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  • Open Access

Perfect-entangler spectrum as a tool to analyze crosstalk

Matthias G. Krauss and Christiane P. Koch

  • Freie Universität Berlin, Fachbereich Physik and Dahlem Center for Complex Quantum Systems, Arnimallee 14, 14195, Berlin, Germany

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Phys. Rev. Applied 26, 014017 – Published 7 July, 2026

DOI: https://doi.org/10.1103/8nj6-qnzf

Abstract

Crosstalk is a key obstacle to scaling up quantum computers. It may arise from persistent qubit-qubit couplings or dynamically during gate operation, with the latter being particularly difficult to detect. Here, we introduce the perfect-entangler spectrum as a means to identify dynamic crosstalk leading to undesired entanglement. It leverages the geometric classification of two-qubit gates in terms of perfect entanglers. We exemplify the application of the spectroscopy for fixed-frequency transmons and parametrically driven gates. When scanning the frequency of a spectator qubit, peaks in the perfect-entangler spectrum signal dynamic crosstalk, and analysis of the peaks reveals the mechanisms causing the crosstalk. We discuss the experimental implementation of the crosstalk spectroscopy, which requires two two-qubit gate tomographies.

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References (73)

  1. D. P. DiVincenzo, The physical implementation of quantum computation, Fortschr. Phys. 48, 771 (2000).
  2. M. Sarovar, T. Proctor, K. Rudinger, K. Young, E. Nielsen, and R. Blume-Kohout, Detecting crosstalk errors in quantum information processors, Quantum 4, 321 (2020).
  3. A. Ash- Saki, M. Alam, and S. Ghosh, Experimental characterization, modeling, and analysis of crosstalk in a quantum computer, IEEE Trans. Quantum Eng. 1, 1 (2020).
  4. A. Ketterer and T. Wellens, Characterizing crosstalk of superconducting transmon processors, Phys. Rev. Appl. 20, 034065 (2023).
  5. T. Strohm, K. Wintersperger, F. Dommert, D. Basilewitsch, G. Reuber, A. Hoursanov, T. Ehmer, D. Vodola, and S. Luber, Ion-based quantum computing hardware: Performance and end-user perspective, arXiv:2405.11450.
  6. D. M. Abrams, N. Didier, S. A. Caldwell, B. R. Johnson, and C. A. Ryan, Methods for measuring magnetic flux crosstalk between tunable transmons, Phys. Rev. Appl. 12, 064022 (2019).
  7. S. Kosen, H.-X. Li, M. Rommel, R. Rehammar, M. Caputo, L. Grönberg, J. Fernández-Pendás, A. F. Kockum, J. Biznárová, L. Chen, C. Križan, A. Nylander, A. Osman, A. F. Roudsari, D. Shiri, G. Tancredi, J. Govenius, and J. Bylander, Signal crosstalk in a flip-chip quantum processor, PRX Quantum 5, 030350 (2024).
  8. K. A. Landsman, Y. Wu, P. H. Leung, D. Zhu, N. M. Linke, K. R. Brown, L. Duan, and C. Monroe, Two-qubit entangling gates within arbitrarily long chains of trapped ions, Phys. Rev. A 100, 022332 (2019).
  9. D. Schwerdt, L. Peleg, Y. Shapira, N. Priel, Y. Florshaim, A. Gross, A. Zalic, G. Afek, N. Akerman, A. Stern, A. B. Kish, and R. Ozeri, Scalable architecture for trapped-ion quantum computing using rf traps and dynamic optical potentials, Phys. Rev. X 14, 041017 (2024).
