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Exploring the fidelity of flux-qubit measurement in different bases via the quantum flux parametron

Yanjun Ji1,*, Susanna Kirchhoff1,2, and Frank K. Wilhelm1,2,†

  • *Contact author: y.ji@fz-juelich.de
  • †Contact author: f.wilhelm-mauch@fz-juelich.de
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Phys. Rev. A 113, 032623 – Published 26 March, 2026

DOI: https://doi.org/10.1103/86jt-by9x

Abstract

High-fidelity qubit readout is a fundamental requirement for practical quantum computing systems. In this work, we investigate methods to enhance the measurement fidelity of flux qubits via a quantum flux parametron-mediated readout scheme. Through theoretical modeling and numerical simulations, we analyze the impact of different measurement bases on fidelity in single-qubit and coupled two-qubit systems. For single-qubit systems, we show that energy bases consistently outperform flux bases in achieving higher fidelity. In coupled two-qubit systems, we explore two measurement models: sequential and simultaneous measurements, both aimed at reading out a single target qubit. Our results indicate that the highest fidelity can be achieved either by performing sequential measurement in a dressed basis over a longer duration or by conducting simultaneous measurement in a bare basis over a shorter duration. Importantly, the sequential measurement model consistently yields more robust and higher-fidelity readouts compared to the simultaneous approach. These findings quantify achievable fidelities and provide valuable guidance for optimizing measurement protocols in emerging quantum computing architectures.

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References (75)

