- Physical Review Journals
All JournalsPhysics Magazine

PRX Quantum

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

Symmetrically Threaded Superconducting Quantum Interference Devices as Next-Generation Kerr-Cat Qubits

Bibek Bhandari1,*,†, Irwin Huang2,*, Ahmed Hajr3,4, Kagan Yanik2, Bingcheng Qing3, Ke Wang3, David I. Santiago3,5, Justin Dressel6,1, Irfan Siddiqi3,5 et al.

Andrew N. Jordan7,6,1,2

  • *These authors contributed equally.
  • †Contact author: bbhandari@chapman.edu
PDF

PRX Quantum 6, 030338 – Published 29 August, 2025

DOI: https://doi.org/10.1103/c661-yr2z

Abstract

Kerr-cat qubits are bosonic qubits offering autonomous bit-flip protection, traditionally studied using driven superconducting nonlinear asymmetric inductive element (SNAIL) oscillators. Here, we theoretically explore an alternative circuit for Kerr-cat qubits based on symmetrically threaded superconducting quantum interference devices (SQUIDs). The symmetrically threaded SQUID (STS) architecture employs a simplified flux-pumped design that suppresses two-photon dissipation, a dominant loss mechanism in high-Kerr regimes, by engineering the drive Hamiltonian’s flux operator to generate only even-order harmonics. By fulfilling two critical criteria for practical Kerr-cat qubit operation, the STS emerges as an ideal platform: (1) a static Hamiltonian with diluted Kerr nonlinearity (achieved via the STS’s middle branch) and (2) a drive Hamiltonian restricted to even harmonics, which ensures robust two-photon driving with reduced dissipation. For weak Kerr nonlinearity, we find that the coherent state lifetime (Tα) is similar between STS and SNAIL circuits. However, STS Kerr-cat qubits exhibit enhanced resistance to higher-order photon dissipation, enabling significantly extended Tα even with stronger Kerr nonlinearities (approximately 10 MHz). In contrast to SNAIL, STS Kerr-cat qubits display a Tα dip under weak two-photon driving for a high Kerr coefficient. We demonstrate that this dip can be suppressed by applying drive-dependent detuning, enabling Kerr-cat qubit operation with only eight Josephson junctions (of energies 80 GHz); fewer junctions suffice for higher junction energies. We further validate the robustness of the STS design by studying the impact of strong flux driving and asymmetric Josephson junctions on Tα. With the proposed design and considering a cat size of ten photons, we predict Tα of the order of tens of milliseconds, even in the presence of multiphoton heating and dephasing effects. The robustness of the STS Kerr-cat qubit makes it a promising component for fault-tolerant quantum processors.

View figure in article

Physics Subject Headings (PhySH)

Popular Summary

Quantum computing is currently an area of intense research because of its potential to perform tasks that are infeasible for classical computers. Superconducting circuits are one of the most promising platforms to realize quantum computing. One obstacle currently limiting superconducting circuits for quantum computing is the time in which the circuit remains a qubit. The short lifetime limits the operations that can be performed on the qubit. This motivates us to design a qubit with a long lifetime so that operations for quantum computing can be implemented on said qubits.

We propose an alternative superconducting Kerr-cat qubit design, the symmetrically threaded SQUID (STS). The STS Kerr-cat qubit is a driven nonlinear oscillator that consists mainly of a quantum harmonic oscillator with a Kerr nonlinearity and two-photon drive. We study how the lifetime of the STS Kerr-cat qubit is influenced by environmental factors, such as dissipation from higher-order effects. We find that the lifetime of STS Kerr-cat qubits is much higher than that of existing superconducting Kerr-cat qubits. This is because the STS Kerr-cat qubit is robust against higher-order multiphoton dissipation. Further, the STS Kerr-cat qubit has a stable lifetime even for relatively high Kerr nonlinearity, which can cause instability in previous qubit designs based on driven nonlinear oscillators.

The STS Kerr-cat qubit design is a promising component for fault-tolerant quantum processors. Due to the robustness and versatility of the STS, this opens up the STS to other quantum processing applications as well, such as amplification for quantum sensing.

