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  • Open Access

Implementing a nonpairwise three-body interaction of superconducting qubits and its applications in realizing three-qubit entanglement and quantum gates

Tong Liu*

  • Quantum Information Research Center and Jiangxi Province Key Laboratory of Applied Optical Technology, Shangrao Normal University, Shangrao 334001, China

  • *Contact author: liutong7500755@163.com
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Phys. Rev. Research 8, 013023 – Published 12 January, 2026

DOI: https://doi.org/10.1103/sysd-pg74

Abstract

Nonpairwise multibody interactions have recently attracted much attention due to their promising applications in the realm of quantum information science and technology. In this work, we propose a method to synthesize a nonpairwise three-body interaction of superconducting qubits using a coupler qubit dispersively coupled to two spatially separated qubits and a microwave pulse. This interaction describes physical processes of an excitation from the coupler qubit to two spatially separated qubits and the reverse process. We show that the interaction can be utilized to deterministically generate three-body Greenberger-Horne-Zeilinger (GHZ) entangled states, transfer the state of the coupler qubit into a two-qubit entangled state, and construct three-qubit controlled-controlled-phase and Toffoli gates. Our proposal only requires a coupler qubit and a single-step operation; thus, the system architecture and method are quite simple. As examples, we numerically simulate the dynamics of the system, and the numerical results demonstrate that high-fidelity preparation of the proposed three-body GHZ entangled state and quantum gates is feasible with current superconducting circuit technology. This approach is general and applicable to a wide range of quantum systems.

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References (96)

