- Physical Review Journals
All JournalsPhysics Magazine

APS Open Science

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

Energy relaxation via quantum thermalization: A superconducting qubit coupled to an interacting many-body two-level system

Xue-Yi Guo*

  • *Contact author: guoxy@baqis.ac.cn
PDF

APS Open Sci. 1, 000099 – Published 19 August, 2026

DOI: https://doi.org/10.1103/b11b-3hm4

Abstract

Two-level systems (TLS) are widely recognized as a dominant source of energy relaxation in superconducting qubits, limiting coherence times and device performance. While TLS-induced dissipation is often modeled as independent channels, interacting TLS can form finite many-body environments whose dynamical role in qubit relaxation remains insufficiently understood. Building on the information-erasure-based framework for irreversible thermalization developed in our previous work, we present a microscopic model and numerical simulations of a superconducting qubit coupled to a finite interacting many-body TLS environment as a concrete physical realization of this mechanism. We show that effective irreversible energy relaxation can emerge from intrinsic many-body dynamics without invoking external baths or phenomenological dissipation. The introduction of information erasure drives a transition from coherent oscillatory energy exchange to nonoscillatory exponential relaxation of the qubit. The relaxation times exhibit the scaling T1,T2∝Jq,τ−2 with respect to the qubit-TLS coupling strength, consistent with Fermi's golden rule and Lindblad-type descriptions. Importantly, both exponential decay and its scaling behavior arise directly from microscopic many-body dynamics. These results provide quantitative insight into TLS-induced decoherence mechanisms and establish a microscopic link between information erasure, many-body thermalization, and irreversible relaxation in superconducting quantum systems.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (38)