  1. J. Clarke and F. K. Wilhelm, Superconducting quantum bits, Nature (London) 453, 1031 (2008).
  2. 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).
  3. V. Bouchiat, D. Vion, P. Joyez, D. Esteve, and M. H. Devoret, Quantum coherence with a single Cooper pair, Phys. Scr. 1998, 165 (1998).
  4. Y. Nakamura, C. D. Chen, and J. S. Tsai, Spectroscopy of energy-level splitting between two macroscopic quantum states of charge coherently superposed by Josephson coupling, Phys. Rev. Lett. 79, 2328 (1997).
  5. J. M. Martinis, Superconducting phase qubits, Quantum Inf. Proc. 8, 81 (2009).
  6. J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, Quantum superposition of distinct macroscopic states, Nature (London) 406, 43 (2000).
  7. C. H. van der Wal, A. C. J. ter Haar, F. K. Wilhelm, R. N. Schouten, C. J. P. M. Harmans, T. P. Orlando, S. Lloyd, and J. E. Mooij, Quantum superposition of macroscopic persistent-current states, Science 290, 773 (2000).
  8. 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).
  9. M. Stern, G. Catelani, Y. Kubo, C. Grezes, A. Bienfait, D. Vion, D. Esteve, and P. Bertet, Flux qubits with long coherence times for hybrid quantum circuits, Phys. Rev. Lett. 113, 123601 (2014).
  10. M. Schöndorf, A. Lupaşcu, and F. K. Wilhelm, Flux-qubit readout in the persistent-current basis at arbitrary bias points, Phys. Rev. A 101, 012305 (2020).
  11. R. Harris, J. Johansson, A. J. Berkley, M. W. Johnson, T. Lanting, S. Han, P. Bunyk, E. Ladizinsky, T. Oh, I. Perminov, E. Tolkacheva, S. Uchaikin, E. M. Chapple, C. Enderud, C. Rich, M. Thom, J. Wang, B. Wilson, and G. Rose, Experimental demonstration of a robust and scalable flux qubit, Phys. Rev. B 81, 134510 (2010).
  12. J. Ferber and F. K. Wilhelm, Efficient creation of multipartite entanglement in flux qubits, Nanotechnology 21, 274015 (2010).
  13. A. G. Fowler, W. F. Thompson, Z. Yan, A. M. Stephens, B. L. T. Plourde, and F. K. Wilhelm, Long-range coupling and scalable architecture for superconducting flux qubits, Phys. Rev. B 76, 174507 (2007).
  14. T. L. Robertson, B. L. T. Plourde, T. Hime, S. Linzen, P. A. Reichardt, F. K. Wilhelm, and J. Clarke, Superconducting quantum interference device with frequency-dependent damping: Readout of flux qubits, Phys. Rev. B 72, 024513 (2005).
  15. I. Chiorescu, P. Bertet, K. Semba, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, Coherent dynamics of a flux qubit coupled to a harmonic oscillator, Nature (London) 431, 159 (2004).
  16. 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).
  17. 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).
  18. 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).
  19. Z. R. Lin, K. Inomata, K. Koshino, W. D. Oliver, Y. Nakamura, J. S. Tsai, and T. Yamamoto, Josephson parametric phase-locked oscillator and its application to dispersive readout of superconducting qubits, Nat. Commun. 5, 4480 (2014).
  20. M. Hosoya, W. Hioe, J. Casas, R. Kamikawai, Y. Harada, Y. Wada, H. Nakane, R. Suda, and E. Goto, Quantum flux parametron: A single quantum flux device for Josephson supercomputer, IEEE Trans. Appl. Supercond. 1, 77 (1991).
  21. Y. Yamanashi, T. Matsushima, N. Takeuchi, N. Yoshikawa, and T. Ortlepp, Evaluation of current sensitivity of quantum flux parametron, Supercond. Sci. Technol. 30, 084004 (2017).
  22. 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, Micah 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).
  23. J. C. Pommerening and D. P. DiVincenzo, What is measured when a qubit measurement is performed on a multiqubit chip, Phys. Rev. A 102, 032623 (2020).
  24. M. Khezri, J. Dressel, and A. N. Korotkov, Qubit measurement error from coupling with a detuned neighbor in circuit QED, Phys. Rev. A 92, 052306 (2015).
  25. V. B. Braginsky, F. Y. Khalili, and K. S. Thorne, Quantum Measurement (Cambridge University Press, Cambridge, 1992).
  26. T. Albash and D. A. Lidar, Adiabatic quantum computation, Rev. Mod. Phys. 90, 015002 (2018).
  27. J. Preskill, Quantum Computing in the NISQ era and beyond, Quantum 2, 79 (2018).
  28. K. Bharti, A. Cervera-Lierta, T. H. Kyaw, T. Haug, S. Alperin-Lea, A. Anand, M. Degroote, H. Heimonen, J. S. Kottmann, T. Menke, W.-K. Mok, S. Sim, L.-C. Kwek, and A. Aspuru-Guzik, Noisy intermediate-scale quantum algorithms, Rev. Mod. Phys. 94, 015004 (2022).
  29. Y. Ji, Resilience of quantum optimization algorithms, Ph.D. thesis, Universität Stuttgart, Stuttgart, 2024.
