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Performance analysis for crosstalk errors between parallel entangling gates in trapped-ion quantum error correction

Fangxuan Liu1,2,*, Gaoxiang Tang1,2,*, Luming Duan1,3,4, and Yukai Wu1,2,3,†

  • 1Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People’s Republic of China
  • 2Shanghai Qi Zhi Institute, AI Tower, Xuhui District, Shanghai 200232, China
  • 3Hefei National Laboratory, Hefei 230088, People’s Republic of China
  • 4New Cornerstone Science Laboratory, Beijing 100084, People’s Republic of China

  • *These authors contribute equally to this work.
  • †Contact author: wyukai@mail.tsinghua.edu.cn
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Phys. Rev. Applied 24, 014032 – Published 16 July, 2025

DOI: https://doi.org/10.1103/c7w3-pxls

Abstract

The ability to execute a large number of quantum gates in parallel is a fundamental requirement for quantum error correction, allowing an error threshold to exist under the finite coherence time of physical qubits. Recently, two-dimensional ion crystals have been demonstrated as a plausible approach to scale up the qubit number in a trapped ion quantum computer. However, although the long-range Coulomb interaction between the ions enables their strong connectivity, it also complicates the design of parallel gates and leads to intrinsic crosstalk errors. Here we examine the effects of crosstalk errors on a rotated surface code. We show that, instead of the distance-3 code considered in previous works, a distance-5 code is necessary to correct the two-qubit crosstalk error. We numerically calculate the logical error rates and coherence times under various crosstalk errors, gate infidelities, and coherence times of the physical qubits, and we optimize the parallelism level according to the competition between different error sources. We show that a break-even point can be reached under realistic parameters. We further analyze the spatial dependence of the crosstalk, and discuss the scaling of the logical error rate versus the code distance for the long-term goal of a logical error rate below 10−10.

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References (77)