  1. R. Acharya, D. A. Abanin, L. Aghababaie-Beni, I. Aleiner, T. I. Andersen, M. Ansmann, F. Arute, K. Arya, A. Asfaw, N. Astrakhantsev, et al., Quantum error correction below the surface code threshold, Nature (London) 638, 920 (2025).
  2. T. He, W. Lin, R. Wang, Y. Li, J. Bei, J. Cai, S. Cao, D. Chen, K. Chen, X. Chen, et al., Experimental quantum error correction below the surface code threshold via all-microwave leakage suppression, Phys. Rev. Lett. 135, 260601 (2025).
  3. A. Bilmes, A. Megrant, P. Klimov, G. Weiss, J. M. Martinis, A. V. Ustinov, and J. Lisenfeld, Resolving the positions of defects in superconducting quantum bits, Sci. Rep. 10, 3090 (2020).
  4. M. Odeh, K. Godeneli, E. Li, R. Tangirala, H. Zhou, X. Zhang, Z.-H. Zhang, and A. Sipahigil, Non-Markovian dynamics of a superconducting qubit in a phononic bandgap, Nat. Phys. 21, 406 (2025).
  5. R. Barends, J. Wenner, M. Lenander, Y. Chen, R. C. Bialczak, J. Kelly, E. Lucero, P. O'Malley, M. Mariantoni, D. Sank, H. Wang, T. C. White, Y. Yin, J. Zhao, A. N. Cleland, J. M. Martinis, and J. J. A. Baselmans, Minimizing quasiparticle generation from stray infrared light in superconducting quantum circuits, Appl. Phys. Lett. 99, 113507 (2011).
  6. S. Gustavsson, F. Yan, G. Catelani, J. Bylander, A. Kamal, J. Birenbaum, D. Hover, D. Rosenberg, G. Samach, A. P. Sears, S. J. Weber, J. L. Yoder, J. Clarke, A. J. Kerman, F. Yoshihara, Y. Nakamura, T. P. Orlando, and W. D. Oliver, Suppressing relaxation in superconducting qubits by quasiparticle pumping, Science 354, 1573 (2016).
  7. S. E. d. Graaf, L. Faoro, L. B. Ioffe, S. Mahashabde, J. J. Burnett, T. Lindström, S. E. Kubatkin, A. V. Danilov, and A. Y. Tzalenchuk, Two-level systems in superconducting quantum devices due to trapped quasiparticles, Sci. Adv. 6, eabc5055 (2020).
  8. W. A. Phillips, Tunneling states in amorphous solids, J. Low Temp. Phys. 7, 351 (1972).
  9. W. A. Phillips, Two-level states in glasses, Rep. Prog. Phys. 50, 1657 (1987).
  10. 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).
  11. J. Gao, M. Daal, A. Vayonakis, S. Kumar, J. Zmuidzinas, B. Sadoulet, B. A. Mazin, P. K. Day, and H. G. Leduc, Experimental evidence for a surface distribution of two-level systems in superconducting lithographed microwave resonators, Appl. Phys. Lett. 92, 152505 (2008).
  12. H. Wang, M. Hofheinz, J. Wenner, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, A. D. O'Connell, D. Sank, M. Weides, A. N. Cleland, and J. M. Martinis, Improving the coherence time of superconducting coplanar resonators, Appl. Phys. Lett. 95, 233508 (2009).
  13. W. Woods, G. Calusine, A. Melville, A. Sevi, E. Golden, D. Kim, D. Rosenberg, J. Yoder, and W. Oliver, Determining interface dielectric losses in superconducting coplanar-waveguide resonators, Phys. Rev. Appl. 12, 014012 (2019).
  14. K. D. Crowley, R. A. McLellan, A. Dutta, N. Shumiya, A. P. Place, X. H. Le, Y. Gang, T. Madhavan, M. P. Bland, R. Chang, et al., Disentangling losses in tantalum superconducting circuits, Phys. Rev. X 13, 041005 (2023).
  15. J. Lisenfeld, G. J. Grabovskij, C. Müller, J. H. Cole, G. Weiss, and A. V. Ustinov, Observation of directly interacting coherent two-level systems in an amorphous material, Nat. Commun. 6, 6182 (2015).
  16. J. Lisenfeld, A. Bilmes, A. Megrant, R. Barends, J. Kelly, P. Klimov, G. Weiss, J. M. Martinis, and A. V. Ustinov, Electric field spectroscopy of material defects in transmon qubits, npj Quantum Inf. 5, 105 (2019).
  17. Y. Shalibo, Y. Rofe, D. Shwa, F. Zeides, M. Neeley, J. M. Martinis, and N. Katz, Lifetime and coherence of two-level defects in a Josephson junction, Phys. Rev. Lett. 105, 177001 (2010).
  18. S. M. Meißner, A. Seiler, J. Lisenfeld, A. V. Ustinov, and G. Weiss, Probing individual tunneling fluctuators with coherently controlled tunneling systems, Phys. Rev. B 97, 180505 (2018).
  19. M. Carroll, S. Rosenblatt, P. Jurcevic, I. Lauer, and A. Kandala, Dynamics of superconducting qubit relaxation times, npj Quantum Inf. 8, 132 (2022).
