- 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

Dispersive Qubit Readout with Intrinsic Resonator Reset

M. Jerger1,*, F. Motzoi2,3,†, Y. Gao4, C. Dickel5, L. Buchmann6, F. A. Cárdenas-López2, A. Bengtsson7, G. Tancredi7, C. W. Warren7 et al.

J. Bylander7, D. DiVincenzo8, R. Barends4, and P. A. Bushev1,‡

  • *Contact author: m.jerger@fz-juelich.de
  • †Contact author: f.motzoi@fz-juelich.de
  • ‡Contact author: p.bushev@fz-juelich.de
PDF

PRX Quantum 7, 033042 – Published 31 August, 2026

DOI: https://doi.org/10.1103/z5x1-2mr9

Abstract

Measurement and readout speed impose limits for logical qubit and qudit performance in quantum computing. Here, we experimentally demonstrate a universal analytical method for designing bandwidth-efficient dispersive readout pulses that intrinsically reset the resonator and extend it to multiple quantum states. The approach is based on universal analytical pulses and requires knowledge of the qubit and resonator parameters, but needs no direct optimization of the pulse shape, even when accounting for the nonlinearity of the system. When correcting for the Kerr nonlinearity, we find even more precise solutions to the speed-versus-photon-number trade-off, achieving 102 photon readout with reset to 10−2 within 3κ−1 duration and amplifier efficiency- and T1-limited assignment error around 0.6%. Results on qubits and qutrits validate the approach.

View figure in article

Physics Subject Headings (PhySH)

Popular Summary

Reading out a state of a quantum bit (qubit) is one of the slowest steps in superconducting quantum computing. After a measurement, the microwave resonator continues to ring and remains populated with photons. These residual photons disturb the qubit, forcing the processor to pause before the next operation. In repeated rounds of quantum error correction, such delays become a serious bottleneck. We introduce DRACHMA, an analytical method for designing readout pulses that both distinguish the qubit state with high fidelity and empty the resonator by the end of the measurement. The pulse shapes follow directly from the nonlinear dynamics of the coupled qubit-resonator system and require neither numerical optimization nor additional hardware. DRACHMA achieves 99.4% readout fidelity while reducing the residual photon population by more than a factor of one thousand, effectively removing post-measurement delay. The method also extends to multilevel quantum systems, offering a practical route toward faster, more scalable superconducting quantum processors.

Article Text

References (58)

