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Calibrating magnetic flux control in superconducting circuits by compensating distortions on timescales from nanoseconds up to tens of microseconds

Christoph Hellings1,2,*, Nathan Lacroix1,2,†, Ants Remm1,2,‡, Richard Boell1, Johannes Herrmann1,2, Stefania Lazăr1,2,§, Sebastian Krinner1,2,§, François Swiadek1,2, Christian Kraglund Andersen1,∥ et al.

Christopher Eichler1,2,¶ and Andreas Wallraff1,2,3

  • 1Department of Physics, ETH Zurich, CH-8093 Zurich, Switzerland
  • 2Quantum Center, ETH Zurich, CH-8093 Zurich, Switzerland
  • 3ETH Zurich – PSI Quantum Computing Hub, Paul Scherrer Institute, CH-5232 Villigen, Switzerland

  • *Contact author: christoph.hellings@phys.ethz.ch
  • †Present address: Google Quantum AI, Goleta, CA, USA.
  • ‡Present address: Atlantic Quantum, Cambridge, MA, USA.
  • §Present address: Zurich Instruments AG, Zurich, Switzerland.
  • ∥Present address: QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands.
  • Present address: Department of Physics, Friedrich-Alexander University Erlangen-Nürnberg (FAU), Erlangen, Germany.

Phys. Rev. Research 7, 043142 – Published 7 November, 2025

DOI: https://doi.org/10.1103/1qhb-r4fb

Abstract

Fast tuning of the transition frequency of superconducting qubits using magnetic flux is essential, for example, for realizing high-fidelity two-qubit gates with low leakage or for reducing errors in dispersive qubit readout. To apply accurately shaped flux pulses, signal distortions induced by the flux control lines need to be carefully compensated for. This requires their in situ characterization at the reference plane of the qubit. However, many existing approaches are limited in time resolution or in pulse duration. Here, we overcome these limitations and demonstrate accurate flux control with subpermille residual frequency errors on timescales ranging from nanoseconds to tens of microseconds. We achieve this by combining two complementary methods to characterize and compensate for pulse distortions. We have deployed this approach successfully in a quantum error correction experiment calibrating 24 flux-activated two-qubit gates. Reliable calibration methods, as the ones presented here, are essential in experiments scaling up superconducting quantum processors.

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References (72)