  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. S. Crain, C. Cahall, G. Vrijsen, E. E. Wollman, M. D. Shaw, V. B. Verma, S. W. Nam, and J. Kim, High-speed low-crosstalk detection of a 171Yb+ qubit using superconducting nanowire single photon detectors, Commun. Phys. 2, 97 (2019).
  3. C. Roman, A. Ransford, M. Ip, and W. C. Campbell, Coherent control for qubit state readout, New J. Phys. 22, 073038 (2020).
  4. C. L. Edmunds, T. R. Tan, A. R. Milne, A. Singh, M. J. Biercuk, and C. Hempel, Scalable hyperfine qubit state detection via electron shelving in the 2D5/2 and 2F7/2 manifolds in 171yb+, Phys. Rev. A 104, 012606 (2021).
  5. F. A. An, A. Ransford, A. Schaffer, L. R. Sletten, J. Gaebler, J. Hostetter, and G. Vittorini, High fidelity state preparation and measurement of ion hyperfine qubits with i>12, Phys. Rev. Lett. 129, 130501 (2022).
  6. T. P. Harty, D. T. C. Allcock, C. J. Ballance, L. Guidoni, H. A. Janacek, N. M. Linke, D. N. Stacey, and D. M. Lucas, High-fidelity preparation, gates, memory, and readout of a trapped-ion quantum bit, Phys. Rev. Lett. 113, 220501 (2014).
  7. M. C. Smith, A. D. Leu, K. Miyanishi, M. F. Gely, and D. M. Lucas, Single-qubit gates with errors at the 10−7 level, ArXiv:2412.04421.
  8. 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).
  9. 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, High-fidelity universal gate set for 9Be+ ion qubits, Phys. Rev. Lett. 117, 060505 (2016).
  10. 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, High-fidelity Bell-state preparation with 40Ca+ optical qubits, Phys. Rev. Lett. 127, 130505 (2021).
  11. C. M. Löschnauer, J. M. 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, Scalable, high-fidelity all-electronic control of trapped-ion qubits, ArXiv:2407.07694.
  12. J.-S. Chen, E. Nielsen, M. Ebert, V. Inlek, K. Wright, V. Chaplin, A. Maksymov, E. Páez, A. Poudel, P. Maunz, and J. Gamble, Benchmarking a trapped-ion quantum computer with 30 qubits, Quantum 8, 1516 (2024).
  13. L. Postler, S. Heuβen, I. Pogorelov, M. Rispler, T. Feldker, M. Meth, C. D. Marciniak, R. Stricker, M. Ringbauer, R. Blatt, P. Schindler, M. Müller, and T. Monz, Demonstration of fault-tolerant universal quantum gate operations, Nature 605, 675 (2022).
  14. S. A. Moses, et al., A race-track trapped-ion quantum processor, Phys. Rev. X 13, 041052 (2023).
  15. M. DeCross, et al., The computational power of random quantum circuits in arbitrary geometries, Phys. Rev. X 15, 021052 (2025).
  16. D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, Experimental issues in coherent quantum-state manipulation of trapped atomic ions, J. Res. Natl. Inst. Stand. Technol. 103, 259 (1998).
  17. D. Kielpinski, C. Monroe, and D. J. Wineland, Architecture for a large-scale ion-trap quantum computer, Nature 417, 709 (2002).
  18. R. J. Hughes, D. F. V. James, E. H. Knill, R. Laflamme, and A. G. Petschek, Decoherence bounds on quantum computation with trapped ions, Phys. Rev. Lett. 77, 3240 (1996).
  19. R. Clark, Proceedings of the 1st International Conference on Experimental Implementation of Quantum Computation: Sydney, Australia, 16-19 January 2001 (Rinton Press, Princeton, NJ, USA, 2001).
  20. B. Szymanski, R. Dubessy, B. Dubost, S. Guibal, J.-P. Likforman, and L. Guidoni, Large two dimensional Coulomb crystals in a radio frequency surface ion trap, Appl. Phys. Lett. 100, 171110 (2012).
  21. Y. Wang, M. Qiao, Z. Cai, K. Zhang, N. Jin, P. Wang, W. Chen, C. Luan, B. Du, H. Wang, Y. Song, D. Yum, and K. Kim, Coherently manipulated 2D ion crystal in a monolithic Paul trap, Adv. Quantum Technol. 3, 2000068 (2020).
  22. Y. Xie, J. Cui, M. D’Onofrio, A. J. Rasmusson, S. W. Howell, and P. Richerme, An open-endcap blade trap for radial-2D ion crystals, Quantum Sci. Technol. 6, 044009 (2021).
  23. A. Kato, A. Goel, R. Lee, Z. Ye, S. Karki, J. J. Liu, A. Nomerotski, and B. B. Blinov, Two-tone Doppler cooling of radial two-dimensional crystals in a radio-frequency ion trap, Phys. Rev. A 105, 023101 (2022).
  24. D. Kiesenhofer, H. Hainzer, A. Zhdanov, P. C. Holz, M. Bock, T. Ollikainen, and C. F. Roos, Controlling two-dimensional coulomb crystals of more than 100 ions in a monolithic radio-frequency trap, PRX Quantum 4, 020317 (2023).
  25. M. Qiao, Z. Cai, Y. Wang, B. Du, N. Jin, W. Chen, P. Wang, C. Luan, E. Gao, X. Sun, H. Tian, J. Zhang, and K. Kim, Tunable quantum simulation of spin models with a two-dimensional ion crystal, Nat. Phys. 20, 623 (2024).