  1. A. Yu Kitaev, Quantum Error Correction with Imperfect Gates (Springer US, Boston, MA, 1997), pp. 181–188.
  2. A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Phys. Rev. A 86, 032324 (2012).
  3. Steven M. Girvin, Introduction to quantum error correction and fault tolerance, SciPost Phys. Lect. Notes 70 (2023).
  4. M. Takita, A. D. Córcoles, E. Magesan, B. Abdo, M. Brink, A. Cross, J. M. Chow, and J. M. Gambetta, Demonstration of weight-four parity measurements in the surface code architecture, Phys. Rev. Lett. 117, 210505 (2016).
  5. T. Walter, P. Kurpiers, S. Gasparinetti, P. Magnard, A. Potočnik, Y. Salathé, M. Pechal, M. Mondal, M. Oppliger, C. Eichler, and A. Wallraff, Rapid high-fidelity single-shot dispersive readout of superconducting qubits, Phys. Rev. Appl. 7, 054020 (2017).
  6. B. Foxen et al., Demonstrating a continuous set of two-qubit gates for near-term quantum algorithms, Phys. Rev. Lett. 125, 120504 (2020).
  7. Q. Ficheux, L. B. Nguyen, A. Somoroff, H. Xiong, K. N. Nesterov, M. G. Vavilov, and V. E. Manucharyan, Fast logic with slow qubits: Microwave-activated controlled-z gate on low-frequency fluxoniums, Phys. Rev. X 11, 021026 (2021).
  8. Youwei Zhao et al., Realization of an error-correcting surface code with superconducting qubits, Phys. Rev. Lett. 129, 030501 (2022).
  9. J. Gambetta, A. Blais, D. I. Schuster, A. Wallraff, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Qubit-photon interactions in a cavity: Measurement-induced dephasing and number splitting, Phys. Rev. A 74, 042318 (2006).
  10. Zijun Chen et al., Exponential suppression of bit or phase errors with cyclic error correction, Nature (London) 595, 383 (2021).
  11. A D. Córcoles, M. Takita, K. Inoue, S. Lekuch, Z. K. Minev, J. M. Chow, and J. M. Gambetta, Exploiting dynamic quantum circuits in a quantum algorithm with superconducting qubits, Phys. Rev. Lett. 127, 100501 (2021).
  12. S. Krinner, N. Lacroix, A. Remm, A. Di 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).
  13. Y. Sunada, K. Yuki, Z. Wang, T. Miyamura, J. Ilves, K. Matsuura, P. A. Spring, S. Tamate, S. Kono, and Y. Nakamura, Photon-noise-tolerant dispersive readout of a superconducting qubit using a nonlinear purcell filter, PRX Quantum 5, 010307 (2024).
  14. D T. McClure, H. Paik, L S. Bishop, M. Steffen, J. M. Chow, and J. M. Gambetta, Rapid driven reset of a qubit readout resonator, Phys. Rev. Appl. 5, 011001 (2016).
  15. C. C. Bultink, M. A. Rol, T. E. O’Brien, X. Fu, B. C. S. Dikken, C. Dickel, R. F. L. Vermeulen, J. C. de Sterke, A. Bruno, R. N. Schouten, and L. DiCarlo, Active resonator reset in the nonlinear dispersive regime of circuit qed, Phys. Rev. Appl. 6, 034008 (2016).
  16. A. Bengtsson, P. Vikstål, C. Warren, M. Svensson, X. Gu, A. F. Kockum, P. Krantz, C. Križan, D. Shiri, I.-M. Svensson, G. Tancredi, G. Johansson, P. Delsing, G. Ferrini, and J. Bylander, Improved success probability with greater circuit depth for the quantum approximate optimization algorithm, Phys. Rev. Appl. 14, 034010 (2020).
  17. A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
  18. S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics 2: Correlation Theory of Random Processes (Springer-Verlag, Berlin Heidelberg, 1988).
  19. J. M. C. Duhamel, Mémoir sur les vibrations d’un système quelconque de points materiels, J. L’Ecole Polytech. 23, 1 (1834), https://gallica.bnf.fr/ark:/12148/bpt6k4336791
  20. M. J. Collett and C. W. Gardiner, Squeezing of intracavity and traveling-wave light fields produced in parametric amplification, Phys. Rev. A 30, 1386 (1984).
  21. B. Yurke, Input-Output Theory (Springer-Verlag, Berlin Heidelberg, 2004).
