- Open Access
Photon-mediated entanglement between spin qubits beyond the dispersive regime
Phys. Rev. B 114, 045420 – Published 16 July, 2026
DOI: https://doi.org/10.1103/y6d1-nsxs
Abstract
Dispersively coupled distant qubits in a shared cavity can become entangled through virtual photon exchange with energy-conserving phase evolution of their quantum states. This interaction can potentially be accelerated by operating on resonance, allowing for the exchange of real photons. In this theoretical study, we examine photon-mediated entanglement between two distant spins of electrons confined in double quantum dots formed in a Si/SiGe heterostructure. We calculate the dynamics of the combined system comprised of both spin qubits and the cavity, assuming that both spin qubits can be tuned into and out of resonance with the host cavity. We demonstrate that the exchange of real photons between the two spin qubits can result in rapid entanglement that is robust against decoherence. These results pave the way for the development of quantum gates on resonantly coupled distant semiconductor spin qubits.
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References (45)
- D. Loss and D. P. DiVincenzo, Quantum computation with quantum dots, Phys. Rev. A 57, 120 (1998).
- G. Burkard, T. D. Ladd, A. Pan, J. M. Nichol, and J. R. Petta, Semiconductor spin qubits, Rev. Mod. Phys. 95, 025003 (2023).
- T. Hayashi, T. Fujisawa, H. D. Cheong, Y. H. Jeong, and Y. Hirayama, Coherent manipulation of electronic states in a double quantum dot, Phys. Rev. Lett. 91, 226804 (2003).
- J. R. Petta, A. C. Johnson, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Manipulation of a single charge in a double quantum dot, Phys. Rev. Lett. 93, 186802 (2004).
- Y. Dovzhenko, J. Stehlik, K. D. Petersson, J. R. Petta, H. Lu, and A. C. Gossard, Nonadiabatic quantum control of a semiconductor charge qubit, Phys. Rev. B 84, 161302(R) (2011).
- G. Cao, H.-O. Li, T. Tu, L. Wang, C. Zhou, M. Xiao, G.-C. Guo, H.-W. Jiang, and G.-P. Guo, Ultrafast universal quantum control of a quantum-dot charge qubit using Landau–Zener–Stückelberg interference, Nat. Commun. 4, 1401 (2013).
- F. Kayatz, J. Mielke, and G. Burkard, Resonator-mediated quantum gate between distant charge qubits, Quantum Sci. Technol. 9, 045048 (2024).
- A. Cottet and T. Kontos, Spin quantum bit with ferromagnetic contacts for circuit QED, Phys. Rev. Lett. 105, 160502 (2010).
- M. Russ, D. M. Zajac, A. J. Sigillito, F. Borjans, J. M. Taylor, J. R. Petta, and G. Burkard, High-fidelity quantum gates in Si/SiGe double quantum dots, Phys. Rev. B 97, 085421 (2018).
- M. Benito, X. Croot, C. Adelsberger, S. Putz, X. Mi, J. R. Petta, and G. Burkard, Electric-field control and noise protection of the flopping-mode spin qubit, Phys. Rev. B 100, 125430 (2019).
- X. Croot, X. Mi, S. Putz, M. Benito, F. Borjans, G. Burkard, and J. R. Petta, Flopping-mode electric dipole spin resonance, Phys. Rev. Res. 2, 012006(R) (2020).
- P. M. Mutter and G. Burkard, Natural heavy-hole flopping mode qubit in germanium, Phys. Rev. Res. 3, 013194 (2021).
- 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).
- M. Benito, X. Mi, J. M. Taylor, J. R. Petta, and G. Burkard, Input-output theory for spin-photon coupling in Si double quantum dots, Phys. Rev. B 96, 235434 (2017).
- X. Mi, J. V. Cady, D. M. Zajac, P. W. Deelman, and J. R. Petta, Strong coupling of a single electron in silicon to a microwave photon, Science 355, 156 (2017).
- 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).
- 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).
- 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 oscillations between distant spins, Nat. Phys. 21, 168 (2025).
- J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, Strong coupling in a single quantum dot–semiconductor microcavity system, Nature (London) 432, 197 (2004).
- T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity, Nature (London) 432, 200 (2004).
- 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).
- 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).
- Y.-B. Hu, R. Chen, G.-Q. Yan, and X.-Y. Zhu, Long-range entanglement between spin qubits in quantum dots by virtual photon process, Mod. Phys. Lett. A 38, 2350053 (2023).
- A. Warren, U. Güngördü, 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).
- S. R. McMillan and G. Burkard, Resonant direct CNOT in remote double quantum dot spin qubits, Phys. Rev. B 108, 125414 (2023).
