suppressing quantum errors by scaling a surface code logical qubit, Nature (London) 614, 676 (2023).
  6. Google Quantum AI and Collaborators, Quantum error correction below the surface code threshold, Nature (London) 638, 920 (2025).
  7. V. E. Manucharyan, J. Koch, L. I. Glazman, and M. H. Devoret, Fluxonium: Single Cooper-pair circuit free of charge offsets, Science 326, 113 (2009).
  8. I. M. Pop, K. Geerlings, G. Catelani, R. J. Schoelkopf, L. I. Glazman, and M. H. Devoret, Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles, Nature (London) 508, 369 (2014).
  9. A. Somoroff, Q. Ficheux, R. A. Mencia, H. Xiong, R. Kuzmin, and V. E. Manucharyan, Millisecond coherence in a superconducting qubit, Phys. Rev. Lett. 130, 267001 (2023).
  10. L. Ding, M. Hays, Y. Sung, B. Kannan, J. An, A. Di Paolo, A. H. Karamlou, T. M. Hazard, K. Azar, D. K. Kim, B. M. Niedzielski, A. Melville, M. E. Schwartz, J. L. Yoder, T. P. Orlando, S. Gustavsson, J. A. Grover, K. Serniak, and W. D. Oliver, High-fidelity, frequency-flexible two-qubit fluxonium gates with a transmon coupler, Phys. Rev. X 13, 031035 (2023).
  11. H. Zhang, S. Chakram, T. Roy, N. Earnest, Y. Lu, Z. Huang, D. K. Weiss, J. Koch, and D. I. Schuster, Universal fast-flux control of a coherent, low-frequency qubit, Phys. Rev. X 11, 011010 (2021).
  12. D. A. Rower, L. Ding, H. Zhang, M. Hays, J. An, P. M. Harrington, I. T. Rosen, J. M. Gertler, T. M. Hazard, B. M. Niedzielski, M. E. Schwartz, S. Gustavsson, K. Serniak, J. A. Grover, and W. D. Oliver, Suppressing counter-rotating errors for fast single-qubit gates with fluxonium, PRX Quantum 5, 040342 (2024).
  13. H. Zhang, C. Ding, D. K. Weiss, Z. Huang, Y. Ma, C. Guinn, S. Sussman, S. P. Chitta, D. Chen, A. A. Houck, J. Koch, and D. I. Schuster, Tunable inductive coupler for high-fidelity gates between fluxonium qubits, PRX Quantum 5, 020326 (2024).
  14. W.-J. Lin, H. Cho, Y. Chen, M. G. Vavilov, C. Wang, and V. E. Manucharyan, 24 days-stable CNOT-gate on fluxonium qubits with over 99.9% fidelity, arXiv:2407.15783.
  15. L. B. Nguyen, Y.-H. Lin, A. Somoroff, R. Mencia, N. Grabon, and V. E. Dirac, High-coherence fluxonium qubit, Phys. Rev. X 9, 041041 (2019).
  16. T. M. Hazard, A. Gyenis, A. Di Paolo, A. T. Asfaw, S. A. Lyon, A. Blais, and A. A. Houck, Nanowire superinductance fluxonium qubit, Phys. Rev. Lett. 122, 010504 (2019).
  17. H. Sun, F. Wu, H.-S. Ku, X. Ma, J. Qin, Z. Song, T. Wang, G. Zhang, J. Zhou, Y. Shi, H.-H. Zhao, and C. Deng, Characterization of loss mechanisms in a fluxonium qubit, Phys. Rev. Appl. 20, 034016 (2023).
  18. W. Ardati, S. Léger, S. Kumar, V. N. Suresh, D. Nicolas, C. Mori, F. D’Esposito, T. Vakhtel, O. Buisson, Q. Ficheux, and N. Roch, Using bifluxon tunneling to protect the fluxonium qubit, Phys. Rev. X 14, 041014 (2024).
  19. L. Ateshian, M. Hays, D. A. Rower, H. Zhang, K. Azar, R. Assouly, L. Ding, M. Gingras, H. Stickler, B. M. Niedzielski, M. E. Schwartz, T. P. Orlando, J.  Î.-j. Wang, S. Gustavsson, J. A. Grover, K. Serniak, and W. D. Oliver, Temperature and magnetic-field dependence of energy relaxation in a fluxonium qubit, arXiv:2507.01175.