  22. F. Motzoi, L. Buchmann, and C. Dickel, Simple, smooth and fast pulses for dispersive measurements in cavities and quantum networks, arXiv:1809.04116.
  23. J. Heinsoo, C. K. Andersen, A. Remm, S. Krinner, T. Walter, Y. Salathé, S. Gasparinetti, J.-C. Besse, A. Potočnik, A. Wallraff, and C. Eichler, Rapid high-fidelity multiplexed readout of superconducting qubits, Phys. Rev. Appl. 10, 034040 (2018).
  24. M. Boissonneault, J. M. Gambetta, and A. Blais, Improved superconducting qubit readout by qubit-induced nonlinearities, Phys. Rev. Lett. 105, 100504 (2010).
  25. J. Gambetta, W. A. Braff, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Protocols for optimal readout of qubits using a continuous quantum nondemolition measurement, Phys. Rev. A 76, 012325 (2007).
  26. E. A. Sete, J. M. Martinis, and A. N. Korotkov, Quantum theory of a bandpass purcell filter for qubit readout, Phys. Rev. A 92, 012325 (2015).
  27. E. Jeffrey, D. Sank, J Y. Mutus, T C. White, J. Kelly, R. Barends, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. Megrant, P J J. O’Malley, C. Neill, P. Roushan, A. Vainsencher, J. Wenner, A N. Cleland, and J. M. Martinis, Fast accurate state measurement with superconducting qubits, Phys. Rev. Lett. 112, 190504 (2014).
  28. J. Gough and M. R. James, The series product and its application to quantum feedforward and feedback networks, IEEE Trans. Autom. Control 54, 2530 (2009).
  29. N. T. Bronn, Y. Liu, J. B. Hertzberg, A. D. Córcoles, A. A. Houck, J. M. Gambetta, and J. M. Chow, Broadband filters for abatement of spontaneous emission in circuit quantum electrodynamics, Appl. Phys. Lett. 107, 172601 (2015).
  30. J. Kerckhoff, L. Bouten, A. Silberfarb, and H. Mabuchi, Physical model of continuous two-qubit parity measurement in a cavity-QED network, Phys. Rev. A 79, 024305 (2009).
  31. N. Roch, M E. Schwartz, F. Motzoi, C. Macklin, R. Vijay, A W. Eddins, A N. Korotkov, K B. Whaley, M. Sarovar, and I. Siddiqi, Observation of measurement-induced entanglement and quantum trajectories of remote superconducting qubits, Phys. Rev. Lett. 112, 170501 (2014).
  32. C. Dickel, J. J. Wesdorp, N. K. Langford, S. Peiter, R. Sagastizabal, A. Bruno, B. Criger, F. Motzoi, and L. DiCarlo, Chip-to-chip entanglement of transmon qubits using engineered measurement fields, Phys. Rev. B 97, 064508 (2018).
  33. L. Martin, F. Motzoi, H. Li, M. Sarovar, and K. B. Whaley, Deterministic generation of remote entanglement with active quantum feedback, Phys. Rev. A 92, 062321 (2015).
  34. F. Motzoi, K. B. Whaley, and M. Sarovar, Continuous joint measurement and entanglement of qubits in remote cavities, Phys. Rev. A 92, 032308 (2015).
  35. R. Dassonneville, T. Ramos, V. Milchakov, L. Planat, É Dumur, F. Foroughi, J. Puertas, S. Leger, K. Bharadwaj, J. Delaforce, C. Naud, W. Hasch-Guichard, J J. García-Ripoll, N. Roch, and O. Buisson, Fast high-fidelity quantum nondemolition qubit readout via a nonperturbative cross-Kerr coupling, Phys. Rev. 10, 011045 (2020).
  36. S. Touzard, A. Kou, N. E. Frattini, V. V. Sivak, S. Puri, A. Grimm, L. Frunzio, S. Shankar, and M. H. Devoret, Gated conditional displacement readout of superconducting qubits, Phys. Rev. Lett. 122, 080502 (2019).
  37. Google Quantum AI, Exponential suppression of bit or phase errors with cyclic error correction, Nature (London) 595, 383 (2021).
  38. C. K. Andersen, A. Remm, S. Lazar, S. Krinner, N. Lacroix, G. J. Norris, M. Gabureac, C. Eichler, and A. Wallraff, Repeated quantum error detection in a surface code, Nat. Phys. 16, 875 (2020).
  39. 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).
  40. P. A. Spring, L. Milanovic, Y. Sunada, S. Wang, A. F. van Loo, S. Tamate, and Y. Nakamura, Fast multiplexed superconducting-qubit readout with intrinsic purcell filtering using a multiconductor transmission line, PRX Quantum 6, 020345 (2025).