  1. I. M. Georgescu, S. Ashhab, and F. Nori, Quantum simulation, Rev. Mod. Phys. 86, 153 (2014).
  2. L. Garziano, V. Macrì, R. Stassi, O. D. Stefano, F. Nori, and S. Savasta, One photon can simultaneously excite two or more atoms, Phys. Rev. Lett. 117, 043601 (2016).
  3. R. Stassi, V. Macrì, A. F. Kockum, O. D. Stefano, A. Miranowicz, S. Savasta, and F. Nori, Quantum nonlinear optics without photons, Phys. Rev. A 96, 023818 (2017).
  4. P. Zhao, X. Tan, H. Yu, S. L. Zhu, and Y. Yu, Simultaneously exciting two atoms with photon-mediated Raman interactions, Phys. Rev. A 95, 063848 (2017).
  5. X. Wang, A. Miranowicz, H. R. Li, and F. Nori, Observing pure effects of counter-rotating terms without ultrastrong coupling: A single photon can simultaneously excite two qubits, Phys. Rev. A 96, 063820 (2017).
  6. P. Zhao, X. Tan, H. Yu, S. L. Zhu, and Y. Yu, and Circuit, QED with qutrits: Coupling three or more atoms via virtual-photon exchange, Phys. Rev. A 96, 043833 (2017).
  7. A. F. Kockum, A. Miranowicz, V. Macrí, S. Savasta, and F. Nori, Deterministic quantum nonlinear optics with single atoms and virtual photons, Phys. Rev. A 95, 063849 (2017).
  8. T. Liu, J. Xu, Q. P. Su, Y. H. Zhou, and Q. C. Wu, Two-photon process of a single two-level atom simultaneously absorbing or emitting two photons distributed in different cavities and its applications, Phys. Rev. A 106, 063721 (2022).
  9. X. L. Hei, P. B. Li, X. F. Pan, and F. Nori, Enhanced tripartite interactions in spin-magnon-mechanical hybrid systems, Phys. Rev. Lett. 130, 073602 (2023).
  10. A. Tomonaga, R. Stassi, H. Mukai, F. Nori, F. Yoshihara, and J. S. Tsai, One photon simultaneously excites two atoms in a ultrastrongly coupled light-matter system, arXiv:2307.15437.
  11. W. Ren, W. Liu, C. Song, H. Li, Q. Guo, Z. Wang, D. Zheng, G. S. Agarwal, M. O. Scully, S. Y. Zhu, H. Wang, and D. W. Wang, Simultaneous excitation of two noninteracting atoms with time-frequency correlated photon pairs in a superconducting circuit, Phys. Rev. Lett. 125, 133601 (2020).
  12. K. Zhang, H. Li, P. Zhang, J. Yuan, J. Chen, W. Ren, Z. Wang, C. Song, D. W. Wang, H. Wang, S. Zhu, G. S. Agarwal, and M. O. Scully, Synthesizing five-body interaction in a superconducting quantum circuit, Phys. Rev. Lett. 128, 190502 (2022).
  13. N. Chancellor, S. Zohren, and P. A. Warburton, Circuit design for multi-body interactions in superconducting quantum annealing systems with applications to a scalable architecture, npj Quantum Inf. 3, 21 (2017).
  14. M. Schöndorf and F. K. Wilhelm, Nonpairwise interactions induced by virtual transitions in four coupled artificial atoms, Phys. Rev. Appl. 12, 064026 (2019).
  15. T. Menke, W. P. Banner, T. R. Bergamaschi, A. D. Paolo, A. Vepsäläinen, S. J. Weber, R. Winik, A. Melville, B. M. Niedzielski, D. Rosenberg, K. Serniak, M. E. Schwartz, J. L. Yoder, A. Aspuru-Guzik, S. Gustavsson, J. A. Grover, C. F. Hirjibehedin, A. J. Kerman, and W. D. Oliver, Demonstration of tunable three-body interactions between superconducting qubits, Phys. Rev. Lett. 129, 220501 (2022).
  16. O. Katz, L. Feng, A. Risinger, C. Monroe, and M. Cetina, Demonstration of three- and four-body interactions between trapped-ion spins, Nat. Phys. 19, 1452 (2023).
  17. A. Karlsson and M. Bourennane, Quantum teleportation using three-particle entanglement, Phys. Rev. A 58, 4394 (1998).
  18. D. P. DiVincenzo and P. W. Shor, Fault-tolerant error correction with efficient quantum codes, Phys. Rev. Lett. 77, 3260 (1996).
  19. J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, Pulsed energy-time entangled twin-photon source for quantum communication, Phys. Rev. Lett. 82, 2594 (1999).
  20. V. Giovannetti, S. Lloyd, and L. Maccon, Quantum-enhanced measurements: Beating the standard quantum limit, Science 306, 1330 (2004).
  21. J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, Experimental entanglement swapping: Entangling photons that never interacted, Phys. Rev. Lett. 80, 3891 (1998).
  22. N. D. Mermin, Extreme quantum entanglement in a superposition of macroscopically distinct states, Phys. Rev. Lett. 65, 1838 (1990).
  23. S. B. Zheng, One-step synthesis of multiatom Greenberger-Horne-Zeilinger states, Phys. Rev. Lett. 87, 230404 (2001).