  20. Z.-T. Zhuang, D. Rosenstock, B.-J. Liu, A. Somoroff, V. E. Manucharyan, and C. Wang, Non-Markovian relaxation spectroscopy of fluxonium qubits, arXiv:2503.16381.
  21. J. M. Martinis, K. B. Cooper, R. McDermott, M. Steffen, M. Ansmann, K. D. Osborn, K. Cicak, S. Oh, D. P. Pappas, R. W. Simmonds, and C. C. Yu, Decoherence in Josephson qubits from dielectric loss, Phys. Rev. Lett. 95, 210503 (2005).
  22. W. D. Oliver and P. Welander, Materials in superconducting quantum bits, MRS Bull. 38, 816 (2013).
  23. A. Dunsworth, A. Megrant, C. Quintana, Z. Chen, R. Barends, B. Burkett, B. Foxen, Y. Chen, B. Chiaro, A. Fowler, et al., Characterization and reduction of capacitive loss induced by sub-micron Josephson junction fabrication in superconducting qubits, Appl. Phys. Lett. 111, 022601 (2017).
  24. H. J. Mamin, E. Huang, S. Carnevale, C. T. Rettner, N. Arellano, M. H. Sherwood, C. Kurter, B. Trimm, M. Sandberg, R. M. Shelby, M. A. Mueed, B. A. Madon, A. Pushp, M. Steffen, and D. Rugar, Merged-element transmons: Design and qubit performance, Phys. Rev. Appl. 16, 024023 (2021).
  25. A. Bilmes, S. Volosheniuk, A. V. Ustinov, and J. Lisenfeld, Probing defect densities at the edges and inside Josephson junctions of superconducting qubits, npj Quantum Inf. 8, 24 (2022).
  26. M. A. Gingras, B. M. Niedzielski, K. A. Grossklaus, D. Miller, F. Contipelli, K. Azar, L. D. Burkhart, G. Calusine, D. Davis, R. D. Piñero, et al., Improving transmon qubit performance with fluorine-based surface treatments, Phys. Rev. Appl. 26, 014040 (2026).
  27. N. A. Masluk, I. M. Pop, A. Kamal, Z. K. Minev, and M. H. Devoret, Microwave characterization of Josephson junction arrays: Implementing a low loss superinductance, Phys. Rev. Lett. 109, 137002 (2012).
  28. M. T. Bell, I. A. Sadovskyy, L. B. Ioffe, A. Y. Kitaev, and M. E. Gershenson, Quantum superinductor with tunable nonlinearity, Phys. Rev. Lett. 109, 137003 (2012).
  29. F. Yan, S. Gustavsson, A. Kamal, J. Birenbaum, A. P. Sears, D. Hover, T. J. Gudmundsen, D. Rosenberg, G. Samach, S. Weber, J. L. Yoder, T. P. Orlando, J. Clarke, A. J. Kerman, and W. D. Oliver, The flux qubit revisited to enhance coherence and reproducibility, Nat. Commun. 7, 12964 (2016).
  30. A. P. M. Place, L. V. H. Rodgers, P. Mundada, B. M. Smitham, M. Fitzpatrick, Z. Leng, A. Premkumar, J. Bryon, A. Vrajitoarea, S. Sussman, et al., New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds, Nat. Commun. 12, 1779 (2021).
  31. M. V. P. Altoé, A. Banerjee, C. Berk, A. Hajr, A. Schwartzberg, C. Song, M. Alghadeer, S. Aloni, M. J. Elowson, J. M. Kreikebaum, E. K. Wong, S. M. Griffin, S. Rao, A. Weber-Bargioni, A. M. Minor, D. I. Santiago, S. Cabrini, I. Siddiqi, and D. F. Ogletree, Localization and mitigation of loss in niobium superconducting circuits, PRX Quantum 3, 020312 (2022).
  32. M. P. Bland, F. Bahrami, J. G. C. Martinez, P. H. Prestegaard, B. M. Smitham, A. Joshi, E. Hedrick, A. Pakpour-Tabrizi, S. Kumar, A. Jindal, R. D. Chang, A. Yang, G. Cheng, N. Yao, R. J. Cava, N. P. de Leon, and A. A. Houck, 2D transmons with lifetimes and coherence times exceeding 1 millisecond, Nature (London) 647, 343 (2025).