Article Text

References (53)

  1. Y. Nakamura, Y. A. Pashkin, and J. Tsai, Coherent control of macroscopic quantum states in a single-Cooper-pair box, Nature 398, 786 (1999).
  2. 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).
  3. 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).
  4. A. Grimm, N. E. Frattini, S. Puri, S. O. Mundhada, S. Touzard, M. Mirrahimi, S. M. Girvin, S. Shankar, and M. H. Devoret, Stabilization and operation of a Kerr-cat qubit, Nature 584, 205 (2020).
  5. L. B. Nguyen, Y. Kim, A. Hashim, N. Goss, B. Marinelli, B. Bhandari, D. Das, R. K. Naik, J. M. Kreikebaum, A. N. Jordan et al., Programmable Heisenberg interactions between Floquet qubits, Nat. Phys. 20, 240 (2024).
  6. S. M. Anton, C. Müller, J. S. Birenbaum, S. R. O’Kelley, A. D. Fefferman, D. S. Golubev, G. C. Hilton, H.-M. Cho, K. D. Irwin, F. C. Wellstood, G. Schön, A. Shnirman, and J. Clarke, Pure dephasing in flux qubits due to flux noise with spectral density scaling as 1/fα, Phys. Rev. B 85, 224505 (2012).
  7. G. Ithier, E. Collin, P. Joyez, P. J. Meeson, D. Vion, D. Esteve, F. Chiarello, A. Shnirman, Y. Makhlin, J. Schriefl, and G. Schön, Decoherence in a superconducting quantum bit circuit, Phys. Rev. B 72, 134519 (2005).
  8. L. B. Nguyen, Y.-H. Lin, A. Somoroff, R. Mencia, N. Grabon, and V. E. Manucharyan, High-coherence fluxonium qubit, Phys. Rev. X 9, 041041 (2019).
  9. D. D. Briseño-Colunga, B. Bhandari, D. Das, L. B. Nguyen, Y. Kim, D. I. Santiago, I. Siddiqi, A. N. Jordan, and J. Dressel, Dynamical sweet and sour regions in bichromatically driven Floquet qubits, ArXiv:2505.22606.
  10. F. Yoshihara, K. Harrabi, A. O. Niskanen, Y. Nakamura, and J. S. Tsai, Decoherence of flux qubits due to 1/f flux noise, Phys. Rev. Lett. 97, 167001 (2006).
  11. S. Puri, S. Boutin, and A. Blais, Engineering the quantum states of light in a Kerr-nonlinear resonator by two-photon driving, Npj Quantum Inf. 3, 18 (2017).
  12. H. Goto, Universal quantum computation with a nonlinear oscillator network, Phys. Rev. A 93, 050301(R) (2016).
  13. S. Puri, A. Grimm, P. Campagne-Ibarcq, A. Eickbusch, K. Noh, G. Roberts, L. Jiang, M. Mirrahimi, M. H. Devoret, and S. M. Girvin, Stabilized cat in a driven nonlinear cavity: A fault-tolerant error syndrome detector, Phys. Rev. X 9, 041009 (2019).
  14. N. E. Frattini, R. G. Cortiñas, J. Venkatraman, X. Xiao, Q. Su, C. U. Lei, B. J. Chapman, V. R. Joshi, S. M. Girvin, R. J. Schoelkopf, S. Puri, and M. H. Devoret, Observation of pairwise level degeneracies and the quantum regime of the Arrhenius law in a double-well parametric oscillator, Phys. Rev. X 14, 031040 (2024).
  15. J. Venkatraman, R. G. Cortinas, N. E. Frattini, X. Xiao, and M. H. Devoret, A driven Kerr oscillator with two-fold degeneracies for qubit protection, PNAS 121, e2311241121 (2024).
  16. A. Hajr, B. Qing, K. Wang, G. Koolstra, Z. Pedramrazi, Z. Kang, L. Chen, L. B. Nguyen, C. Jünger, N. Goss, I. Huang, B. Bhandari, N. E. Frattini, S. Puri, J. Dressel, A. N. Jordan, D. I. Santiago, and I. Siddiqi, High-coherence Kerr-cat qubit in 2D architecture, Phys. Rev. X 14, 041049 (2024).
  17. D. Iyama, T. Kamiya, S. Fujii, H. Mukai, Y. Zhou, T. Nagase, A. Tomonaga, R. Wang, J.-J. Xue, S. Watabe et al., Observation and manipulation of quantum interference in a superconducting Kerr parametric oscillator, Nat. Commun. 15, 86 (2024).
  18. J. Chávez-Carlos, T. L. Lezama, R. G. Cortiñas, J. Venkatraman, M. H. Devoret, V. S. Batista, F. Pérez-Bernal, and L. F. Santos, Spectral kissing and its dynamical consequences in the squeeze-driven Kerr oscillator, Npj Quantum Inf. 9, 76 (2023).