  1. 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).
  2. J. A. Schreier, A. A. Houck, J. Koch, D. I. Schuster, B. R. Johnson, J. M. Chow, J. M. Gambetta, J. Majer, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Suppressing charge noise decoherence in superconducting charge qubits, Phys. Rev. B 77, 180502 (2008).
  3. P. V. Klimov et al., Fluctuations of energy-relaxation times in superconducting qubits, Phys. Rev. Lett. 121, 090502 (2018).
  4. F. Swiadek, R. Shillito, P. Magnard, A. Remm, C. Hellings, N. Lacroix, Q. Ficheux, D. C. Zanuz, G. J. Norris, A. Blais, S. Krinner, and A. Wallraff, Enhancing dispersive readout of superconducting qubits through dynamic control of the dispersive shift: Experiment and theory, PRX Quantum 5, 040326 (2024).
  5. Y. Zhou, Z. Zhang, Z. Yin, S. Huai, X. Gu, X. Xu, J. Allcock, F. Liu, G. Xi, Q. Yu, H. Zhang, M. Zhang, H. Li, X. Song, Z. Wang, D. Zheng, S. An, Y. Zheng, and S. Zhang, Rapid and unconditional parametric reset protocol for tunable superconducting qubits, Nat. Commun. 12, 5924 (2021).
  6. M. McEwen et al., Removing leakage-induced correlated errors in superconducting quantum error correction, Nat. Commun. 12, 1761 (2021).
  7. N. Lacroix, L. Hofele, A. Remm, O. Benhayoune-Khadraoui, A. McDonald, R. Shillito, S. Lazăr, C. Hellings, F. Swiadek, D. Colao-Zanuz, A. Flasby, M. B. Panah, M. Kerschbaum, G. J. Norris, A. Blais, A. Wallraff, and S. Krinner, Fast flux-activated leakage reduction for superconducting quantum circuits, Phys. Rev. Lett. 134, 120601 (2025).
  8. 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).
  9. L. DiCarlo, J. M. Chow, J. M. Gambetta, L. S. Bishop, B. R. Johnson, D. I. Schuster, J. Majer, A. Blais, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, Demonstration of two-qubit algorithms with a superconducting quantum processor, Nature (London) 460, 240 (2009).
  10. M. A. Rol, F. Battistel, F. K. Malinowski, C. C. Bultink, B. M. Tarasinski, R. Vollmer, N. Haider, N. Muthusubramanian, A. Bruno, B. M. Terhal, and L. DiCarlo, Fast, high-fidelity conditional-phase gate exploiting leakage interference in weakly anharmonic superconducting qubits, Phys. Rev. Lett. 123, 120502 (2019).
  11. V. Negîrneac, H. Ali, N. Muthusubramanian, F. Battistel, R. Sagastizabal, M. S. Moreira, J. F. Marques, W. J. Vlothuizen, M. Beekman, C. Zachariadis, N. Haider, A. Bruno, and L. DiCarlo, High-fidelity controlled-Z gate with maximal intermediate leakage operating at the speed limit in a superconducting quantum processor, Phys. Rev. Lett. 126, 220502 (2021).
  12. B. Royer, A. L. Grimsmo, N. Didier, and A. Blais, Fast and high-fidelity entangling gate through parametrically modulated longitudinal coupling, Quantum 1, 11 (2017).
  13. S. A. Caldwell et al., Parametrically activated entangling gates using transmon qubits, Phys. Rev. Appl. 10, 034050 (2018).
  14. Y. Chen et al., Qubit architecture with high coherence and fast tunable coupling, Phys. Rev. Lett. 113, 220502 (2014).
  15. F. Yan, P. Krantz, Y. Sung, M. Kjaergaard, D. L. Campbell, T. P. Orlando, S. Gustavsson, and W. D. Oliver, Tunable coupling scheme for implementing high-fidelity two-qubit gates, Phys. Rev. Appl. 10, 054062 (2018).
  16. Y. Sung, L. Ding, J. Braumüller, A. Vepsäläinen, B. Kannan, M. Kjaergaard, A. Greene, G. O. Samach, C. McNally, D. Kim, A. Melville, B. M. Niedzielski, M. E. Schwartz, J. L. Yoder, T. P. Orlando, S. Gustavsson, and W. D. Oliver, Realization of high-fidelity CZ and ZZ-free iSWAP gates with a tunable coupler, Phys. Rev. X 11, 021058 (2021).