  24. C. P. Yang and S. Han, Preparation of Greenberger-Horne-Zeilinger entangled states with multiple superconducting quantum-interference device qubits or atoms in cavity QED, Phys. Rev. A 70, 062323 (2004).
  25. S. L. Zhu, Z. D. Wang, and P. Zanardi, Geometric quantum computation and multiqubit entanglement with superconducting qubits inside a cavity, Phys. Rev. Lett. 94, 100502 (2005).
  26. C. S. Yu, X. X. Yi, H. S. Song, and D. Mei, Robust preparation of Greenberger-Horne-Zeilinger and W states of three distant atoms, Phys. Rev. A 75, 044301 (2007).
  27. Y. D. Wang, S. Chesi, D. Loss, and C. Bruder, One-step multiqubit Greenberger-Horne-Zeilinger state generation in a circuit QED system, Phys. Rev. B 81, 104524 (2010).
  28. W. Feng, P. Wang, X. Ding, L. Xu, and X. Q. Li, Generating and stabilizing the Greenberger-Horne-Zeilinger state in circuit QED: Joint measurement, Zeno effect, and feedback, Phys. Rev. A 83, 042313 (2011).
  29. S. Aldana, Y. D. Wang, and C. Bruder, Greenberger-Horne-Zeilinger generation protocol for N superconducting transmon qubits capacitively coupled to a quantum bus, Phys. Rev. B 84, 134519 (2011).
  30. C. P. Yang, Q. P. Su, and S. Han, Generation of Greenberger-Horne-Zeilinger entangled states of photons in multiple cavities via a superconducting qutrit or an atom through resonant interaction, Phys. Rev. A 86, 022329 (2012).
  31. X. T. Mo and Z. Y. Xue, Single-step multipartite entangled states generation from coupled circuit cavities, Front. Phys. 14, 31602 (2019).
  32. T. Liu, Q. P. Su, Y. Zhang, Y. L. Fang, and C. P. Yang, Generation of quantum entangled states of multiple groups of qubits distributed in multiple cavities, Phys. Rev. A 101, 012337 (2020).
  33. Y. Zhang, T. Liu, J. Zhao, Y. Yu, and C. P. Yang, Generation of hybrid Greenberger-Horne-Zeilinger entangled states of particlelike and wavelike optical qubits in circuit QED, Phys. Rev. A 101, 062334 (2020).
  34. Q. C. Wu, Y. H. Zhou, B. L. Ye, T. Liu, J. L. Zhao, D. X. Chen, and C. P. Yang, Generation of an enhanced multi-mode optomechanical-like quantum system and its application in creating hybrid entangled states, Ann. Phys. 534, 2100393 (2022).
  35. S. F. Qi and J. Jing, Generation of Bell and Greenberger-Horne-Zeilinger states from a hybrid qubit-photon-magnon system, Phys. Rev. A 105, 022624 (2022).
  36. T. Liu, Y. H. Zhou, Q. C. Wu, and C. P. Yang, Generation of a GHZ-type optical entangled coherent state without measurements, Appl. Phys. Lett. 121, 244001 (2022).
  37. T. Haase, G. Alber, and V. M. Stojanović, Dynamical generation of chiral W and Greenberger-Horne-Zeilinger states in laser-controlled Rydberg-atom trimers, Phys. Rev. Res. 4, 033087 (2022).
  38. W. Feng, G. Q. Zhang, Q. P. Su, J. X. Zhang, and C. P. Yang, Generation of Greenberger-Horne-Zeilinger states on two-dimensional superconducting-qubit lattices via parallel multiqubit-gate operations, Phys. Rev. Appl. 18, 064036 (2022).
  39. D. S. Li, Y. H. Kang, Y. H. Chen, Y. Wang, J. Song, and Y. Xia, Efficient generation of Greenberger-Horne-Zeilinger states of N driven qubits mediated by a cavity, Quantum Inf. Process. 23, 2 (2024).
  40. T. Liu, Y. H. Zhou, Q. P. Su, and C. P. Yang, Generation of large-scale hybrid entangled states between superconducting qubits and microwave-field qubits, Phys. Rev. A 110, 062402 (2024).
  41. X. L. Wang, Y. H. Luo, H. L. Huang, M. C. Chen, Z. E. Su, C. Liu, C. Chen, W. Li, Y. Q. Fang, X. Jiang, J. Zhang, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, 18-Qubit entanglement with six photons’ three degrees of freedom, Phys. Rev. Lett. 120, 260502 (2018).
  42. P. Neumann, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, Multipartite entanglement among single spins in diamond, Science 320, 1326 (2008).
  43. A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, Generation and manipulation of Schrödinger cat states in Rydberg atom arrays, Science 365, 570 (2019).
  44. T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Hansel, M. Hennrich, and R. Blatt, 14-Qubit entanglement: Creation and coherence, Phys. Rev. Lett. 106, 130506 (2011).
  45. M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and J. M. Martinis, Generation of three-qubit entangled states using superconducting phase qubits, Nature (London) 467, 570 (2010).
