- Open Access
Chaotic Fluctuations in a Universal Set of Transmon Qubit Gates
Phys. Rev. Lett. 136, 170601 – Published 29 April, 2026
DOI: https://doi.org/10.1103/8nch-ld18
Abstract
Transmon qubits arise from the quantization of nonlinear resonators, systems that are prone to the buildup of strong, possibly chaotic, fluctuations. Such instabilities will likely affect fast gate operations which involve the transient population of higher excited states outside the computational subspace. Here, we extend the statistical analysis from the spectrum of the generator to that of dynamics itself and show that the instantaneous eigenphases of the time evolution operator, in particular of their curvatures, allows for identifying the subspace most affected by instabilities. Our analysis shows that fast entangling gates, operating at speeds close to the so-called quantum speed limit, contain transient regimes where the dynamics indeed becomes partially chaotic for just two transmons. Surprisingly, this does not reflect in gate reliability, rather, slower operations lead to relatively enhanced errors.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (27)
- P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gustavsson, and W. D. Oliver, A quantum engineer’s guide to superconducting qubits, Appl. Phys. Rev. 6, 021318 (2019).
- J. J. García-Ripoll, Quantum Information and Quantum Optics with Superconducting Circuits (Cambridge University Press, Cambridge, England, 2022).
- C. Berke, E. Varvelis, S. Trebst, A. Altland, and D. P. DiVincenzo, Transmon platform for quantum computing challenged by chaotic fluctuations, Nat. Commun. 13, 2495 (2022).
- R. Shillito, A. Petrescu, J. Cohen, J. Beall, M. Hauru, M. Ganahl, A. G. Lewis, G. Vidal, and A. Blais, Dynamics of transmon ionization, Phys. Rev. Appl. 18, 034031 (2022).
- J. Cohen, A. Petrescu, R. Shillito, and A. Blais, Reminiscence of classical chaos in driven transmons, PRX Quantum 4, 020312 (2023).
- S.-D. Börner, C. Berke, D. P. DiVincenzo, S. Trebst, and A. Altland, Classical chaos in quantum computers, Phys. Rev. Res. 6, 033128 (2024).
- F. W. Strauch, P. R. Johnson, A. J. Dragt, C. J. Lobb, J. R. Anderson, and F. C. Wellstood, Quantum logic gates for coupled superconducting phase qubits, Phys. Rev. Lett. 91, 167005 (2003).
- P. Magnard, P. Kurpiers, B. Royer, T. Walter, J.-C. Besse, S. Gasparinetti, M. Pechal, J. Heinsoo, S. Storz, A. Blais, and A. Wallraff, Fast and unconditional all-microwave reset of a superconducting qubit, Phys. Rev. Lett. 121, 060502 (2018).
- S. Deffner and S. Campbell, Quantum speed limits: From Heisenberg’s uncertainty principle to optimal quantum control, J. Phys. A 50, 453001 (2017).
- M. H. Goerz, F. Motzoi, K. B. Whaley, and C. P. Koch, Charting the circuit QED design landscape using optimal control theory, npj Quantum Inf. 3, 37 (2017).
- C. P. Koch, U. Boscain, T. Calarco, G. Dirr, S. Filipp, S. J. Glaser, R. Kosloff, S. Montangero, T. Schulte-Herbrüggen, D. Sugny, and F. K. Wilhelm, Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe, Eur. Phys. J. Quantum Technol. 9, 19 (2022).
- J. Zhang, J. Vala, S. Sastry, and K. B. Whaley, Minimum construction of two-qubit quantum operations, Phys. Rev. Lett. 93, 020502 (2004).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/8nch-ld18 for a brief recap and further details of the analysis, which includes Refs. [14–19].
- Y. Makhlin, Nonlocal properties of two-qubit gates and mixed states, and the optimization of quantum computations, Quantum Inf. Process. 1, 243 (2002).
- J. Zhang, J. Vala, S. Sastry, and K. B. Whaley, Geometric theory of nonlocal two-qubit operations, Phys. Rev. A 67, 042313 (2003).
- V. Oganesyan and D. A. Huse, Localization of interacting fermions at high temperature, Phys. Rev. B 75, 155111 (2007).
- T. Guhr, A. Müller-Groeling, and H. A. Weidenmüller, Random-matrix theories in quantum physics: Common concepts, Phys. Rep. 299, 189 (1998).
- Y. Y. Atas, E. Bogomolny, O. Giraud, and G. Roux, Distribution of the ratio of consecutive level spacings in random matrix ensembles, Phys. Rev. Lett. 110, 084101 (2013).
- B. Swingle, Unscrambling the physics of out-of-time-order correlators, Nat. Phys. 14, 988 (2018).
- S. Kullback and R. A. Leibler, On information and sufficiency, Ann. Math. Stat. 22, 79 (1951).
- M. Filippone, P. W. Brouwer, J. Eisert, and F. von Oppen, Drude weight fluctuations in many-body localized systems, Phys. Rev. B 94, 201112(R) (2016).
- F. von Oppen, Exact distribution of eigenvalue curvatures of chaotic quantum systems, Phys. Rev. Lett. 73, 798 (1994).
- A. Maksymov, P. Sierant, and J. Zakrzewski, Energy level dynamics across the many-body localization transition, Phys. Rev. B 99, 224202 (2019).
- S. J. Garratt, S. Roy, and J. T. Chalker, Local resonances and parametric level dynamics in the many-body localized phase, Phys. Rev. B 104, 184203 (2021).
- T. Guhr, A. Müller–Groeling, and H. A. Weidenmüller, Random-matrix theories in quantum physics: Common concepts, Phys. Rep. 299, 189 (1998).
- D. Willsch et al., Observation of Josephson harmonics in tunnel junctions, Nat. Phys. 20, 815 (2024).
- D. Basilewitsch, S.-D. Börner, C. Berke, A. Altland, S. Trebst, and C. P. Koch, Data underpinning “Chaotic fluctuations in a universal set of transmon qubit gates,” 2026, 10.5281/zenodo.10160591.