  17. Y. Xu, J. Chu, J. Yuan, J. Qiu, Y. Zhou, L. Zhang, X. Tan, Y. Yu, S. Liu, J. Li, F. Yan, and D. Yu, High-fidelity, high-scalability two-qubit gate scheme for superconducting qubits, Phys. Rev. Lett. 125, 240503 (2020).
  18. M. C. Collodo, J. Herrmann, N. Lacroix, C. K. Andersen, A. Remm, S. Lazar, J.-C. Besse, T. Walter, A. Wallraff, and C. Eichler, Implementation of conditional phase gates based on tunable ZZ interactions, Phys. Rev. Lett. 125, 240502 (2020).
  19. B. Foxen et al., Demonstrating a continuous set of two-qubit gates for near-term quantum algorithms, Phys. Rev. Lett. 125, 120504 (2020).
  20. S. Krinner, N. Lacroix, A. Remm, A. D. Paolo, E. Genois, C. Leroux, C. Hellings, S. Lazar, F. Swiadek, J. Herrmann, G. J. Norris, C. K. Andersen, M. Müller, A. Blais, C. Eichler, and A. Wallraff, Realizing repeated quantum error correction in a distance-three surface code, Nature (London) 605, 669 (2022).
  21. J. F. Marques, B. M. Varbanov, M. S. Moreira, H. Ali, N. Muthusubramanian, C. Zachariadis, F. Battistel, M. Beekman, N. Haider, W. Vlothuizen, A. Bruno, B. M. Terhal, and L. DiCarlo, Logical-qubit operations in an error-detecting surface code, Nat. Phys. 18, 80 (2022).
  22. Google Quantum AI, Suppressing quantum errors by scaling a surface code logical qubit, Nature (London) 614, 676 (2023).
  23. N. Sundaresan, T. J. Yoder, Y. Kim, M. Li, E. H. Chen, G. Harper, T. Thorbeck, A. W. Cross, A. D. Córcoles, and M. Takita, Demonstrating multi-round subsystem quantum error correction using matching and maximum likelihood decoders, Nat. Commun. 14, 2852 (2023).
  24. R. Acharya et al., Quantum error correction below the surface code threshold, Nature (London) 638, 920 (2025).
  25. M. A. Rol, L. Ciorciaro, F. K. Malinowski, B. M. Tarasinski, R. E. Sagastizabal, C. C. Bultink, Y. Salathe, N. Haandbaek, J. Sedivy, and L. DiCarlo, Time-domain characterization and correction of on-chip distortion of control pulses in a quantum processor, Appl. Phys. Lett. 116, 054001 (2020).
  26. B. Foxen et al., High speed flux sampling for tunable superconducting qubits with an embedded cryogenic transducer, Supercond. Sci. Technol. 32, 015012 (2019).
  27. B. Johnson, Controlling photons in superconducting electrical circuits, Ph.D. thesis, Yale University, 2011.
  28. R. Barends et al., Superconducting quantum circuits at the surface code threshold for fault tolerance, Nature (London) 508, 500 (2014).
  29. J. S. Kelly, Fault-tolerant superconducting qubits, Ph.D. thesis, University of California, Santa Barbara, 2015.
  30. M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, Synthesizing arbitrary quantum states in a superconducting resonator, Nature (London) 459, 546 (2009).
  31. C.-T. Chen, Y.-H. Shi, Z. Xiang, Z.-A. Wang, T.-M. Li, H.-Y. Sun, T.-S. He, X. Song, S. Zhao, D. Zheng, K. Xu, and H. Fan, ScQ cloud quantum computation for generating Greenberger-Horne-Zeilinger states of up to 10 qubits, Sci. China Phys. Mech. Astron. 65, 110362 (2022).
  32. Z. Chen, Metrology of quantum control and measurement in superconducting qubits, Ph.D. thesis, University of California, Santa Barbara, 2018.
  33. C. Neill et al., A blueprint for demonstrating quantum supremacy with superconducting qubits, Science 360, 195 (2018).
  34. J. Braumüller, A. H. Karamlou, Y. Yanay, B. Kannan, D. Kim, M. Kjaergaard, A. Melville, B. M. Niedzielski, Y. Sung, A. Vepsäläinen, R. Winik, J. L. Yoder, T. P. Orlando, S. Gustavsson, C. Tahan, and W. D. Oliver, Probing quantum information propagation with out-of-time-ordered correlators, Nat. Phys. 18, 172 (2022).