  33. A. A. Murthy, M. Bal, M. J. Bedzyk, H. Cansizoglu, R. K. Chan, V. Chandrasekhar, F. Crisa, A. Datta, Y. Deng, C. D. M. Diaz, et al., Identifying materials-level sources of performance variation in superconducting transmon qubits, arXiv:2503.14424.
  34. R. Gao, F. Wu, H. Sun, J. Chen, H. Deng, X. Ma, X. Miao, Z. Song, X. Wan, F. Wang, T. Xia, M. Ying, C. Zhang, Y. Shi, H.-H. Zhao, and C. Deng, The effects of disorder in superconducting materials on qubit coherence, Nat. Commun. 16, 3620 (2025).
  35. F. Wang, K. Lu, H. Zhan, L. Ma, F. Wu, H. Sun, H. Deng, Y. Bai, F. Bao, X. Chang, et al., High-coherence fluxonium qubits manufactured with a wafer-scale-uniformity process, Phys. Rev. Appl. 23, 044064 (2025).
  36. G. J. Dolan, Offset masks for lift‐off photoprocessing, Appl. Phys. Lett. 31, 337 (1977).
  37. M. T. Randeria, T. M. Hazard, A. Di Paolo, K. Azar, M. Hays, L. Ding, J. An, M. Gingras, B. M. Niedzielski, H. Stickler, J. A. Grover, J. L. Yoder, M. E. Schwartz, W. D. Oliver, and K. Serniak, Dephasing in fluxonium qubits from coherent quantum phase slips, PRX Quantum 5, 030341 (2024).
  38. J. Braumüller, L. Ding, A. P. Vepsäläinen, Y. Sung, M. Kjaergaard, T. Menke, R. Winik, D. Kim, B. M. Niedzielski, A. Melville, J. L. Yoder, C. F. Hirjibehedin, T. P. Orlando, S. Gustavsson, and W. D. Oliver, Characterizing and optimizing qubit coherence based on SQUID geometry, Phys. Rev. Appl. 13, 054079 (2020).
  39. H. Nyquist, Thermal agitation of electric charge in conductors, Phys. Rev. 32, 110 (1928).
  40. A. O. Caldeira and A. J. Leggett, Quantum tunnelling in a dissipative system, Ann. Phys. 149, 374 (1983).
  41. C. Wang, C. Axline, Y. Y. Gao, T. Brecht, Y. Chu, L. Frunzio, M. H. Devoret, and R. J. Schoelkopf, Surface participation and dielectric loss in superconducting qubits, Appl. Phys. Lett. 107, 162601 (2015).
  42. K. Geerlings, Z. Leghtas, I. M. Pop, S. Shankar, L. Frunzio, R. J. Schoelkopf, M. Mirrahimi, and M. H. Devoret, Demonstrating a driven reset protocol for a superconducting qubit, Phys. Rev. Lett. 110, 120501 (2013).
  43. X. Y. Jin, A. Kamal, A. P. Sears, T. Gudmundsen, D. Hover, J. Miloshi, R. Slattery, F. Yan, J. Yoder, T. P. Orlando, S. Gustavsson, and W. D. Oliver, Thermal and residual excited-state population in a 3D transmon qubit, Phys. Rev. Lett. 114, 240501 (2015).
  44. A. P. Sears, A. Petrenko, G. Catelani, L. Sun, H. Paik, G. Kirchmair, L. Frunzio, L. I. Glazman, S. M. Girvin, and R. J. Schoelkopf, Photon shot noise dephasing in the strong-dispersive limit of circuit QED, Phys. Rev. B 86, 180504(R) (2012).
  45. F. Yan, S. Gustavsson, J. Bylander, X. Jin, F. Yoshihara, D. G. Cory, Y. Nakamura, T. P. Orlando, and W. D. Oliver, Rotating-frame relaxation as a noise spectrum analyser of a superconducting qubit undergoing driven evolution, Nat. Commun. 4, 2337 (2013).
  46. B. L. WELCH, The generalization of ‘student's’ problem when several different population varlances are involved, Biometrika 34, 28 (1947).