  19. R. Gautier, A. Sarlette, and M. Mirrahimi, Combined dissipative and Hamiltonian confinement of cat qubits, PRX Quantum 3, 020339 (2022).
  20. S. Kwon, S. Watabe, and J.-S. Tsai, Autonomous quantum error correction in a four-photon Kerr parametric oscillator, Npj Quantum Inf. 8, 40 (2022).
  21. S. Puri, L. St-Jean, J. A. Gross, A. Grimm, N. E. Frattini, P. S. Iyer, A. Krishna, S. Touzard, L. Jiang, A. Blais, S. T. Flammia, and S. M. Girvin, Bias-preserving gates with stabilized cat qubits, Sci. Adv. 6, eaay5901 (2020).
  22. J. Venkatraman, X. Xiao, R. G. Cortiñas, and M. H. Devoret, Nonlinear dissipation in a driven superconducting circuit, Phys. Rev. A 110, 042411 (2024).
  23. X. You, J. A. Sauls, and J. Koch, Circuit quantization in the presence of time-dependent external flux, Phys. Rev. B 99, 174512 (2019).
  24. D. Ruiz, R. Gautier, J. Guillaud, and M. Mirrahimi, Two-photon driven Kerr quantum oscillator with multiple spectral degeneracies, Phys. Rev. A 107, 042407 (2023).
  25. C. K. Andersen, A. Kamal, N. A. Masluk, I. M. Pop, A. Blais, and M. H. Devoret, Quantum versus classical switching dynamics of driven dissipative Kerr resonators, Phys. Rev. Appl. 13, 044017 (2020).
  26. A. Miano, G. Liu, V. V. Sivak, N. E. Frattini, V. R. Joshi, W. Dai, L. Frunzio, and M. H. Devoret, Frequency-tunable Kerr-free three-wave mixing with a gradiometric SNAIL, Appl. Phys. Lett. 120, 184002 (2022).
  27. A. S. Darmawan, B. J. Brown, A. L. Grimsmo, D. K. Tuckett, and S. Puri, Practical quantum error correction with the XZZX code and Kerr-cat qubits, PRX Quantum 2, 030345 (2021).
  28. X. He, Y. Lu, D. Bao, H. Xue, W. Jiang, Z. Wang, A. Roudsari, P. Delsing, J. Tsai, and Z. Lin, Fast generation of Schrödinger cat states using a Kerr-tunable superconducting resonator, Nat. Commun. 14, 6358 (2023).
  29. M. Mirrahimi, Z. Leghtas, V. V. Albert, S. Touzard, R. J. Schoelkopf, L. Jiang, and M. H. Devoret, Dynamically protected cat-qubits: A new paradigm for universal quantum computation, New J. Phys. 16, 045014 (2014).
  30. B. Qing, A. Hajr, K. Wang, G. Koolstra, L. B. Nguyen, J. Hines, I. Huang, B. Bhandari, Z. Padramrazi, L. Chen et al., Benchmarking single-qubit gates on a noise-biased qubit beyond the fault-tolerant threshold, ArXiv:2411.04442.
  31. J. Venkatraman, Controlling the effective Hamiltonian of a driven quantum superconducting circuit, PhD thesis, Yale University, 2023, https://bpb-us-w2.wpmucdn.com/campuspress.yale.edu/dist/2/3627/files/2023/11/Jaya_thesis.pdf.
  32. P. Kapitza, Dynamic stability of the pendulum with vibrating suspension point (1951), Collected Papers of PL Kapitza 2, 714 (1965).
  33. Z. Leghtas, S. Touzard, I. M. Pop, A. Kou, B. Vlastakis, A. Petrenko, K. M. Sliwa, A. Narla, S. Shankar, M. J. Hatridge, M. Reagor, L. Frunzio, R. J. Schoelkopf, M. Mirrahimi, and M. H. Devoret, Confining the state of light to a quantum manifold by engineered two-photon loss, Science 347, 853 (2015).
  34. R. Lescanne, M. Villiers, T. Peronnin, A. Sarlette, M. Delbecq, B. Huard, T. Kontos, M. Mirrahimi, and Z. Leghtas, Exponential suppression of bit-flips in a qubit encoded in an oscillator, Nat. Phys. 16, 509 (2020).
  35. C. Berdou et al., One hundred second bit-flip time in a two-photon dissipative oscillator, PRX Quantum 4, 020350 (2023).
  36. U. Réglade, A. Bocquet, R. Gautier, J. Cohen, A. Marquet, E. Albertinale, N. Pankratova, M. Hallén, F. Rautschke, L.-A. Sellem, et al., Quantum control of a cat qubit with bit-flip times exceeding ten seconds, Nature 629, 778 (2024).
