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Broadband high-precision measurement of two-level-system loss using multiwavelength superconducting resonators

Cliff Chen*, Shahriar Aghaeimeibodi, Yuki Sato, Matthew H. Matheny, Oskar Painter, and Jiansong Gao

  • *Contact author: clfchen@amazon.com
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Phys. Rev. Applied 25, 014045 – Published 20 January, 2026

DOI: https://doi.org/10.1103/2l7h-zn9s

Abstract

Two-level systems (TLSs) are known to be a dominant source of dissipation and decoherence in superconducting qubits. Superconducting resonators provide a convenient way to study TLS-induced loss due to easier design and fabrication in comparison with devices that include nonlinear elements such as Josephson junctions. However, precisely measuring TLS-induced loss in a resonator in the quantum regime is challenging due to low signal-to-noise ratio (SNR) and the temporal fluctuations of the TLS, leading to uncertainties of 20% or more in the loss measurement. To address these limitations, we develop a multiwavelength resonator device that extends the resonator length from a standard quarter wavelength λ/4 to Nλ/4, where N=37, at 6 GHz. This design provides two key advantages: the TLS-induced fluctuations are reduced by a factor of N due to spatial averaging over an increased number of independent TLSs, and the measurement SNR for a given intraresonator energy density increases by a factor of N. The multiwavelength resonator also has fundamental and harmonic resonances spanning a wide frequency range, allowing one to study the frequency dependence of TLS-induced loss. In this work we fabricate both multiwavelength and quarter-wave coplanar waveguide resonators formed from thin-film aluminum on a silicon substrate, and characterize their TLS properties at 10 and 200 mK. Our results show that the power-dependent TLS-induced loss measured from the Nλ/4 resonator agrees well with that measured from the λ/4 resonator, while achieving a fivefold reduction in measurement uncertainty due to TLS fluctuations, down to 5%. The Nλ/4 resonator also provides a measure of the fully unsaturated TLS-induced loss due to the increased measurement SNR at low intraresonator energy densities. Finally, measurements across seven harmonic resonances of the Nλ/4 resonator between 4 and 6.5 GHz reveal no frequency dependence in the TLS-induced loss over this range. These results highlight the benefits of the multiwavelength resonator approach for material development in superconducting quantum circuits.

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References (32)