  46. R. Barends, J. Kelly, A. Megrant, A. Veitia, D. Sank, E. Jeffrey, T. C. White, J. Mutus, A. G. Fowler, B. Campbell, et al., Superconducting quantum circuits at the surface code threshold for fault tolerance, Nature (London) 508, 500 (2014).
  47. C. Song, K. Xu, H. Li, Y. R. Zhang, X. Zhang, W. Liu, Q. Guo, Z. Wang, W. Ren, J. Hao, H. Feng, H. Fan, D. Zheng, D. W. Wang, H. Wang, and S. Y. Zhu, Generation of multicomponent atomic Schrödinger cat states of up to 20 qubits, Science 365, 574 (2019).
  48. S. Cao, B. Wu, F. Chen, M. Gong, Y. Wu, Y. Ye, C. Zha, H. Qian, C. Ying, S. Guo, et al., Generation of genuine entanglement up to 51 superconducting qubits, Nature (London) 619, 738 (2023).
  49. L. K. Grover, Quantum computers can search rapidly by using almost any transformation, Phys. Rev. Lett. 80, 4329 (1998).
  50. P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM Rev. 41, 303 (1999).
  51. P. W. Shor, Scheme for reducing decoherence in quantum computer memory, Phys. Rev. A 52, R2493(R) (1995).
  52. D. G. Cory, M. D. Price, W. Maas, E. Knill, R. Laflamme, W. H. Zurek, T. F. Havel, and S. S. Somaroo, Experimental quantum error correction, Phys. Rev. Lett. 81, 2152 (1998).
  53. P. Schindler, J. T. Barreiro, T. Monz, V. Nebendahl, D. Nigg, M. Chwalla, M. Hennrich, and R. Blatt, Experimental repetitive quantum error correction, Science 332, 1059 (2011).
  54. S. L. Braunstein, V. Bužek, and M. Hillery, Quantum-information distributors: Quantum network for symmetric and asymmetric cloning in arbitrary dimension and continuous limit, Phys. Rev. A 63, 052313 (2001).
  55. V. Vedral, A. Barenco, and A. Ekert, Quantum networks for elementary arithmetic operations, Phys. Rev. A 54, 147 (1996).
  56. T. Beth and M. Rötteler, Quantum Information (Springer, Berlin, 2001), Vol. 173, Chap. 4, p. 96.
  57. Y. Nam, Y. Su, and D. Maslov, Approximate quantum Fourier transform with O(nlog(n))T gates, npj Quantum Inf. 6, 26 (2020).
  58. M. Šašura and V. Bužek, Multiparticle entanglement with quantum logic networks: Application to cold trapped ions, Phys. Rev. A 64, 012305 (2001).
  59. B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, Simplifying quantum logic using higher-dimensional Hilbert spaces, Nat. Phys. 5, 134 (2009).
  60. T. Monz, K. Kim, W. Hänsel, M. Riebe, A. S. Villar, P. Schindler, M. Chwalla, M. Hennrich, and R. Blatt, Realization of the quantum Toffoli gate with trapped ions, Phys. Rev. Lett. 102, 040501 (2009).
  61. H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletixć, H. Pichler, and M. D. Lukin, Parallel implementation of high-fidelity multiqubit gates with neutral atoms, Phys. Rev. Lett. 123, 170503 (2019).
  62. N. W. Hendrickx, W. I. L. Lawrie, M. Russ, F. van Riggelen, S. L. de Snoo, R. N. Schouten, A. Sammak, G. Scappucci, and M. Veldhorst, A four-qubit germanium quantum processor, Nature (London) 591, 580 (2021).
  63. K. Takeda, A. Noiri, T. Nakajima, T. Kobayashi, and S. Tarucha, Quantum error correction with silicon spin qubits, Nature (London) 608, 682 (2022).
  64. M. Mariantoni, H. Wang, T. Yamamoto, M. Neeley, R. C. Bialczak, Y. Chen, M. Lenander, E. Lucero, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, Implementing the quantum von Neumann architecture with superconducting circuits, Science 334, 61 (2011).
  65. A. Fedorov, L. Steffen, M. Baur, M. P. da Silva, and A. Wallraff, Implementation of a Toffoli gate with superconducting circuits, Nature (London) 481, 170 (2012).
  66. M. D. Reed, L. DiCarlo, S. E. Nigg, L. Sun, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, Realization of three-qubit quantum error correction with superconducting circuits, Nature (London) 482, 382 (2012).
  67. Y. Kim, A. Morvan, L. B. Nguyen, R. K. Naik, C. Jünger, L. Chen, J. M. Kreikebaum, D. I. Santiago, and I. Siddiqi, High-fidelity three-qubit iToffoli gate for fixed-frequency superconducting qubits, Nat. Phys. 18, 783 (2022).
  68. A. J. Baker, G. B. P. Huber, N. J. Glaser, F. Roy, I. Tsitsilin, S. Filipp, and M. J. Hartmann, Single shot i-Toffoli gate in dispersively coupled superconducting qubits, Appl. Phys. Lett. 120, 054002 (2022).
  69. N. J. Glaser, F. Roy, and S. Filipp, Controlled-controlled-phase gates for superconducting qubits mediated by a shared tunable coupler, Phys. Rev. Appl. 19, 044001 (2023).