  10. K. Rudinger, C. W. Hogle, R. K. Naik, A. Hashim, D. Lobser, D. I. Santiago, M. D. Grace, E. Nielsen, T. Proctor, S. Seritan, S. M. Clark, R. Blume-Kohout, I. Siddiqi, and K. C. Young, Experimental characterization of crosstalk errors with simultaneous gate set tomography, PRX Quantum 2, 040338 (2021).
  11. D. Shnaiderov, M. B. Dov, Y. Woldiger, A. Hamo, E. Demler, and E. G. D. Torre, Optimal calibration of qubit detuning and crosstalk, arXiv:2507.10661.
  12. S. Sarker, O. Khriyenko, T. Mikkonen, and M. Haghparast, A machine learning approach to detecting crosstalk-induced fidelity degradation in quantum computing systems, Phys. Scr. 101, 065102 (2026).
  13. J. M. Gambetta, A. D. Córcoles, S. T. Merkel, B. R. Johnson, J. A. Smolin, J. M. Chow, C. A. Ryan, C. Rigetti, S. Poletto, T. A. Ohki, M. B. Ketchen, and M. Steffen, Characterization of addressability by simultaneous randomized benchmarking, Phys. Rev. Lett. 109, 240504 (2012).
  14. Z. Zhou, A. Ji, and Y. Ding, Characterization and mitigation of crosstalk in quantum error correction, arXiv:2503.04642.
  15. P. Mundada, G. Zhang, T. Hazard, and A. Houck, Suppression of qubit crosstalk in a tunable coupling superconducting circuit, Phys. Rev. Appl. 12, 054023 (2019).
  16. P. Parrado-Rodríguez, C. Ryan-Anderson, A. Bermudez, and M. Müller, Crosstalk suppression for fault-tolerant quantum error correction with trapped ions, Quantum 5, 487 (2021). .
  17. 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).
  18. A. Kandala, K. X. Wei, S. Srinivasan, E. Magesan, S. Carnevale, G. A. Keefe, D. Klaus, O. Dial, and D. C. McKay, Demonstration of a high-fidelity cnot gate for fixed-frequency transmons with engineered ZZ suppression, Phys. Rev. Lett. 127, 130501 (2021).
  19. J. Flannery, R. Matt, L. I. Huber, K. Wang, C. Axline, R. Oswald, and J. P. Home, Physical coherent cancellation of optical addressing crosstalk in a trapped-ion experiment, Quantum Sci. Technol. 10, 015012 (2025).
  20. D. C. McKay, S. Sheldon, J. A. Smolin, J. M. Chow, and J. M. Gambetta, Three-qubit randomized benchmarking, Phys. Rev. Lett. 122, 200502 (2019).
  21. A. Morvan, L. Chen, J. M. Larson, D. I. Santiago, and I. Siddiqi, Optimizing frequency allocation for fixed-frequency superconducting quantum processors, Phys. Rev. Res. 4, 023079 (2022).
  22. J. Zhang, H. Wang, Q. Ding, J. Gu, R. Assouly, W. D. Oliver, S. Han, K. R. Brown, H. H. Li, and Y. Chen, Qplacer: Frequency-aware component placement for superconducting quantum computers, arXiv:2401.17450.
  23. H. Ai, and Y.-X. Liu, Scalable parameter design for superconducting quantum circuits with graph neural networks, Phys. Rev. Lett. 135, 040601 (2025).
  24. M. Alghadeer, S. Cao, S. D. Fasciati, M. Piscitelli, P. C. Gow, J. C. Gates, M. Bakr, and P. J. Leek, Low crosstalk in a scalable superconducting quantum lattice, EPJ Quantum Technol. 13, 19 (2026).
  25. Z. Zhou, R. Sitler, Y. Oda, K. Schultz, and G. Quiroz, Quantum crosstalk robust quantum control, Phys. Rev. Lett. 131, 210802 (2023).