  26. S.-A. Guo, Y.-K. Wu, J. Ye, L. Zhang, W.-Q. Lian, R. Yao, Y. Wang, R.-Y. Yan, Y.-J. Yi, Y.-L. Xu, B.-W. Li, Y.-H. Hou, Y.-Z. Xu, W.-X. Guo, C. Zhang, B.-X. Qi, Z.-C. Zhou, L. He, and L.-M. Duan, A site-resolved two-dimensional quantum simulator with hundreds of trapped ions, Nature 630, 613 (2024).
  27. Y.-H. Hou, Y.-J. Yi, Y.-K. Wu, Y.-Y. Chen, L. Zhang, Y. Wang, Y.-L. Xu, C. Zhang, Q.-X. Mei, H.-X. Yang, J.-Y. Ma, S.-A. Guo, J. Ye, B.-X. Qi, Z.-C. Zhou, P.-Y. Hou, and L.-M. Duan, Individually addressed entangling gates in a two-dimensional ion crystal, Nat. Commun. 15, 9710 (2024).
  28. C. Figgatt, A. Ostrander, N. M. Linke, K. A. Landsman, D. Zhu, D. Maslov, and C. Monroe, Parallel entangling operations on a universal ion-trap quantum computer, Nature 572, 368 (2019).
  29. 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 572, 363 (2019).
  30. M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, UK, 2000).
  31. N. Grzesiak, R. Blümel, K. Wright, K. M. Beck, N. C. Pisenti, M. Li, V. Chaplin, J. M. Amini, S. Debnath, J.-S. Chen, and Y. Nam, Efficient arbitrary simultaneously entangling gates on a trapped-ion quantum computer, Nat. Commun. 11, 2963 (2020).
  32. T. Olsacher, L. Postler, P. Schindler, T. Monz, P. Zoller, and L. M. Sieberer, Scalable and parallel tweezer gates for quantum computing with long ion strings, PRX Quantum 1, 020316 (2020).
  33. L. Cheng, S.-C. Liu, L.-Y. Peng, and Q. Gong, Crosstalk suppression of parallel gates for fault-tolerant quantum computation with trapped ions via optical tweezers, Phys. Rev. Appl. 22, 034021 (2024).
  34. L. Cheng, S.-C. Liu, G.-Z. Yao, Y.-X. Wang, L.-Y. Peng, and Q. Gong, High-quality parallel entangling gates in long mixed-species ion chains, Phys. Rev. A 108, 042603 (2023).
  35. C. Shen, Z.-X. Gong, and L.-M. Duan, Individual addressing in quantum computation through spatial refocusing, Phys. Rev. A 88, 052325 (2013).
  36. D. M. Debroy, M. Li, S. Huang, and K. R. Brown, Logical performance of 9 qubit compass codes in ion traps with crosstalk errors, Quantum Sci. Technol. 5, 034002 (2020).
  37. P. Parrado-Rodríguez, C. Ryan-Anderson, A. Bermudez, and M. Müller, Crosstalk suppression for fault-tolerant quantum error correction with trapped ions, Quantum 5, 487 (2021).
  38. C. Fang, Y. Wang, S. Huang, K. R. Brown, and J. Kim, Crosstalk suppression in individually addressed two-qubit gates in a trapped-ion quantum computer, Phys. Rev. Lett. 129, 240504 (2022).
  39. M. N. H. Chow, C. G. Yale, A. D. Burch, M. Ivory, D. S. Lobser, M. C. Revelle, and S. M. Clark, First-order crosstalk mitigation in parallel quantum gates driven with multi-photon transitions, Appl. Phys. Lett. 124, 044002 (2024).
  40. J. Flannery, R. Matt, L. Huber, K. Wang, C. Axline, R. Oswald, and J. P. Home, Physical coherent cancellation of optical addressing crosstalk in a trapped-ion experiment, Quantum Sci. Technol. 10, 015012 (2025).
  41. S. B. Bravyi and A. Y. Kitaev, Quantum codes on a lattice with boundary, ArXiv:quant-ph/9811052.
  42. H. Bombin and M. A. Martin-Delgado, Optimal resources for topological two-dimensional stabilizer codes: Comparative study, Phys. Rev. A 76, 012305 (2007).
  43. A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Phys. Rev. A 86, 032324 (2012).
  44. R. Acharya, et al., Google Quantum AI and Collaborators, Quantum error correction below the surface code threshold, Nature 638, 920 (2024).
  45. J. Edmonds, Paths, trees, and flowers, Can. J. Math. 17, 449 (1965).
  46. J. Edmonds, Maximum matching and a polyhedron with 0, 1-vertices, J. Res. Natl. Bur. Stand. 69B, 125 (1965).
  47. C. Gidney, Stim: A fast stabilizer circuit simulator, Quantum 5, 497 (2021).
  48. A. Sørensen and K. Mølmer, Quantum computation with ions in thermal motion, Phys. Rev. Lett. 82, 1971 (1999).
  49. K. Mølmer and A. Sørensen, Multiparticle entanglement of hot trapped ions, Phys. Rev. Lett. 82, 1835 (1999).
  50. G. Milburn, S. Schneider, and D. James, Ion trap quantum computing with warm ions, Fortschr. Phys. 48, 801 (2000).
  51. D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, and D. J. Wineland, Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate, Nature 422, 412 (2003).
  52. Shi-Liang Zhu, C. Monroe, and L.-M. Duan, Arbitrary-speed quantum gates within large ion crystals through minimum control of laser beams, Europhys. Lett. 73, 485 (2006).
  53. T. J. Green and M. J. Biercuk, Phase-modulated decoupling and error suppression in qubit-oscillator systems, Phys. Rev. Lett. 114, 120502 (2015).
  54. P. H. Leung and K. R. Brown, Entangling an arbitrary pair of qubits in a long ion crystal, Phys. Rev. A 98, 032318 (2018).
  55. Y. Wu, S.-T. Wang, and L.-M. Duan, Noise analysis for high-fidelity quantum entangling gates in an anharmonic linear Paul trap, Phys. Rev. A 97, 062325 (2018).
  56. O. Kern, G. Alber, and D. L. Shepelyansky, Quantum error correction of coherent errors by randomization, Eur. Phys. J. D—At. Mol. Opt. Plasma Phys. 32, 153 (2005).
  57. J. J. Wallman and J. Emerson, Noise tailoring for scalable quantum computation via randomized compiling, Phys. Rev. A 94, 052325 (2016).
  58. D. Porras and J. I. Cirac, Effective quantum spin systems with trapped ions, Phys. Rev. Lett. 92, 207901 (2004).
  59. 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).
  60. Y. Tomita and K. M. Svore, Low-distance surface codes under realistic quantum noise, Phys. Rev. A 90, 062320 (2014).
  61. F. Liu, G. Tang, L. Duan, and Y. Wu, Data and code for “performance analysis for crosstalk errors between parallel entangling gates in trapped ion quantum error correction, 2025, https://doi.org/10.5281/zenodo.15552654.
  62. K. A. Landsman, Y. Wu, P. H. Leung, D. Zhu, N. M. Linke, K. R. Brown, L. Duan, and C. Monroe, Two-qubit entangling gates within arbitrarily long chains of trapped ions, Phys. Rev. A 100, 022332 (2019).
  63. Y.-K. Wu and L.-M. Duan, A two-dimensional architecture for fast large-scale trapped-ion quantum computing, Chin. Phys. Lett. 37, 070302 (2020).
  64. J. J. García-Ripoll, P. Zoller, and J. I. Cirac, Speed optimized two-qubit gates with laser coherent control techniques for ion trap quantum computing, Phys. Rev. Lett. 91, 157901 (2003).
  65. L.-M. Duan, Scaling ion trap quantum computation through fast quantum gates, Phys. Rev. Lett. 93, 100502 (2004).
  66. J. D. Wong-Campos, S. A. Moses, K. G. Johnson, and C. Monroe, Demonstration of two-atom entanglement with ultrafast optical pulses, Phys. Rev. Lett. 119, 230501 (2017).
  67. A. K. Ratcliffe, R. L. Taylor, J. J. Hope, and A. R. R. Carvalho, Scaling trapped ion quantum computers using fast gates and microtraps, Phys. Rev. Lett. 120, 220501 (2018).
  68. P. Wang, C.-Y. Luan, M. Qiao, M. Um, J. Zhang, Y. Wang, X. Yuan, M. Gu, J. Zhang, and K. Kim, Single ion qubit with estimated coherence time exceeding one hour, Nat. Commun. 12, 233 (2021).
  69. R. Yao, W.-Q. Lian, Y.-K. Wu, G.-X. Wang, B.-W. Li, Q.-X. Mei, B.-X. Qi, L. Yao, Z.-C. Zhou, L. He, and L.-M. Duan, Experimental realization of a multiqubit quantum memory in a 218-ion chain, Phys. Rev. A 106, 062617 (2022).
  70. Y. Wang, S. Crain, C. Fang, B. Zhang, S. Huang, Q. Liang, P. H. Leung, K. R. Brown, and J. Kim, High-fidelity two-qubit gates using a microelectromechanical-system-based beam steering system for individual qubit addressing, Phys. Rev. Lett. 125, 150505 (2020).
  71. M. Kang, Y. Wang, C. Fang, B. Zhang, O. Khosravani, J. Kim, and K. R. Brown, Designing filter functions of frequency-modulated pulses for high-fidelity two-qubit gates in ion chains, Phys. Rev. Appl. 19, 014014 (2023).
  72. I. Pogorelov, T. Feldker, C. D. Marciniak, L. Postler, G. Jacob, O. Krieglsteiner, V. Podlesnic, M. Meth, V. Negnevitsky, M. Stadler, B. Höfer, C. Wächter, K. Lakhmanskiy, R. Blatt, P. Schindler, and T. Monz, Compact ion-trap quantum computing demonstrator, PRX Quantum 2, 020343 (2021).
  73. P. J. Lee, K.-A. Brickman, L. Deslauriers, P. C. Haljan, L.-M. Duan, and C. Monroe, Phase control of trapped ion quantum gates, J. Opt. B: Quantum Semiclassical Opt. 7, S371 (2005).
  74. D. Gottesman, Fault-tolerant quantum computation with constant overhead, Quantum Inf. Comput. 14, 1338 (2014).
  75. N. P. Breuckmann and J. N. Eberhardt, Quantum low-density parity-check codes, PRX Quantum 2, 040101 (2021).
  76. A. G. Fowler, Analytic asymptotic performance of topological codes, Phys. Rev. A 87, 040301 (2013).
  77. H.-X. Yang, J.-Y. Ma, Y.-K. Wu, Y. Wang, M.-M. Cao, W.-X. Guo, Y.-Y. Huang, L. Feng, Z.-C. Zhou, and L.-M. Duan, Realizing coherently convertible dual-type qubits with the same ion species, Nat. Phys. 18, 1058 (2022).

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Phys. Rev. Applied 24, 014032– Published 16 July, 2025
  • Received 16 January 2025
  • Revised 30 May 2025
  • Accepted 27 June 2025
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