  35. M. Jerger, A. Kulikov, Z. Vasselin, and A. Fedorov, In situ characterization of qubit control lines: A qubit as a vector network analyzer, Phys. Rev. Lett. 123, 150501 (2019).
  36. T.-M. Li et al., High-precision pulse calibration of tunable couplers for high-fidelity two-qubit gates in superconducting quantum processors, Phys. Rev. Appl. 23, 024059 (2025).
  37. J. Kelly et al., Optimal quantum control using randomized benchmarking, Phys. Rev. Lett. 112, 240504 (2014).
  38. 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).
  39. M. Rice, Digital Communications: A Discrete-Time Approach (Pearson Prentice Hall, Upper Saddle River, NJ, 2009).
  40. N. Vitanov, B. Shore, L. Yatsenko, K. Böhmer, T. Halfmann, T. Rickes, and K. Bergmann, Power broadening revisited: Theory and experiment, Opt. Commun. 199, 117 (2001).
  41. L. O. Chua, C. A. Desoer, and E. S. Kuh, Linear and Nonlinear Circuits (McGraw-Hill, New York, NY, 1987).
  42. A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing, 2nd ed. (Prentice Hall, Upper Saddle River, NJ, 1999).
  43. G. M. Wing, A Primer on Integral Equations of the First Kind (Society for Industrial and Applied Mathematics, Philadelphia, PA, 1991).
  44. B. Borchers and R. Aster, Time series/data processing and analysis: Notes on deconvolution, Lecture notes, University of Memphis, 2013.
  45. V. S. Ferreira, G. Kim, A. Butler, H. Pichler, and O. Painter, Deterministic generation of multidimensional photonic cluster states with a single quantum emitter, Nat. Phys. 20, 865 (2024).
  46. E. Magesan, J. M. Gambetta, B. R. Johnson, C. A. Ryan, J. M. Chow, S. T. Merkel, M. P. da Silva, G. A. Keefe, M. B. Rothwell, T. A. Ohki, M. B. Ketchen, and M. Steffen, Efficient measurement of quantum gate error by interleaved randomized benchmarking, Phys. Rev. Lett. 109, 080505 (2012).
  47. A. D. Córcoles, J. M. Gambetta, J. M. Chow, J. A. Smolin, M. Ware, J. Strand, B. L. T. Plourde, and M. Steffen, Process verification of two-qubit quantum gates by randomized benchmarking, Phys. Rev. A 87, 030301 (2013).
  48. C. J. Wood and J. M. Gambetta, Quantification and characterization of leakage errors, Phys. Rev. A 97, 032306 (2018).
  49. A. H. Karamlou, J. Braumüller, Y. Yanay, A. Di Paolo, P. M. Harrington, B. Kannan, D. Kim, M. Kjaergaard, A. Melville, S. Muschinske, B. M. Niedzielski, A. Vepsäläinen, R. Winik, J. L. Yoder, M. Schwartz, C. Tahan, T. P. Orlando, S. Gustavsson, and W. D. Oliver, Quantum transport and localization in 1d and 2d tight-binding lattices, npj Quantum Inf. 8, 35 (2022).
  50. A. Aggarwal, J. Fernández-Pendás, T. Abad, D. Shiri, H. Jakobsson, M. Rommel, A. Nylander, E. Hogedal, A. Osman, J. Biznárová, R. Rehammar, M. F. Giannelli, A. F. Roudsari, J. Bylander, and G. Tancredi, Mitigating transients in flux-control signals in a superconducting quantum processor, arXiv:2503.08645.
  51. 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).
  52. N. Earnest, S. Chakram, Y. Lu, N. Irons, R. K. Naik, N. Leung, L. Ocola, D. A. Czaplewski, B. Baker, J. Lawrence, J. Koch, and D. I. Schuster, Realization of a Λ system with metastable states of a capacitively shunted fluxonium, Phys. Rev. Lett. 120, 150504 (2018).
  53. J. A. Grover, J. I. Basham, A. Marakov, S. M. Disseler, R. T. Hinkey, M. Khalil, Z. A. Stegen, T. Chamberlin, W. DeGottardi, D. J. Clarke, J. R. Medford, J. D. Strand, M. J. A. Stoutimore, S. Novikov, D. G. Ferguson, D. Lidar, K. M. Zick, and A. J. Przybysz, Fast, lifetime-preserving readout for high-coherence quantum annealers, PRX Quantum 1, 020314 (2020).
