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  • Open Access

Multi-ion entangling gates mediated by spectrally unresolved modes

Modesto Orozco-Ruiz and Florian Mintert

  • Physics Department, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom

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Phys. Rev. A 114, 012422 – Published 8 July, 2026

DOI: https://doi.org/10.1103/357p-y5qf

Abstract

High-fidelity entangling gates in trapped-ion processors are most commonly realized by spectrally isolating a single motional bus mode. As the ion chain grows, however, the coupling of each ion to any one mode weakens, making single-mode gates progressively slower. Existing multimode schemes offer a partial remedy but rely on perturbative driving and rotating-wave approximations, imposing trade-offs between speed and fidelity that become more severe with chain length. We introduce a nonperturbative magnetic-gradient scheme in which all axial motional modes participate collectively in mediating the entangling interaction. Exact spin-motion decoupling is enforced at the end of the protocol by construction, so that the achievable gate speed is limited only by the available gradient strength and control bandwidth. The framework supports both multiqubit gates and selective two-qubit gates between arbitrary pairs in a linear string, including simultaneous operation on multiple pairs, and remains effective as the ion number increases.

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References (32)

  1. C. D. Bruzewicz, J. Chiaverini, R. McConnell, and J. M. Sage, Trapped-ion quantum computing: Progress and challenges, Appl. Phys. Rev. 6, 021314 (2019).
  2. A. Sørensen and K. Mølmer, Quantum computation with ions in thermal motion, Phys. Rev. Lett. 82, 1971 (1999).
  3. C. Monroe, W. C. Campbell, L.-M. Duan, Z.-X. Gong, A. V. Gorshkov, P. W. Hess, R. Islam, K. Kim, N. M. Linke, G. Pagano, et al., Programmable quantum simulations of spin systems with trapped ions, Rev. Mod. Phys. 93, 025001 (2021).
  4. A. Sørensen and K. Mølmer, Entanglement and quantum computation with ions in thermal motion, Phys. Rev. A 62, 022311 (2000).
  5. K. Kim, M.-S. Chang, R. Islam, S. Korenblit, L.-M. Duan, and C. Monroe, Entanglement and tunable spin-spin couplings between trapped ions using multiple transverse modes, Phys. Rev. Lett. 103, 120502 (2009).
  6. T. Choi, S. Debnath, T. Manning, C. Figgatt, Z.-X. Gong, L.-M. Duan, and C. Monroe, Optimal quantum control of multimode couplings between trapped ion qubits for scalable entanglement, Phys. Rev. Lett. 112, 190502 (2014).
  7. Y. Lu, S. Zhang, K. Zhang, W. Chen, Y. Shen, J. Zhang, J.-N. Zhang, and K. Kim, Global entangling gates on arbitrary ion qubits, Nature (London) 572, 363 (2019).
  8. D. Porras and J. I. Cirac, Effective quantum spin systems with trapped ions, Phys. Rev. Lett. 92, 207901 (2004).
  9. F. Mintert and C. Wunderlich, Ion-trap quantum logic using long-wavelength radiation, Phys. Rev. Lett. 87, 257904 (2001).
  10. C. Ospelkaus, U. Warring, Y. Colombe, K. Brown, J. Amini, D. Leibfried, and D. J. Wineland, Microwave quantum logic gates for trapped ions, Nature (London) 476, 181 (2011).
  11. J. Chiaverini, R. B. Blakestad, J. Britton, J. D. Jost, C. Langer, D. Leibfried, R. Ozeri, and D. J. Wineland, Surface-electrode architecture for ion-trap quantum information processing, Quantum Inf. Comput. 5, 419 (2005).
  12. B. Lekitsch, S. Weidt, A. G. Fowler, K. Mølmer, S. J. Devitt, C. Wunderlich, and W. K. Hensinger, Blueprint for a microwave trapped ion quantum computer, Sci. Adv. 3, e1601540 (2017).