  30. J. Clarke and A. I. Braginski, The SQUID Handbook: Fundamentals and Technology of SQUIDs and SQUID Systems (Wiley-Vch, Weinheim, Germany, 2004), Vol. 1.
  31. A. J. Berkley, M. W. Johnson, P. Bunyk, R. Harris, J. Johansson, T. Lanting, E. Ladizinsky, E. Tolkacheva, M. H. S. Amin, and G. Rose, A scalable readout system for a superconducting adiabatic quantum optimization system, Supercond. Sci. Technol. 23, 105014 (2010).
  32. R. Harris, T. Lanting, A. J. Berkley, J. Johansson, M. W. Johnson, P. Bunyk, E. Ladizinsky, N. Ladizinsky, T. Oh, and S. Han, Compound Josephson-junction coupler for flux qubits with minimal crosstalk, Phys. Rev. B 80, 052506 (2009).
  33. D. Kafri, C. Quintana, Y. Chen, A. Shabani, J. M. Martinis, and H. Neven, Tunable inductive coupling of superconducting qubits in the strongly nonlinear regime, Phys. Rev. A 95, 052333 (2017).
  34. E. Jaynes and F. Cummings, Comparison of quantum and semiclassical radiation theories with application to the beam maser, Proc. IEEE 51, 89 (1963).
  35. X. Gu, A. F. Kockum, A. Miranowicz, Y.-x. Liu, and F. Nori, Microwave photonics with superconducting quantum circuits, Phys. Rep. 718-719, 1 (2017).
  36. F. K. Wilhelm, Asymptotic von Neumann measurement strategy for solid-state qubits, Phys. Rev. B 68, 060503(R) (2003).
  37. G. Lüders, Concerning the state-change due to the measurement process, Ann. Phys. (NY) 518, 663 (2006).
  38. V. Fiorentino and S. Weigert, Beyond the projection postulate and back: Quantum theories with generalized state-update rules, Phys. Rev. A 113, 012204 (2026).
  39. 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).
  40. K. Lalumière, J. M. Gambetta, and A. Blais, Tunable joint measurements in the dispersive regime of cavity QED, Phys. Rev. A 81, 040301(R) (2010).
  41. X. Dai, D. M. Tennant, R. Trappen, A. J. Martinez, D. Melanson, M. A. Yurtalan, Y. Tang, S. Novikov, J. A. Grover, S. M. Disseler, J. I. Basham, R. Das, D. K. Kim, A. J. Melville, B. M. Niedzielski, S. J. Weber, J. L. Yoder, D. A. Lidar, and A. Lupascu, Calibration of flux crosstalk in large-scale flux-tunable superconducting quantum circuits, PRX Quantum 2, 040313 (2021).
  42. M. A. C. Aguila, N.-Y. Li, C.-H. Ma, L.-C. Hsiao, Y.-S. Huang, Y.-C. Chen, T.-H. Lee, C.-C. Chang, J.-Y. Wang, S.-Y. Huang, H.-S. Goan, C.-H. Wang, C.-S. Wu, C.-D. Chen, and C.-T. Ke, Characterizing and mitigating flux crosstalk in superconducting qubits-couplers system, APL Quantum 3, 016112 (2026).
  43. C. Hellings, N. Lacroix, A. Remm, R. Boell, J. Herrmann, S. Lazăr, S. Krinner, F. Swiadek, C. K. Andersen, C. Eichler, and A. Wallraff, Calibrating magnetic flux control in superconducting circuits by compensating distortions on timescales from nanoseconds up to tens of microseconds, Phys. Rev. Res. 7, 043142 (2025).
  44. 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.
  45. 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).
  46. M. Khezri, J. A. Grover, J. I. Basham, S. M. Disseler, H. Chen, S. Novikov, K. M. Zick, and D. A. Lidar, Anneal-path correction in flux qubits, npj Quantum Inf. 7, 36 (2021).
  47. M. W. Johnson, P. Bunyk, F. Maibaum, E. Tolkacheva, A. J. Berkley, E. M. Chapple, R. Harris, J. Johansson, T. Lanting, I. Perminov, E. Ladizinsky, T. Oh, and G. Rose, A scalable control system for a superconducting adiabatic quantum optimizationprocessor, Supercond. Sci. Technol. 23, 065004 (2010).
  48. N. Takeuchi, T. Yamae, W. Luo, F. Hirayama, T. Yamamoto, and N. Yoshikawa, Scalable flux controllers using adiabatic superconductor logic for quantum processors, Phys. Rev. Res. 5, 013145 (2023).
  49. N. Takeuchi, T. Yamae, T. Yamashita, T. Yamamoto, and N. Yoshikawa, Microwave-multiplexed qubit controller using adiabatic superconductor logic, npj Quantum Inf. 10, 53 (2024).
  50. C. M. Quintana, Y. Chen, D. Sank, A. G. Petukhov, T. C. White, D. Kafri, B. Chiaro, A. Megrant, R. Barends, B. Campbell, Z. Chen, A. Dunsworth, A. G. Fowler, R. Graff, E. Jeffrey, J. Kelly, E. Lucero, J. Y. Mutus, M. Neeley, C. Neill, et al., Observation of classical-quantum crossover of 1/f flux noise and its paramagnetic temperature dependence, Phys. Rev. Lett. 118, 057702 (2017).
  51. D. A. Rower, L. Ateshian, L. H. Li, M. Hays, D. Bluvstein, L. Ding, B. Kannan, A. Almanakly, J. Braumüller, D. K. Kim, A. Melville, B. M. Niedzielski, M. E. Schwartz, J. L. Yoder, T. P. Orlando, Joel I.-Jan Wang, S. Gustavsson, J. A. Grover, K. Serniak, R. Comin, et al., Evolution of 1/f flux noise in superconducting qubits with weak magnetic fields, Phys. Rev. Lett. 130, 220602 (2023).