  54. N. Wittler, F. Roy, K. Pack, M. Werninghaus, A. S. Roy, D. J. Egger, S. Filipp, F. K. Wilhelm, and S. Machnes, Integrated tool set for control, calibration, and characterization of quantum devices applied to superconducting qubits, Phys. Rev. Appl. 15, 034080 (2021).
  55. T. Proctor, M. Revelle, E. Nielsen, K. Rudinger, D. Lobser, P. Maunz, R. Blume-Kohout, and K. Young, Detecting and tracking drift in quantum information processors, Nat. Commun. 11, 5396 (2020).
  56. C. Hellings, N. Lacroix, A. Remm, R. Boell, J. Herrmann, S. Lazar, S. Krinner, F. Swiadek, C. K. Andersen, C. Eichler, and A. Wallraff, Supporting Data: Calibrating Magnetic Flux Control in Superconducting Circuits by Compensating Distortions on Time Scales from Nanoseconds up to Tens of Microseconds (2025), https://doi.org/10.3929/ethz-c-000783499.
  57. A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
  58. S. Krinner, S. Storz, P. Kurpiers, P. Magnard, J. Heinsoo, R. Keller, J. Lütolf, C. Eichler, and A. Wallraff, Engineering cryogenic setups for 100-qubit scale superconducting circuit systems, EPJ Quantum Technol. 6, 2 (2019).
  59. 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).
  60. J. G. Baldwin and D. F. Dubbert, Quadrature mixer LO leakage suppression through quadrature DC bias, Technical Report, Sandia National Laboratories, 2002.
  61. J. Herrmann, C. Hellings, S. Lazar, F. Pfäffli, F. Haupt, T. Thiele, D. C. Zanuz, G. J. Norris, F. Heer, C. Eichler, and A. Wallraff, Frequency up-conversion schemes for controlling superconducting qubits, arXiv:2210.02513.
  62. S. W. Jolin, R. Borgani, M. O. Tholén, D. Forchheimer, and D. B. Haviland, Calibration of mixer amplitude and phase imbalance in superconducting circuits, Rev. Sci. Instrum. 91, 124707 (2020).
  63. P. Stoica and Y. Selen, Model-order selection: A review of information criterion rules, IEEE Signal Process. Mag. 21, 36 (2004).
  64. Handbook of Mathematical Functions, edited by M. Abramowitz and I. Stegun (United States Department of Commerce, Washington, DC, 1972).
  65. G. E. Collins and W. Krandick, An efficient algorithm for infallible polynomial complex root isolation, in Proceedings of International Symposium on Symbolic and Algebraic Computation (ACM Press, New York, NY, 1992), pp. 189–194.
  66. A. S. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems (Prentice Hall, Upper Saddle River, NJ, 1997).
  67. H. P. Gavin, The Levenberg-Marquardt algorithm for nonlinear least squares curve-fitting problems, Technical Report, Department of Civil and Environmental Engineering, Duke University, Durham, NC, 2024.
  68. Y. Salathé, P. Kurpiers, T. Karg, C. Lang, C. K. Andersen, A. Akin, S. Krinner, C. Eichler, and A. Wallraff, Low-latency digital signal processing for feedback and feedforward in quantum computing and communication, Phys. Rev. Appl. 9, 034011 (2018).
  69. S. M. Riad, The deconvolution problem: An overview, Proc. IEEE 74, 82 (1986).
  70. A. Neumaier, Solving ill-conditioned and singular linear systems: A tutorial on regularization, SIAM Rev. 40, 636 (1998).
  71. A. N. Tikhonov, On the solution of ill-posed problems and the method of regularization, Dokl. Akad. Nauk 151, 501 (1963).
  72. R. Adams and J. Fournier, Sobolev Spaces (Academic Press, Cambridge, MA, 2003).

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