  1. Chenlu Wang, Xuegang Li, Huikai Xu, Zhiyuan Li, Junhua Wang, Zhen Yang, Zhenyu Mi, Xuehui Liang, Tang Su, Chuhong Yang, et al., Towards practical quantum computers: Transmon qubit with a lifetime approaching 0.5 milliseconds, npj Quantum Inf. 8, 3 (2022).
  2. Olivier Ezratty, Perspective on superconducting qubit quantum computing, Eur. Phys. J. A 59, 94 (2023).
  3. Harald Putterman, Kyungjoo Noh, Connor T. Hann, Gregory S. MacCabe, Shahriar Aghaeimeibodi, Rishi N. Patel, Menyoung Lee, William M. Jones, Hesam Moradinejad, Roberto Rodriguez, et al., Hardware-efficient quantum error correction via concatenated bosonic qubits, Nature 638, 927 (2025).
  4. Rajeev Acharya, Dmitry A. Abanin, Laleh Aghababaie-Beni, Igor Aleiner, Trond I. Andersen, Markus Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Nikita Astrakhantsev, et al., Quantum error correction below the surface code threshold, Nature 638, 920 (2025).
  5. Clemens Müller, Jared H. Cole, and Jürgen Lisenfeld, Towards understanding two-level-systems in amorphous solids: Insights from quantum circuits, Rep. Prog. Phys. 82, 124501 (2019).
  6. Morten Kjaergaard, Mollie E. Schwartz, Jochen Braumüller, Philip Krantz, Joel I.-J. Wang, Simon Gustavsson, and William D. Oliver, Superconducting qubits: Current state of play, Annu. Rev. Condens. Matter Phys. 11, 369 (2020).
  7. John M. Martinis, K. B. Cooper, R. McDermott, Matthias Steffen, Markus Ansmann, K. D. Osborn, K. Cicak, Seongshik Oh, D. P. Pappas, R. W. Simmonds, and Clare C. Yu, Decoherence in Josephson qubits from dielectric loss, Phys. Rev. Lett. 95, 210503 (2005).
  8. Jiansong Gao, Miguel Daal, Anastasios Vayonakis, Shwetank Kumar, Jonas Zmuidzinas, Bernard Sadoulet, Benjamin A. Mazin, Peter K. Day, and Henry G. Leduc, Experimental evidence for a surface distribution of two-level systems in superconducting lithographed microwave resonators, Appl. Phys. Lett. 92, 152505 (2008).
  9. Jürgen Lisenfeld, Alexander Bilmes, Shlomi Matityahu, Sebastian Zanker, Michael Marthaler, Moshe Schechter, Gerd Schön, Alexander Shnirman, Georg Weiss, and Alexey V. Ustinov, Decoherence spectroscopy with individual two-level tunneling defects, Sci. Rep. 6, 23786 (2016).
  10. W. Woods, G. Calusine, A. Melville, A. Sevi, E. Golden, D. K. Kim, D. Rosenberg, J. L. Yoder, and W. D. Oliver, Determining interface dielectric losses in superconducting coplanar-waveguide resonators, Phys. Rev. Appl. 12, 014012 (2019).
  11. Conal E. Murray, Material matters in superconducting qubits, Mater. Sci. Eng.: R: Rep. 146, 100646 (2021).
  12. Alexander P. M. Place, Lila V. H. Rodgers, Pranav Mundada, Basil M. Smitham, Mattias Fitzpatrick, Zhaoqi Leng, Anjali Premkumar, Jacob Bryon, Andrei Vrajitoarea, Sara Sussman, et al., New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds, Nat. Commun. 12, 1779 (2021).
  13. C. R. H. McRae, H. Wang, J. Gao, M. R. Vissers, T. Brecht, A. Dunsworth, D. P. Pappas, and J. Mutus, Materials loss measurements using superconducting microwave resonators, Rev. Sci. Instrum. 91, 091101 (2020).
  14. J. Gao, L. R. Vale, J. A. B. Mates, D. R. Schmidt, G. C. Hilton, K. D. Irwin, F. Mallet, M. A. Castellanos-Beltran, K. W. Lehnert, J. Zmuidzinas, and H. G. Leduc, Strongly quadrature-dependent noise in superconducting microresonators measured at the vacuum-noise limit, Appl. Phys. Lett. 98, 232508 (2011).
  15. Cliff Chen, David Perello, Shahriar Aghaeimeibodi, Guillaume Marcaud, Ignace Jarrige, Hanho Lee, Warren Fon, Matt Matheny, and Jiansong Gao, Efficient methods for extracting superconducting resonator loss in the single-photon regime, J. Appl. Phys. 137, 044401 (2025).
  16. Qianxu Wang, Sara Magdalena Gómez, Juan S. Salcedo-Gallo, Roy Leibovitz, Jake Freeman, Salil Bedkihal, and Mattias Fitzpatrick, Evidence of memory effects in the dynamics of two-level system defect ensembles using broadband, cryogenic transient dielectric spectroscopy, arXiv:2505.18263 [quant-ph].
  17. W. A. Phillips, Two-level states in glasses, Rep. Prog. Phys. 50, 1657 (1987).
  18. P. V. Klimov, J. Kelly, Z. Chen, M. Neeley, A. Megrant, B. Burkett, R. Barends, K. Arya, B. Chiaro, Yu Chen, et al., Fluctuations of energy-relaxation times in superconducting qubits, Phys. Rev. Lett. 121, 090502 (2018).
  19. J. H. Béjanin, Y. Ayadi, X. Xu, C. Zhu, H. R. Mohebbi, and M. Mariantoni, Fluctuation spectroscopy of two-level systems in superconducting resonators, Phys. Rev. Appl. 18, 034009 (2022).
  20. André Vallières, Megan E. Russell, Xinyuan You, David A. Garcia-Wetten, Dominic P. Goronzy, Mitchell J. Walker, Michael J. Bedzyk, Mark C. Hersam, Alexander Romanenko, Yao Lu, et al., Loss tangent fluctuations due to two-level systems in superconducting microwave resonators, Appl. Phys. Lett. 126, 124001 (2025).
  21. C. T. Earnest, J. H. Béjanin, T. G. McConkey, E. A. Peters, A. Korinek, H. Yuan, and M. Mariantoni, Substrate surface engineering for high-quality silicon/aluminum superconducting resonators, Supercond. Sci. Technol. 31, 125013 (2018).
  22. Jiansong Gao, The Physics of Superconducting Microwave Resonators, Ph.D. thesis, California Instituate of Technology, 2008, https://resolver.caltech.edu/CaltechETD:etd-06092008-235549.
  23. M. S. Khalil, M. J. A. Stoutimore, F. C. Wellstood, and K. D. Osborn, An analysis method for asymmetric resonator transmission applied to superconducting devices, J. Appl. Phys. 111, 054510 (2012).
  24. W. A. Phillips, Amorphous Solids (Springer-Verlag, New York, 1981).
  25. Lara Faoro and Lev B. Ioffe, Interacting tunneling model for two-level systems in amorphous materials and its predictions for their dephasing and noise in superconducting microresonators, Phys. Rev. B 91, 014201 (2015).
  26. J. Gao, J. Zmuidzinas, A. Vayonakis, P. Day, B. Mazin, and H. Leduc, Equivalence of the effects on the complex conductivity of superconductor due to temperature change and external pair breaking, J. Low Temp. Phys. 151, 557 (2008).
  27. C. Neill, A. Megrant, R. Barends, Yu Chen, B. Chiaro, J. Kelly, J. Y. Mutus, P. J. J. O’Malley, D. Sank, J. Wenner, et al., Fluctuations from edge defects in superconducting resonators, Appl. Phys. Lett. 103, 072601 (2013).
  28. P. Welch, The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms, IEEE Trans. Audio Electroacoust. 15, 70 (1967).
  29. A. Dvoretzky, J. Kiefer, and J. Wolfowitz, Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator, Ann. Math. Stat. 27, 642 (1956).
  30. Tamin Tai, Jingnan Cai, and Steven M. Anlage, Anomalous loss reduction below two-level system saturation in aluminum superconducting resonators, Adv. Quantum Technol. 7, 2200145 (2024).
  31. Paul Szypryt, Development of Microwave Kinetic Inductance Detectors for Applications in Optical to Near-IR Astronomy, Ph.D. thesis, University of California Santa Barbara, 2017.
  32. Cliff Chen, Shahriar Aghaeimeibodi, Yuki Sato, Matthew H. Matheny, Oskar Painter, and Jiansong Gao, Supporting data for “Broadband high-precision measurement of two-level-system loss using multi wavelength superconducting resonators” (2025), https://doi.org/10.6084/m9.figshare.30193276.v1.

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Phys. Rev. Applied 25, 014045– Published 20 January, 2026
  • Received 12 June 2025
  • Revised 24 September 2025
  • Accepted 16 December 2025
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