  26. S. Watanabe, Y. Tabuchi, K. Heya, S. Tamate, and Y. Nakamura, Z Z -interaction-free single-qubit-gate optimization in superconducting qubits, Phys. Rev. A 109, 012616 (2024).
  27. X. You, Y. Lu, T. Kim, Da M. Kürkçüolu, S. Zhu, D. van Zanten, T. Roy, Y. Lu, S. Chakram, A. Grassellino, A. Romanenko, J. Koch, and S. Zorzetti, Crosstalk-robust quantum control in multimode bosonic systems, Phys. Rev. Appl. 22, 044072 (2024).
  28. U. von Lüpke, Félix Beaudoin, L. M. Norris, Y. Sung, R. Winik, J. Y. Qiu, M. Kjaergaard, D. Kim, J. Yoder, S. Gustavsson, L. Viola, and W. D. Oliver, Two-qubit spectroscopy of spatiotemporally correlated quantum noise in superconducting qubits, PRX Quantum 1, 010305 (2020).
  29. L. Greggio, R. Robin, M. Mirrahimi, and A. Petrescu, Strongly driven transmon as an incoherent noise source, arXiv:2505.24549.
  30. J. Stehlik, D. M. Zajac, D. L. Underwood, T. Phung, J. Blair, S. Carnevale, D. Klaus, G. A. Keefe, A. Carniol, M. Kumph, M. Steffen, and O. E. Dial, Tunable coupling architecture for fixed-frequency transmon superconducting qubits, Phys. Rev. Lett. 127, 080505 (2021).
  31. H. Zhang, C. Ding, D. K. Weiss, Z. Huang, Y. Ma, C. Guinn, S. Sussman, S. P. Chitta, D. Chen, A. A. Houck, J. Koch, and D. I. Schuster, Tunable inductive coupler for high-fidelity gates between fluxonium qubits, PRX Quantum 5, 020326 (2024).
  32. F. Lange, L. Heunisch, H. Fehske, D. P. DiVincenzo, and M. J. Hartmann, Cross-talk in superconducting qubit lattices with tunable couplers—comparing transmon and fluxonium architectures, Quantum Sci. Technol. 11, 015020 (2026).
  33. I. N. Moskalenko, I. A. Simakov, N. N. Abramov, A. A. Grigorev, D. O. Moskalev, A. A. Pishchimova, N. S. Smirnov, E. V. Zikiy, I. A. Rodionov, and I. S. Besedin, High fidelity two-qubit gates on fluxoniums using a tunable coupler, npj Quantum Inf 8, 130 (2022).
  34. L. Heunisch, C. Eichler, and M. J. Hartmann, Tunable coupler to fully decouple and maximally localize superconducting qubits, Phys. Rev. Appl. 20, 064037 (2023).
  35. X. Dai, D. Tennant, R. Trappen, A. Martinez, D. Melanson, M. Yurtalan, Y. Tang, S. Novikov, J. Grover, S. Disseler, J. Basham, R. Das, D. Kim, A. Melville, B. Niedzielski, S. Weber, J. Yoder, D. Lidar, and A. Lupascu, Calibration of flux crosstalk in large-scale flux-tunable superconducting quantum circuits, PRX Quantum 2, 040313 (2021).
  36. J. Balewski, A. Winick, Y. Xu, N. Vora, G. Huang, D. Santiago, J. Emerson, and I. Siddiqi, First-principle crosstalk dynamics and Hamiltonian learning via Rabi experiments, arXiv:2502.05362.
  37. S. Krinner, S. Lazar, A. Remm, C. K. Andersen, N. Lacroix, G. J. Norris, C. Hellings, M. Gabureac, C. Eichler, and A. Wallraff, Benchmarking coherent errors in controlled-phase gates due to spectator qubits, Phys. Rev. Appl. 14, 024042 (2020).
  38. M. Malekakhlagh, E. Magesan, and D. C. McKay, First-principles analysis of cross-resonance gate operation, Phys. Rev. A 102, 042605 (2020).
  39. T.-Q. Cai, X.-Y. Han, Y.-K. Wu, Y.-L. Ma, J.-H. Wang, Z.-L. Wang, H.-Y. Zhang, H.-Y. Wang, Y.-P. Song, and L.-M. Duan, Impact of spectators on a two-qubit gate in a tunable coupling superconducting circuit, Phys. Rev. Lett. 127, 060505 (2021).