- D. J. van Woerkom, P. Scarlino, J. H. Ungerer, C. Müller, J. V. Koski, A. J. Landig, C. Reichl, W. Wegscheider, T. Ihn, K. Ensslin, and A. Wallraff, Microwave photon-mediated interactions between semiconductor qubits, Phys. Rev. X 8, 041018 (2018).
- M. S. Domínguez, H. Vinck-Posada, and E. A. Gómez, Entanglement generation between two solid-state qubits mediated by microwave photons, Phys. Lett. A 388, 127045 (2021).
- K. D. Petersson, J. R. Petta, H. Lu, and A. C. Gossard, Quantum coherence in a one-electron semiconductor charge qubit, Phys. Rev. Lett. 105, 246804 (2010).
- D. M. Zajac, A. J. Sigillito, M. Russ, F. Borjans, J. M. Taylor, G. Burkard, and J. R. Petta, Resonantly driven CNOT gate for electron spins, Science 359, 439 (2018).
- C. E. Bradley, J. Randall, M. H. Abobeih, R. C. Berrevoets, M. J. Degen, M. A. Bakker, M. Markham, D. J. Twitchen, and T. H. Taminiau, A ten-qubit solid-state spin register with quantum memory up to one minute, Phys. Rev. X 9, 031045 (2019).
- V. John, C. X. Yu, B. van Straaten, E. A. Rodríguez-Mena, M. Rodríguez, S. D. Oosterhout, L. E. A. Stehouwer, G. Scappucci, M. Rimbach-Russ, S. Bosco, F. Borsoi, Y.-M. Niquet, and M. Veldhorst, Robust and localised control of a 10-spin qubit array in germanium, Nat. Commun. 16, 10560 (2025).
- V. N. Golovach, M. Borhani, and D. Loss, Electric-dipole-induced spin resonance in quantum dots, Phys. Rev. B 74, 165319 (2006).
- S. Nadj-Perge, S. Frolov, E. Bakkers, and L. P. Kouwenhoven, Spin–orbit qubit in a semiconductor nanowire, Nature (London) 468, 1084 (2010).
- M. D. Schroer, K. D. Petersson, M. Jung, and J. R. Petta, Field tuning the factor in InAs nanowire double quantum dots, Phys. Rev. Lett. 107, 176811 (2011).
- C. X. Yu, S. Zihlmann, J. C. Abadillo-Uriel, V. P. Michal, N. Rambal, H. Niebojewski, T. Bedecarrats, M. Vinet, É. Dumur, M. Filippone, S. Bertrand, B. De Franceschi, Y.-M. Niquet, and R. Maurand, Strong coupling between a photon and a hole spin in silicon, Nat. Nanotechnol. 18, 741 (2023).
- M. Rimbach-Russ, V. John, B. van Straaten, and S. Bosco, Gapless single-spin qubit, Phys. Rev. Lett. 135, 197001 (2025).
- M. Pioro-Ladriere, T. Obata, Y. Tokura, Y.-S. Shin, T. Kubo, K. Yoshida, T. Taniyama, and S. Tarucha, Electrically driven single-electron spin resonance in a slanting Zeeman field, Nat. Phys. 4, 776 (2008).
- 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).
- V. Srinivasa, J. M. Taylor, and J. R. Petta, Cavity-mediated entanglement of parametrically driven spin qubits via sidebands, PRX Quantum 5, 020339 (2024).
- G. Burkard, M. J. Gullans, X. Mi, and J. R. Petta, Superconductor–semiconductor hybrid-circuit quantum electrodynamics, Nat. Rev. Phys. 2, 129 (2020).
- R. U. Haq and K. Singh, A systematic method for Schrieffer-Wolff transformation and its generalizations, arXiv:2004.06534.
- J. R. Schrieffer and P. A. Wolff, Relation between the Anderson and Kondo Hamiltonians, Phys. Rev. 149, 491 (1966).
- D. R. Ward, D. Kim, D. E. Savage, M. G. Lagally, R. H. Foote, M. Friesen, S. N. Coppersmith, and M. A. Eriksson, State-conditional coherent charge qubit oscillations in a Si/SiGe quadruple quantum dot, npj Quantum Inf. 2, 16032 (2016).
- W. K. Wootters, Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett. 80, 2245 (1998).
- L. R. B. Picard, A. J. Park, G. E. Patenotte, S. Gebretsadkan, D. Wellnitz, A. M. Rey, and K.-K. Ni, Entanglement and iSWAP gate between molecular qubits, Nature (London) 637, 821 (2025).