  52. F. Setiawan, P. Groszkowski, H. Ribeiro, and A. A. Clerk, Analytic design of accelerated adiabatic gates in realistic qubits: General theory and applications to superconducting circuits, PRX Quantum 2, 030306 (2021).
  53. R. Trappen, X. Dai, M. A. Yurtalan, D. Melanson, D. M. Tennant, A. J. Martinez, Y. Tang, J. Gibson, J. A. Grover, S. M. Disseler, J. I. Basham, R. Das, D. K. Kim, A. J. Melville, B. M. Niedzielski, C. F. Hirjibehedin, K. Serniak, S. J. Weber, J. L. Yoder, W. D. Oliver, et al., Decoherence of a tunable capacitively shunted flux qubit, Commun. Phys. 8, 453 (2025).
  54. M. Boissonneault, J. M. Gambetta, and A. Blais, Dispersive regime of circuit QED: Photon-dependent qubit dephasing and relaxation rates, Phys. Rev. A 79, 013819 (2009).
  55. D. H. Slichter, R. Vijay, S. J. Weber, S. Boutin, M. Boissonneault, J. M. Gambetta, A. Blais, and I. Siddiqi, Measurement-induced qubit state mixing in circuit QED from up-converted dephasing noise, Phys. Rev. Lett. 109, 153601 (2012).
  56. 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).
  57. 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).
  58. R.-Z. Zhao, Z.-A. Zhao, T.-L. Wang, P. Wang, S. Zhang, X.-Y. Yang, H.-F. Zhang, Z.-F. Li, Y. Wu, Z.-H. Fu, S.-R. Liu, P. Duan, and G.-P. Guo, Single-step phase-engineered pulse for active readout cavity reset in superconducting circuits, arXiv:2512.08393.
  59. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2007).
  60. A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, Introduction to quantum noise, measurement, and amplification, Rev. Mod. Phys. 82, 1155 (2010).
  61. A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
  62. 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).
  63. Y. Ji, X. Chen, I. Polian, and Y. Ban, Algorithm-oriented qubit mapping for variational quantum algorithms, Phys. Rev. Appl. 23, 034022 (2025).
  64. Y. Ji, K. F. Koenig, and I. Polian, Improving the performance of digitized counterdiabatic quantum optimization via algorithm-oriented qubit mapping, Phys. Rev. A 110, 032421 (2024).
  65. Y. Ji, K. F. Koenig, and I. Polian, Optimizing quantum algorithms on bipotent architectures, Phys. Rev. A 108, 022610 (2023).
  66. Y. Ji and I. Polian, Synergistic dynamical decoupling and circuit design for enhanced algorithm performance on near-term quantum devices, Entropy 26, 586 (2024).
  67. A. Bengtsson, A. Opremcak, M. Khezri, D. Sank, A. Bourassa, K. J. Satzinger, S. Hong, C. Erickson, B. J. Lester, K. C. Miao, A. N. Korotkov, J. Kelly, Z. Chen, and P. V. Klimov, Model-based optimization of superconducting qubit readout, Phys. Rev. Lett. 132, 100603 (2024).
  68. A. Chatterjee, J. Schwinger, and Y. Y. Gao, Enhanced qubit readout via reinforcement learning, Phys. Rev. Appl. 23, 054057 (2025).
  69. A. Seif, H. Liao, V. Tripathi, K. Krsulich, M. Malekakhlagh, M. Amico, P. Jurcevic, and A. Javadi-Abhari, Suppressing correlated noise in quantum computers via context-aware compiling, in 2024 ACM/IEEE 51st Annual International Symposium on Computer Architecture (ISCA), edited by A. Vega, E. Mocskos, S. Dwarkadas, and R. Balasubramonian (IEEE Computer Society, Buenos Aires, Argentina, 2024), pp. 310–324.
  70. S. Khandavilli, I. Palanisamy, M. V. Nguyen, T. V. Le, T. N. Nguyen, and T. N. Dinh, Towards fidelity-optimal qubit mapping on NISQ computers, in 2023 IEEE International Conference on Quantum Computing and Engineering (QCE), edited by H. Müller, Y. Alexeev, A. Delgado, and G. Byrd (IEEE Computer Society, Bellevue, WA, USA, 2023), Vol. 01, pp. 89–98.
  71. C. Zhu, X. Wu, Z. Yang, J. Wang, A. Wu, S. Zheng, and X. Wang, Quantum compiler design for qubit mapping and routing: A cross-architectural survey of superconducting, trapped-ion, and neutral atom systems, arXiv:2505.16891.
  72. On the adiabatic theorem of quantum mechanics, J. Phys. Soc. Jpn. 5, 435 (1950).
  73. S. Teufel, Adiabatic Perturbation Theory in Quantum Dynamics (Springer, Berlin, Germany, 2003).
  74. S. Bravyi, D. P. DiVincenzo, and D. Loss, Schrieffer-Wolff transformation for quantum many-body systems, Ann. Phys. (NY) 326, 2793 (2011).
  75. E. K. Twyeffort Irish, J. Gea-Banacloche, I. Martin, and K. C. Schwab, Dynamics of a two-level system strongly coupled to a high-frequency quantum oscillator, Phys. Rev. B 72, 195410 (2005).

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Phys. Rev. A 113, 032623– Published 26 March, 2026
  • Received 28 October 2025
  • Accepted 9 March 2026
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