  40. P. Zhao, K. Linghu, Z. Li, P. Xu, R. Wang, G. Xue, Y. Jin, and H. Yu, Quantum crosstalk analysis for simultaneous gate operations on superconducting qubits, PRX Quantum 3, 020301 (2022).
  41. M. F. S. Zwanenburg and C. K. Andersen, Crosstalk in Multi-qubit fluxonium architectures with transmon couplers, arXiv:2603.09870.
  42. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, 10th ed. (Cambridge University Press, Cambridge; New York, 2010),
  43. Y. Makhlin, Nonlocal properties of two-qubit gates and mixed states, and the optimization of quantum computations, Quantum Inf. Process. 1, 243 (2002).
  44. J. Zhang, J. Vala, S. Sastry, and K. B. Whaley, Geometric theory of nonlocal two-qubit operations, Phys. Rev. A 67, 042313 (2003).
  45. P. Watts, J. Vala, M. M. Müller, T. Calarco, K. B. Whaley, D. M. Reich, M. H. Goerz, and C. P. Koch, Optimizing for an arbitrary perfect entangler. I. Functionals, Phys. Rev. A 91, 062306 (2015).
  46. M. H. Goerz, G. Gualdi, D. M. Reich, C. P. Koch, F. Motzoi, K. B. Whaley, J. Vala, M. M. Müller, S. Montangero, and T. Calarco, Optimizing for an arbitrary perfect entangler. II. Application, Phys. Rev. A 91, 062307 (2015).
  47. D. C. McKay, S. Filipp, A. Mezzacapo, E. Magesan, J. M. Chow, and J. M. Gambetta, Universal gate for fixed-frequency qubits via a tunable bus, Phys. Rev. Appl. 6, 064007 (2016).
  48. M. Reagor et al., Demonstration of universal parametric entangling gates on a multi-qubit lattice, Sci. Adv. 4, eaao3603 (2018).
  49. 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).
  50. F. Arute et al., Quantum supremacy using a programmable superconducting processor, Nature (London) 574, 505 (2019).
  51. L. Ding, M. Hays, Y. Sung, B. Kannan, J. An, A. Di Paolo, A. H. Karamlou, T. M. Hazard, K. Azar, D. K. Kim, B. M. Niedzielski, A. Melville, M. E. Schwartz, J. L. Yoder, T. P. Orlando, S. Gustavsson, J. A. Grover, K. Serniak, and W. D. Oliver, High-fidelity, frequency-flexible two-qubit fluxonium gates with a transmon coupler, Phys. Rev. X 13, 031035 (2023).
  52. X. Zhang, X. Zhang, C. Chen, K. Tang, K. Yi, K. Luo, Z. Xie, Y. Chen, and T. Yan, Characterization and optimization of tunable couplers via adiabatic control in superconducting circuits, Phys. Rev. Appl. 24, 034003 (2025).
  53. J. Majer, J. M. Chow, J. M. Gambetta, J. Koch, B. R. Johnson, J. A. Schreier, L. Frunzio, D. I. Schuster, A. A. Houck, A. Wallraff, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Coupling superconducting qubits via a cavity bus, Nature (London) 449, 443 (2007).
  54. E. A. Sete, N. Didier, A. Q. Chen, S. Kulshreshtha, R. Manenti, and S. Poletto, Parametric-resonance entangling gates with a tunable coupler, Phys. Rev. Appl. 16, 024050 (2021).
  55. R. Acharya et al. Google Quantum AI, Suppressing quantum errors by scaling a surface code logical qubit, Nature (London) 614, 676 (2023).
  56. G. Huber et al., Parametric multielement coupling architecture for coherent and dissipative control of superconducting qubits, PRX Quantum 6, 030313 (2025).
  57. P. Bertet, C. J. P. M. Harmans, and J. E. Mooij, Parametric coupling for superconducting qubits, Phys. Rev. B 73, 064512 (2006).