  13. T. Harty, M. Sepiol, D. Allcock, C. Ballance, J. Tarlton, and D. Lucas, High-fidelity trapped-ion quantum logic using near-field microwaves, Phys. Rev. Lett. 117, 140501 (2016).
  14. S. Weidt, J. Randall, S. Webster, K. Lake, A. Webb, I. Cohen, T. Navickas, B. Lekitsch, A. Retzker, and W. Hensinger, Trapped-ion quantum logic with global radiation fields, Phys. Rev. Lett. 117, 220501 (2016).
  15. V. Schäfer, C. Ballance, K. Thirumalai, L. Stephenson, T. Ballance, A. Steane, and D. Lucas, Fast quantum logic gates with trapped-ion qubits, Nature (London) 555, 75 (2018).
  16. C. Ospelkaus, C. E. Langer, J. M. Amini, K. R. Brown, D. Leibfried, and D. J. Wineland, Trapped-ion quantum logic gates based on oscillating magnetic fields, Phys. Rev. Lett. 101, 090502 (2008).
  17. S. Banerjee, Open Quantum Systems Dynamics of Nonclassical Evolution, Texts and Readings in Physical Sciences (Springer, Singapore, 2018), Vol. 20.
  18. E. L. Hahn, Spin echoes, Phys. Rev. 80, 580 (1950).
  19. H. Y. Carr and E. M. Purcell, Effects of diffusion on free precession in nuclear magnetic resonance experiments, Phys. Rev. 94, 630 (1954).
  20. S. X. Wang, J. Labaziewicz, Y. Ge, R. Shewmon, and I. L. Chuang, Individual addressing of ions using magnetic field gradients in a surface-electrode ion trap, Appl. Phys. Lett. 94, 094103 (2009).
  21. A. Leu, M. Gely, M. Weber, M. Smith, D. Nadlinger, and D. Lucas, Fast, high-fidelity addressed single-qubit gates using efficient composite pulse sequences, Phys. Rev. Lett. 131, 120601 (2023).
  22. C. J. Ballance, T. P. Harty, N. M. Linke, M. A. Sepiol, and D. M. Lucas, High-fidelity quantum logic gates using trapped-ion hyperfine qubits, Phys. Rev. Lett. 117, 060504 (2016).
  23. See Supplemental Material at https://link.aps.org/supplemental/10.1103/357p-y5qf for additional derivations and numerical details.
  24. N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbrüggen, and S. J. Glaser, Optimal control of coupled spin dynamics: Design of NMR pulse sequences by gradient ascent algorithms, J. Magn. Reson. 172, 296 (2005).
  25. T. Caneva, T. Calarco, and S. Montangero, Chopped random-basis quantum optimization, Phys. Rev. A 84, 022326 (2011).
  26. C. P. Koch, U. Boscain, T. Calarco, G. Dirr, S. Filipp, S. J. Glaser, R. Kosloff, S. Montangero, T. Schulte-Herbrüggen, D. Sugny, et al., Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe, EPJ Quantum Technol. 9, 19 (2022).
  27. I. Gerasin, I. Semerikov, and W. Zhang, Surface ion trap for fast microwave gates, Chips 4, 41 (2025).
  28. G. Ramírez, J. Rodríguez-Laguna, and G. Sierra, Entanglement over the rainbow, J. Stat. Mech. (2015) P06002.
  29. G. Vitagliano, A. Riera, and J. I. Latorre, Volume-law scaling for the entanglement entropy in spin-1/2 chains, New J. Phys. 12, 113049 (2010).
  30. M. B. Hastings, An area law for one-dimensional quantum systems, J. Stat. Mech. (2007) P08024.
  31. C. M. Langlett, Z.-C. Yang, J. Wildeboer, A. V. Gorshkov, T. Iadecola, and S. Xu, Rainbow scars: From area to volume law, Phys. Rev. B 105, L060301 (2022).
  32. M. Harvey, Imperial College Research Computing Service, https://doi.org/10.14469/hpc/2232.

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Phys. Rev. A 114, 012422– Published 8 July, 2026
  • Received 13 December 2025
  • Accepted 11 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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