  37. R. Gautier, M. Mirrahimi, and A. Sarlette, Designing high-fidelity Zeno gates for dissipative cat qubits, PRX Quantum 4, 040316 (2023).
  38. J. Guillaud and M. Mirrahimi, Repetition cat qubits for fault-tolerant quantum computation, Phys. Rev. X 9, 041053 (2019).
  39. H. Putterman, J. Iverson, Q. Xu, L. Jiang, O. Painter, F. G. S. L. Brandão, and K. Noh, Stabilizing a bosonic qubit using colored dissipation, Physical Review Letter 128, 110502 (2022).
  40. S. Touzard, A. Grimm, Z. Leghtas, S. O. Mundhada, P. Reinhold, C. Axline, M. Reagor, K. Chou, J. Blumoff, K. M. Sliwa, S. Shankar, L. Frunzio, R. J. Schoelkopf, M. Mirrahimi, and M. H. Devoret, Coherent oscillations inside a quantum manifold stabilized by dissipation, Phys. Rev. X 8, 021005 (2018).
  41. T. Aoki, T. Kanao, H. Goto, S. Kawabata, and S. Masuda, Control of the zz coupling between Kerr cat qubits via transmon couplers, Phys. Rev. Appl. 21, 014030 (2024).
  42. Y.-H. Kang, Y. Xiao, Z.-C. Shi, Y. Wang, J.-Q. Yang, J. Song, and Y. Xia, Effective implementation of nonadiabatic geometric quantum gates of cat-state qubits using an auxiliary qutrit, New J. Phys. 25, 033029 (2023).
  43. Y. Suzuki, S. Kawabata, T. Yamamoto, and S. Masuda, Quantum state tomography for Kerr parametric oscillators, Phys. Rev. Appl. 20, 034031 (2023).
  44. S. Boutin, D. M. Toyli, A. V. Venkatramani, A. W. Eddins, I. Siddiqi, and A. Blais, Effect of higher-order nonlinearities on amplification and squeezing in Josephson parametric amplifiers, Phys. Rev. Appl. 8, 054030 (2017).
  45. G. J. Milburn and C. A. Holmes, Quantum coherence and classical chaos in a pulsed parametric oscillator with a Kerr nonlinearity, Phys. Rev. A 44, 4704 (1991).
  46. B. Wielinga and G. J. Milburn, Quantum tunneling in a Kerr medium with parametric pumping, Phys. Rev. A 48, 2494 (1993).
  47. N. E. Frattini, Three-wave mixing in superconducting circuits: stabilizing cats with SNAILs, PhD thesis, Yale University, 2021, https://elischolar.library.yale.edu/gsas_dissertations/332/.
  48. Y. Lu, A. Maiti, J. W. Garmon, S. Ganjam, Y. Zhang, J. Claes, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, High-fidelity parametric beamsplitting with a parity-protected converter, Nat. Commun. 14, 5767 (2023).
  49. I. García-Mata, R. G. Cortiñas, X. Xiao, J. Chávez-Carlos, V. S. Batista, L. F. Santos, and D. A. Wisniacki, Effective versus Floquet theory for the Kerr parametric oscillator, Quantum 8, 1298 (2024).
  50. Z. Hua, Y. Xu, W. Wang, Y. Ma, J. Zhou, W. Cai, H. Ai, Y.-x. Liu, M. Li, C.-L. Zou, and L. Sun, Engineering the nonlinearity of bosonic modes with a multi-loop SQUID, Phys. Rev. Appl. 23, 054031 (2025).
  51. C. Wang, X. Li, H. Xu, Z. Li, J. Wang, Z. Yang, Z. Mi, X. Liang, T. Su, C. Yang et al., Towards practical quantum computers: Transmon qubit with a lifetime approaching 0.5 milliseconds, Npj Quantum Inf. 8, 3 (2022).
  52. N. Bartolo, F. Minganti, J. Lolli, and C. Ciuti, Homodyne versus photon-counting quantum trajectories for dissipative Kerr resonators with two-photon driving, Eur. Phys. J. Spec. Top. 226, 2705 (2017).
  53. J. Venkatraman, X. Xiao, R. G. Cortiñas, A. Eickbusch, and M. H. Devoret, Static effective Hamiltonian of a rapidly driven nonlinear system, Phys. Rev. Lett. 129, 100601 (2022).

Outline

Information

PRX Quantum 6, 030338– Published 29 August, 2025
  • Received 28 May 2024
  • Revised 6 May 2025
  • Accepted 28 July 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