  58. A. O. Niskanen, K. Harrabi, F. Yoshihara, Y. Nakamura, S. Lloyd, and J. S. Tsai, Quantum coherent tunable coupling of superconducting qubits, Science 316, 723 (2007).
  59. 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).
  60. S. A. Caldwell et al., Parametrically activated entangling gates using transmon qubits, Phys. Rev. Appl. 10, 034050 (2018).
  61. M. Ganzhorn, G. Salis, D. J. Egger, A. Fuhrer, M. Mergenthaler, C. Müller, P. Müller, S. Paredes, M. Pechal, M. Werninghaus, and S. Filipp, Benchmarking the noise sensitivity of different parametric two-qubit gates in a single superconducting quantum computing platform, Phys. Rev. Res. 2, 033447 (2020).
  62. A. Petrescu, C. Le Calonnec, C. Leroux, A. Di Paolo, P. Mundada, S. Sussman, A. Vrajitoarea, A. A. Houck, and A. Blais, Accurate methods for the analysis of strong-drive effects in parametric gates, Phys. Rev. Appl. 19, 044003 (2023).
  63. A. Romer, D. M. Reich, and C. P. Koch, Reconstructing the unitary part of a noisy quantum channel, arXiv:2507.17648.
  64. M. M. Müller, D. M. Reich, M. Murphy, H. Yuan, J. Vala, K. B. Whaley, T. Calarco, and C. P. Koch, Optimizing entangling quantum gates for physical systems, Phys. Rev. A 84, 042315 (2011).
  65. M. Kishmar, P. D. Kurilovich, A. Klots, T. Connolly, I. L. Aleiner, and V. D. Kurilovich, Quasiparticle-induced decoherence of a driven superconducting qubit, arXiv:2505.00769.
  66. S. Chowdhury, M. Hays, S. R. Jha, K. Serniak, T. P. Orlando, J. A. Grover, and W. D. Oliver, Theory of quasiparticle generation by microwave drives in superconducting qubits, Phys. Rev. Appl. 25, 014042 (2026).
  67. J. Helsen, M. Ioannou, J. Kitzinger, E. Onorati, A. H. Werner, J. Eisert, and I. Roth, Shadow estimation of gate-set properties from random sequences, Nat. Commun. 14, 5039 (2023).
  68. S. Mangini, M. Cattaneo, D. Cavalcanti, S. Filippov, M. A. C. Rossi, and G. García-Pérez, Tensor network noise characterization for near-term quantum computers, Phys. Rev. Res. 6, 033217 (2024).
  69. 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, EPJ Quantum Technol. 9,19 (2022).
  70. M. G. Krauss, L. C. Butzke, and C. P. Koch, Mitigating dynamic crosstalk with optimal control, arXiv:2603.24205.
  71. A. Kakkar, S. Marsh, Y. Wang, P. Mundada, P. Coote, G. Hartnett, M. J. Biercuk, and Y. Baum, No need to calibrate: Characterization and compilation for high-fidelity circuit execution using imperfect gates, arXiv:2511.21831.
  72. M. G. Krauss and C. P. Koch, Data for publication “The perfect entangler spectrum as a tool to analyze crosstalk” (2025), https://zenodo.org/records/16882136.
  73. M. Sugawara and T. Satoh, SU(4) gate design via unitary process tomography: Its application to cross-resonance based superconducting quantum devices, IEEE Trans. Quantum Eng. 6, 5100112 (2025).

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Phys. Rev. Applied 26, 014017– Published 7 July, 2026
  • Received 4 August 2025
  • Revised 21 January 2026
  • Accepted 10 June 2026
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