  70. T. Liu, J. Xu, Y. Zhang, Y. Yu, Q. P. Su, Y. H. Zhou, and C. P. Yang, Efficient scheme for implementing a hybrid Toffoli gate with two NV ensembles simultaneously controlling a single superconducting qubit, Appl. Phys. Lett. 123, 134002 (2023).
  71. J. Q. You and F. Nori, Atomic physics and quantum optics using superconducting circuits, Nature (London) 474, 589 (2011).
  72. M. H. Devoret and R. J. Schoelkopf, Superconducting circuits for quantum information: An outlook, Science 339, 1169 (2013).
  73. 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).
  74. A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
  75. 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).
  76. M. Roth, M. Ganzhorn, N. Moll, S. Filipp, G. Salis, and S. Schmidt, Analysis of a parametrically driven exchange-type gate and a two-photon excitation gate between superconducting qubits, Phys. Rev. A 96, 062323 (2017).
  77. 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).
  78. X. Li, T. Cai, H. Yan, Z. Wang, X. Pan, Y. Ma, W. Cai, J. Han, Z. Hua, X. Han, Y. Wu, H. Zhang, H. Wang, Y. Song, L. Duan, and L. Sun, Tunable coupler for realizing a controlled-phase gate with dynamically decoupled regime in a superconducting circuit, Phys. Rev. Appl. 14, 024070 (2020).
  79. 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).
  80. W. Liu, W. Feng, W. Ren, D. W. Wang, and H. Wang, Synthesizing three-body interaction of spin chirality with superconducting qubits, Appl. Phys. Lett. 116, 114001 (2020).
  81. L. Ding, M. Hays, Y. Sung, B. Kannan, J. An, A. D. 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 William D. Oliver, High-fidelity, frequency-flexible two-qubit fluxonium gates with a transmon coupler, Phys. Rev. X 13, 031035 (2023).
  82. 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).
  83. D. F. V. James, Quantum computation with hot and cold ions: An assessment of proposed schemes, Fortschr. Phys. 48, 823 (2000).
  84. W. Shao, C. Wu, and X. L. Feng, Generalized James’ effective Hamiltonian method, Phys. Rev. A 95, 032124 (2017).
  85. N. Zagury, A. Aragão, J. Casanova, and E. Solano, Unitary expansion of the time evolution operator, Phys. Rev. A 82, 042110 (2010).
  86. N. Yu, R. Duan, and M. Ying, Implementation of a three-qubit Toffoli gate in a single step, Phys. Rev. A 88, 010304(R) (2013).
  87. Y. Liu, J. Q. You, L. F. Wei, C. P. Sun, and F. Nori, Optical selection rules and phase-dependent adiabatic state control in a superconducting quantum circuit, Phys. Rev. Lett. 95, 087001 (2005).
  88. J. Q. You, X. Hu, S. Ashhab, and F. Nori, Low-decoherence flux qubit, Phys. Rev. B 75, 140515(R) (2007).
  89. F. Yan, S. Gustavsson, A. Kamal, J. Birenbaum, A. P. Sears, D. Hover, T. J. Gudmundsen, J. L. Yoder, T. P. Orlando, J. Clarke, A. J. Kerman, and W. D. Oliver, The flux qubit revisited to enhance coherence and reproducibility, Nat. Commun. 7, 12964 (2016).
  90. J. R. Johansson, P. D. Nation, and F. Nori, QuTiP: An open source Python framework for the dynamics of open quantum systems, Comput. Phys. Commun. 183, 1760 (2012).
  91. J. R. Johansson, P. D. Nation, and F. Nori, QuTiP 2: A Python framework for the dynamics of open quantum systems, Comput. Phys. Commun. 184, 1234 (2013).
  92. M. Baur, S. Filipp, R. Bianchetti, J. M. Fink, M. Göppl, L. Steffen, P. J. Leek, A. Blais, and A. Wallraff, Measurement of Autler-Townes and Mollow transitions in a strongly driven superconducting qubit, Phys. Rev. Lett. 102, 243602 (2009).
  93. F. Yoshihara, Y. Nakamura, F. Yan, S. Gustavsson, J. Bylander, W. D. Oliver, and J. S. Tsai, Flux qubit noise spectroscopy using Rabi oscillations under strong driving conditions, Phys. Rev. B 89, 020503(R) (2014).
  94. K. Inomata, T. Yamamoto, P. M. Billangeon, Y. Nakamura, and J. S. Tsai, Large dispersive shift of cavity resonance induced by a superconducting flux qubit in the straddling regime, Phys. Rev. B 86, 140508(R) (2012).
  95. Z. H. Peng, Y. Liu, J. T. Peltonen, T. Yamamoto, J. S. Tsai, and O. Astafiev, Correlated emission lasing in harmonic oscillators coupled via a single three-level artificial atom, Phys. Rev. Lett. 115, 223603 (2015).
  96. https://www.scidb.cn/s/aiqUn2.

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Phys. Rev. Research 8, 013023– Published 12 January, 2026
  • Received 7 February 2025
  • Accepted 23 December 2025
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