  41. Pavel D. Kurilovich, Thomas Connolly, Charlotte G. L. Bøttcher, Daniel K. Weiss, Sumeru Hazra, Vidul R. Joshi, Andy Z. Ding, Heekun Nho, Spencer Diamond, Vladislav D. Kurilovich, Wei Dai, Valla Fatemi, Luigi Frunzio, Leonid I. Glazman, and Michel H. Devoret, High-frequency readout free from Transmon multi-excitation resonances, arXiv:2501.09161.
  42. J. Gambetta, A. Blais, M. Boissonneault, A. A. Houck, D. I. Schuster, and S. M. Girvin, Quantum trajectory approach to circuit QED: Quantum jumps and the zeno effect, Phys. Rev. A 77, 012112 (2008).
  43. M. F. Dumas, B. Groleau-Paré, A. McDonald, M. H. Muñoz-Arias, C. Lledó, B. D’Anjou, and A. Blais, Measurement-induced transmon ionization, Phys. Rev. 14, 041023 (2024).
  44. M. Keller, Cavity-qed with single trapped ions, Contemp. Phys. 63, 1 (2022).
  45. S. Garcia, M. Stammeier, J. Deiglmayr, F. Merkt, and A. Wallraff, Single-shot nondestructive detection of Rydberg-atom ensembles by transmission measurement of a microwave cavity, Phys. Rev. Lett. 123, 193201 (2019).
  46. H. Keßler, P. Kongkhambut, C. Georges, L. Mathey, J. G. Cosme, and A. Hemmerich, Observation of a dissipative time crystal, Phys. Rev. Lett. 127, 043602 (2021).
  47. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86, 1391 (2014).
  48. V. Ranjan, J. O’Sullivan, E. Albertinale, B. Albanese, T. Chanelière, T. Schenkel, D. Vion, D. Esteve, E. Flurin, J. J. L. Morton, and P. Bertet, Multimode storage of quantum microwave fields in electron spins over 100 ms, Phys. Rev. Lett. 125, 210505 (2020).
  49. L. M. K. Vandersypen and M. A. Eriksson, Quantum computing with semiconductor spins, Phys. Today 72, 38 (2019).
  50. J. Ikonen, J. Goetz, J. Ilves, A. Keränen, A. M. Gunyho, M. Partanen, K. Y. Tan, D. Hazra, L. Grönberg, V. Vesterinen, S. Simbierowicz, J. Hassel, and M. Möttönen, Qubit measurement by multichannel driving, Phys. Rev. Lett. 122, 080503 (2019).
  51. C. C. Bultink, B. Tarasinski, N. Haandbæk, S. Poletto, N. Haider, D. J. Michalak, A. Bruno, and L. DiCarlo, General method for extracting the quantum efficiency of dispersive qubit readout in circuit qed, Appl. Phys. Lett. 112, 092601 (2018).
  52. F. R. Ong, M. Boissonneault, F. Mallet, A. Palacios-Laloy, A. Dewes, A. C. Doherty, A. Blais, P. Bertet, D. Vion, and D. Esteve, Circuit QED with a nonlinear resonator: ac-stark shift and dephasing, Phys. Rev. Lett. 106, 167002 (2011).
  53. J. J. Sørensen, J. S. øNyemann, F. Motzoi, J. Sherson, and T. Vosegaard, Optimization of pulses with low bandwidth for improved excitation of multiple-quantum coherences in nmr of quadrupolar nuclei, J. Chem. Phys. 152, 054104 (2020).
  54. M. Malekakhlagh, W. Shanks, and H. Paik, Optimization of the resonator-induced phase gate for superconducting qubits, Phys. Rev. A 105, 022607 (2022).
  55. L. S. Theis, F. Motzoi, S. Machnes, and F. K. Wilhelm, Counteracting systems of diabaticities using drag controls: The status after 10 years, Europhys. Lett. 123, 60001 (2018).
  56. E. A. Sete, J. M. Gambetta, and A. N. Korotkov, Purcell effect with microwave drive: Suppression of qubit relaxation rate, Phys. Rev. B 89, 104516 (2014).
  57. F. A. Cárdenas-López, B. Li, A. Lupascu, and F. Motzoi, Universal pulses for superconducting qudit ladder gates, PRX Quantum 6, 030357 (2025).
  58. A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation, Phys. Rev. A 69, 062320 (2004).

Outline

Information

PRX Quantum 7, 033042– Published 31 August, 2026
  • Received 24 July 2024
  • Revised 19 December 2025
  • Accepted 8 July 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