  20. F. Berritta, J. Benestad, J. A. Krzywda, O. Krause, M. A. Marciniak, S. Krøjer, C. W. Warren, E. Hogedal, A. Nylander, I. Ahmad, A. Osman, J. Biznárová, M. Rommel, A. F. Roudsari, J. Bylander, G. Tancredi, J. Danon, J. Hastrup, F. Kuemmeth, and M. Kjaergaard, Real-time adaptive tracking of fluctuating relaxation rates in superconducting qubits, Phys. Rev. X 16, 011025 (2026).
  21. C. Müller, A. Shnirman, and Y. Makhlin, Relaxation of Josephson qubits due to strong coupling to two-level systems, Phys. Rev. B 80, 134517 (2009).
  22. Y. Cho, D. Jasrasaria, K. G. Ray, D. M. Tennant, V. Lordi, J. L. DuBois, and Y. J. Rosen, Simulating noise on a quantum processor: Interactions between a qubit and resonant two-level system bath, Quantum Sci. Technol. 8, 045023 (2023).
  23. B. Karimi, X. Wu, A. N. Cleland, and J. P. Pekola, Blueprint for experiments exploring the quantum recurrence theorem on a coupled multiqubit system, Phys. Rev. Res. 8, L012062 (2026).
  24. X.-Y. Guo, Thermalization and irreversibility of an isolated quantum system, arXiv:2503.04152.
  25. X.-Y. Guo, Thermalization and irreversibility of an isolated quantum system II, arXiv:2506.01351.
  26. J. Lisenfeld, A. Bilmes, S. Matityahu, S. Zanker, M. Marthaler, M. Schechter, G. Schön, A. Shnirman, G. Weiss, and A. V. Ustinov, Decoherence spectroscopy with individual two-level tunneling defects, Sci. Rep. 6, 23786 (2016).
  27. O. Oreshkov and T. A. Brun, Continuous quantum error correction for non-Markovian decoherence, Phys. Rev. A 76, 022318 (2007).
  28. M. P. Bland, F. Bahrami, J. G. C. Martinez, P. H. Prestegaard, B. M. Smitham, A. Joshi, E. Hedrick, S. Kumar, A. Yang, A. C. Pakpour-Tabrizi, A. Jindal, R. D. Chang, G. Cheng, N. Yao, R. J. Cava, N. P. de Leon, and A. A. Houck, Millisecond lifetimes and coherence times in 2D transmon qubits, Nature (London) 647, 343 (2025).
  29. P. Klimov, J. Kelly, Z. Chen, M. Neeley, A. Megrant, B. Burkett, R. Barends, K. Arya, B. Chiaro, Y. Chen, et al., Fluctuations of energy-relaxation times in superconducting qubits, Phys. Rev. Lett. 121, 090502 (2018).
  30. J. Etxezarreta Martinez, P. Fuentes, P. Crespo, and J. Garcia-Frias, Time-varying quantum channel models for superconducting qubits, npj Quantum Inf. 7, 115 (2021).
  31. A. deMarti iOlius, J. Etxezarreta Martinez, P. Fuentes, P. M. Crespo, and J. Garcia-Frias, Performance of surface codes in realistic quantum hardware, Phys. Rev. A 106, 062428 (2022).
  32. J. Etxezarreta Martinez, P. Fuentes, A. deMarti iOlius, J. Garcia-Frias, J. R. Fonollosa, and P. M. Crespo, Multiqubit time-varying quantum channels for NISQ-era superconducting quantum processors, Phys. Rev. Res. 5, 033055 (2023).
  33. M. Hegedüs, R. Banerjee, A. Hutcheson, T. Barker, S. Mahashabde, A. V. Danilov, S. E. Kubatkin, V. Antonov, and S. E. de Graaf, In situ scanning gate imaging of individual quantum two-level system defects in live superconducting circuits, Sci. Adv. 11, eadt8586 (2025).
  34. A. Dane, K. Balakrishnan, B. Wacaser, L.-W. Hung, H. J. Mamin, D. Rugar, R. M. Shelby, C. Murray, K. Rodbell, and J. Sleight, Robust quality factor assessment of high-coherence superconducting qubits, npj Quantum Inf. 12, 62 (2026).
  35. P. Weinberg and M. Bukov, QuSpin: A Python package for dynamics and exact diagonalisation of quantum many body systems. Part I: Spin chains, SciPost Phys. 2, 003 (2017).
  36. P. Weinberg and M. Bukov, QuSpin: A Python package for dynamics and exact diagonalisation of quantum many body systems. Part II: Bosons, fermions and higher spins, SciPost Phys. 7, 020 (2019).
  37. X.-Y. Guo, Energy relaxation via quantum thermalization: A superconducting qubit coupled to an interacting many-body two-level system, Version 1, [Dataset], Zenodo, 2026, https://doi.org/10.5281/zenodo.19346098.
  38. X.-Y. Guo, Numerical simulation code for “Energy relaxation via quantum thermalization: A superconducting qubit coupled to an interacting many-body two-level system”, Version 1.0.0, [Software], Zenodo, 2026, https://doi.org/10.5281/zenodo.19345775.

Outline

Information

APS Open Sci. 1, 000099– Published 19 August, 2026
Vol. 1
  • Received 10 March 2026
  • Revised 1 July 2026
  • Accepted 11 August 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