  47. C. Macklin, K. O’Brien, D. Hover, M. E. Schwartz, V. Bolkhovsky, X. Zhang, W. D. Oliver, and I. Siddiqi, A near–quantum-limited Josephson traveling-wave parametric amplifier, Science 350, 307 (2015).
  48. V. E. Manucharyan, N. A. Masluk, A. Kamal, J. Koch, L. I. Glazman, and M. H. Devoret, Evidence for coherent quantum phase slips across a Josephson junction array, Phys. Rev. B 85, 024521 (2012).
  49. K. Serniak, M. Hays, G. de Lange, S. Diamond, S. Shankar, L. D. Burkhart, L. Frunzio, M. Houzet, and M. H. Devoret, Hot nonequilibrium quasiparticles in transmon qubits, Phys. Rev. Lett. 121, 157701 (2018).
  50. P. A. M. Dirac, The quantum theory of the emission and absorption of radiation, Proc. R. Soc. Lond. A 114, 243 (1927).
  51. M. H. Devoret, Quantum fluctuations in electrical circuits, Les Houches, Session LXIII 7 (1995), https://boulderschool.yale.edu/sites/default/files/files/devoret_quantum_fluct_les_houches.pdf.
  52. D. M. Pozar, Microwave Engineering, 4th ed. (Wiley, Hoboken, NJ, 2012).
  53. C. Smith, Design of protected superconducting qubits, Ph.D. thesis, Yale, 2019.
  54. V. E. Manucharyan, Superinductance, Ph.D. thesis, Yale, 2012.
  55. G. Catelani, R. J. Schoelkopf, M. H. Devoret, and L. I. Glazman, Relaxation and frequency shifts induced by quasiparticles in superconducting qubits, Phys. Rev. B 84, 064517 (2011).
  56. K. Serniak, S. Diamond, M. Hays, V. Fatemi, S. Shankar, L. Frunzio, R. J. Schoelkopf, and M. H. Devoret, Direct dispersive monitoring of charge parity in offset-charge -sensitive transmons, Phys. Rev. Appl. 12, 014052 (2019).
  57. T. Connolly, P. D. Kurilovich, S. Diamond, H. Nho, C. G. L. Bøttcher, L. I. Glazman, V. Fatemi, and M. H. Devoret, Coexistence of nonequilibrium density and equilibrium energy distribution of quasiparticles in a superconducting qubit, Phys. Rev. Lett. 132, 217001 (2024).
  58. F. Yan, J. Bylander, S. Gustavsson, F. Yoshihara, K. Harrabi, D. G. Cory, T. P. Orlando, Y. Nakamura, J.-S. Tsai, and W. D. Oliver, Spectroscopy of low-frequency noise and its temperature dependence in a superconducting qubit, Phys. Rev. B 85, 174521 (2012).
  59. Y. Yu, W. D. Oliver, J. C. Lee, K. K. Berggren, L. S. Levitov, and T. P. Orlando, Multi-photon, multi-level dynamics in a superconducting persistent-current qubit, arXiv:cond-mat/0508587.
  60. C. T. Hann, S. S. Elder, C. S. Wang, K. Chou, R. J. Schoelkopf, and L. Jiang, Robust readout of bosonic qubits in the dispersive coupling regime, Phys. Rev. A 98, 022305 (2018).
  61. P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, et al., SciPy 1.0: Fundamental algorithms for scientific computing in Python, Nat. Methods 17, 261 (2020).
  62. J. A. Nelder and R. Mead, A simplex method for function minimization, Comput. J. 7, 308 (1965).
  63. F. Gao and L. Han, Implementing the Nelder-Mead simplex algorithm with adaptive parameters, Comput. Optim. Appl. 51, 259 (2012).
  64. F. J. Massey, The Kolmogorov-Smirnov test for goodness of fit, J. Am. Stat. Assoc. 46, 68 (1951).
  65. N. Smirnov, Table for estimating the goodness of fit of empirical distributions, Ann. Math. Stat. 19, 279 (1948).
  66. H. B. Mann and D. R. Whitney, On a test of whether one of two random variables is stochastically larger than the other, Ann. Math. Stat. 18, 50 (1947).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation