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

Ab initio modeling of quantum dot qubits: Coupling, gate dynamics, and robustness versus charge noise

Hamza Jnane1,2,* and Simon C. Benjamin1,2

  • 1Quantum Motion, 9 Sterling Way, London, N7 9HJ, United Kingdom
  • 2Department of Materials, University of Oxford, Parks Road, Oxford, OX1 3PH, United Kingdom

  • *Contact author: hjnane.science@gmail.com

Phys. Rev. Applied 24, 044042 – Published 15 October, 2025

DOI: https://doi.org/10.1103/rm43-nh9b

Abstract

Electron spins in semiconductor devices are highly promising building blocks for quantum processors (QPs). Commercial semiconductor foundries can create QPs using the same processes used for conventional chips, once the QP design is suitably specified. There is a vast accessible design space; to identify the most promising options for fabrication, one requires predictive modeling of interacting electrons in real geometries and complex nonideal environments. In this work we explore a modeling method based on real-space grids, an ab initio approach without assumptions relating to device topology and therefore with wide applicability. Given an electrode geometry, we determine the exchange coupling between quantum dot qubits, and model the full evolution of a SWAP gate to predict qubit loss and infidelity rates for various voltage profiles. We determine full, three-dimensional solutions and introduce a method that can obtain near-identical predictions using far more efficient two-dimensional computations. Moreover we explore the impact of unwanted charge defects (static and dynamic) in the environment, and test robust pulse sequences. As an example we exhibit a sequence correcting both systematic errors and (unknown) charge defects, observing an order of magnitude boost in fidelity. The technique can thus identify the most promising device designs for fabrication, as well as bespoke control sequences for each such device.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (52)

  1. G. Burkard, T. D. Ladd, A. Pan, J. M. Nichol, and J. R. Petta, Semiconductor spin qubits, Rev. Mod. Phys. 95, 025003 (2023).
  2. A. R. Mills, C. R. Guinn, M. J. Gullans, A. J. Sigillito, M. M. Feldman, E. Nielsen, and J. R. Petta, Two-qubit silicon quantum processor with operation fidelity exceeding 99%, Sci. Adv. 8, eabn5130 (2022).
  3. X. Xue, M. Russ, N. Samkharadze, B. Undseth, A. Sammak, G. Scappucci, and L. M. K. Vandersypen, Quantum logic with spin qubits crossing the surface code threshold, Nature 601, 343 (2022).
  4. A. Noiri, K. Takeda, T. Nakajima, T. Kobayashi, A. Sammak, G. Scappucci, and S. Tarucha, Fast universal quantum gate above the fault-tolerance threshold in silicon, Nature 601, 338 (2022).
  5. M. D. Michielis, E. Ferraro, E. Prati, L. Hutin, B. Bertrand, E. Charbon, D. J. Ibberson, and M. F. Gonzalez-Zalba, Silicon spin qubits from laboratory to industry, J. Phys. D: Appl. Phys. 56, 363001 (2023).
  6. A. M. J. Zwerver et al., Qubits made by advanced semiconductor manufacturing, Nat. Electron. 5, 184 (2022).
  7. M. Veldhorst, H. G. J. Eenink, C. H. Yang, and A. S. Dzurak, Silicon CMOS architecture for a spin-based quantum computer, Nat. Commun. 8, 1766 (2017).
  8. R. Maurand, X. Jehl, D. Kotekar-Patil, A. Corna, H. Bohuslavskyi, R. Laviéville, L. Hutin, S. Barraud, M. Vinet, M. Sanquer, and S. De Franceschi, A CMOS silicon spin qubit, Nat. Commun. 7, 13575 (2016).
  9. D. Loss and D. P. DiVincenzo, Quantum computation with quantum dots, Phys. Rev. A 57, 120 (1998).
  10. D. P. DiVincenzo, D. Bacon, J. Kempe, G. Burkard, and K. B. Whaley, Universal quantum computation with the exchange interaction, Nature 408, 339 (2000).
  11. T. Meunier, V. E. Calado, and L. M. K. Vandersypen, Efficient controlled-phase gate for single-spin qubits in quantum dots, Phys. Rev. B 83, 121403(R) (2011).
  12. A. L. Saraiva, M. J. Calderón, and B. Koiller, Reliability of the Heitler-London approach for the exchange coupling between electrons in semiconductor nanostructures, Phys. Rev. B 76, 233302 (2007).
  13. C. R. Anderson, M. F. Gyure, S. Quinn, A. Pan, R. S. Ross, and A. A. Kiselev, High-precision real-space simulation of electrostatically confined few-electron states, AIP Adv. 12, 065123 (2022).
  14. H. E. Ercan, S. N. Coppersmith, and M. Friesen, Strong electron-electron interactions in Si/SiGe quantum dots, Phys. Rev. B 104, 235302 (2021).
  15. M. J. Calderón, B. Koiller, and S. Das Sarma, Exchange coupling in semiconductor nanostructures: Validity and limitations of the Heitler-London approach, Phys. Rev. B 74, 045310 (2006).
  16. M. D. Reed, B. M. Maune, R. W. Andrews, M. G. Borselli, K. Eng, M. P. Jura, A. A. Kiselev, T. D. Ladd, S. T. Merkel, I. Milosavljevic, E. J. Pritchett, M. T. Rakher, R. S. Ross, A. E. Schmitz, A. Smith, J. A. Wright, M. F. Gyure, and A. T. Hunter, Reduced sensitivity to charge noise in semiconductor spin qubits via symmetric operation, Phys. Rev. Lett. 116, 110402 (2016).
  17. D. Culcer, X. Hu, and S. Das Sarma, Dephasing of Si spin qubits due to charge noise, Appl. Phys. Lett. 95, 073102 (2009).
  18. E. Nielsen, R. W. Young, R. P. Muller, and M. S. Carroll, Implications of simultaneous requirements for low-noise exchange gates in double quantum dots, Phys. Rev. B 82, 075319 (2010).
  19. J. D. Cifuentes, P. Y. Mai, F. Schlattner, H. E. Ercan, M. Feng, C. C. Escott, A. S. Dzurak, and A. Saraiva, Path-integral simulation of exchange interactions in CMOS spin qubits, Phys. Rev. B 108, 155413 (2023).
  20. B. Buonacorsi, M. Korkusinski, B. Khromets, and J. Baugh, Optimizing lateral quantum dot geometries for reduced exchange noise, arXiv:2012.10512 [cond-mat.mes-hall].
  21. M. M. E. K. Shehata, G. Simion, R. Li, F. A. Mohiyaddin, D. Wan, M. Mongillo, B. Govoreanu, I. Radu, K. D. Greve, and P. V. Dorpe, Modelling semiconductor spin qubits and their charge noise environment for quantum gate fidelity estimation, PhysRevB. 108, 045305 (2023).
  22. A. Elsayed, M. Shehata, C. Godfrin, S. Kubicek, S. Massar, Y. Canvel, J. Jussot, G. Simion, M. Mongillo, D. Wan, B. Govoreanu, I. P. Radu, R. Li, P. V. Dorpe, and K. D. Greve, Low charge noise quantum dots with industrial CMOS manufacturing, npj Quantum Inf. 10, 70 (2024).
  23. M. H. Levitt, Composite pulses, Prog. Nucl. Magn. Reson. Spectrosc. 18, 61 (1986).
  24. K. R. Brown, A. W. Harrow, and I. L. Chuang, Arbitrarily accurate composite pulse sequences, Phys. Rev. A 70, 052318 (2004).
  25. J. A. Jones, Composite pulses in NMR quantum computation, J. Ind. Inst. Sci. 89, 303 (2009).
  26. J. Jones, Systematic errors and NMR composite pulses, https://nmr.physics.ox.ac.uk/teaching/cp.pdf.
  27. J. C. Light and T. Carrington, Jr., Discrete-variable representations and their utilization, Adv. Chem. Phys. 114, 263 (2000).
  28. M. F. J. A. Fleck, Jr. and J. Morris, Time-dependent propagation of high energy laser beams through the atmosphere, Appl. Phys. 10, 129 (1976).
  29. R. Babbush, N. Wiebe, J. McClean, J. McClain, H. Neven, and G. Kin-Lic Chan, Low-depth quantum simulation of materials, Phys. Rev. X 8, 011044 (2018).
  30. H. H. S. Chan, R. Meister, T. Jones, D. P. Tew, and S. C. Benjamin, Grid-based methods for chemistry simulations on a quantum computer, Sci. Adv. 9, eabo7484 (2023).
  31. A good account of the Dirichlet kernel and its relation to the Dirac comb is provided at https://en.wikipedia.org/wiki/Dirichlet_kernel.
  32. The equivalent to Eq. (3) for Ref. [29], with its odd number of basis states M, simply omits the phase prefactor, and has n running from −m to m so that the grid points pn run from −(12−12M) to +(12−12M).
  33. J. D. Cifuentes et al., Bounds to electron spin qubit variability for scalable CMOS architectures, Nat. Commun. 15, 4299 (2024).
  34. A. Saraiva, W. H. Lim, C. H. Yang, C. C. Escott, A. Laucht, and A. S. Dzurak, Materials for silicon quantum dots and their impact on electron spin qubits, Adv. Funct. Mater. 32, 2105488 (2022).
  35. L. Lehtovaara, J. Toivanen, and J. Eloranta, Solution of time-independent Schrödinger equation by the imaginary time propagation method, J. Comput. Phys. 221, 148 (2007).
  36. C. R. Anderson, Efficient solution of the Schroedinger–Poisson equations in layered semiconductor devices, J. Comput. Phys. 228, 4745 (2009).
  37. E. J. Connors, J. Nelson, L. F. Edge, and J. M. Nichol, Charge-noise spectroscopy of Si/SiGe quantum dots via dynamically-decoupled exchange oscillations, Nat. Commun. 13, 940 (2022).
  38. J. Yoneda, K. Takeda, T. Otsuka, T. Nakajima, M. R. Delbecq, G. Allison, T. Honda, T. Kodera, S. Oda, Y. Hoshi, N. Usami, K. M. Itoh, and S. Tarucha, A quantum-dot spin qubit with coherence limited by charge noise and fidelity higher than 99.9%, Nat. Nanotechnol. 13, 102 (2018).
  39. B. Paquelet Wuetz, D. Degli Esposti, A.-M. J. Zwerver, S. V. Amitonov, M. Botifoll, J. Arbiol, A. Sammak, L. M. K. Vandersypen, M. Russ, and G. Scappucci, Reducing charge noise in quantum dots by using thin silicon quantum wells, Nat. Commun. 14, 1385 (2023).
  40. J. S. Rojas-Arias, A. Noiri, P. Stano, T. Nakajima, J. Yoneda, K. Takeda, T. Kobayashi, A. Sammak, G. Scappucci, D. Loss, and S. Tarucha, Spatial noise correlations beyond nearest neighbors in 28Si/Si−Ge spin qubits, Phys. Rev. Appl. 20, 054024 (2023).
  41. M. Kȩpa, N. Focke, Ł. Cywiński, and J. A. Krzywda, Simulation of 1/f charge noise affecting a quantum dot in a Si/SiGe structure, Appl. Phys. Lett. 123, 034005 (2023).
  42. D. L. Mickelsen, H. M. Carruzzo, and C. C. Yu, Interacting two-level systems as a source of 1/f charge noise in quantum dot qubits, Phys. Rev. B 108, 195307 (2023).
  43. J. S. Rojas-Arias, A. Noiri, J. Yoneda, P. Stano, T. Nakajima, K. Takeda, T. Kobayashi, G. Scappucci, S. Tarucha, and D. Loss, Inferring charge noise source locations from correlations in spin qubits, arXiv:2505.05875 [cond-mat.mes-hall].
  44. J. F. Chittock-Wood, R. C. C. Leon, M. A. Fogarty, T. Murphy, S. M. Patomäki, G. A. Oakes, J. Williams, F.-E. von Horstig, N. Johnson, J. Jussot, S. Kubicek, B. Govoreanu, D. F. Wise, M. F. Gonzalez-Zalba, and J. J. L. Morton, Radio-frequency cascade readout and coherent exchange control of spin qubits fabricated using a 300 mm wafer process, arXiv:2408.01241 [cond-mat.mes-hall].
  45. L. H. Pedersen, N. M. Møller, and K. Mølmer, Fidelity of quantum operations, Phys. Lett. A 367, 47 (2007).
  46. T. Jones, A. Brown, I. Bush, and S. C. Benjamin, QuEST and High Performance Simulation of Quantum Computers, Sci. Rep. 9, 10736 (2019).
  47. R. Meister, pyQuEST – A Python interface for the Quantum Exact Simulation Toolkit, 2022, https://github.com/rrmeister/pyQuEST.
  48. A. Richards, University of Oxford Advanced Research Computing, 2015.
  49. S. Birner, T. Zibold, T. Andlauer, T. Kubis, M. Sabathil, A. Trellakis, and P. Vogl, nextnano: General purpose 3-D simulations, IEEE Trans. Electron Devices 54, 2137 (2007).
  50. R. Loudon, One-dimensional hydrogen atom, Proc. R. Soc. A 472, 201505342 (2016).
  51. As a check, this was done to ensure the numerical simulations come to the same value.
  52. See however the approach in Ref. [29], where it is explained that indeed the Coulomb matrix is diagonal if one evaluates integrals only at the grid points, and this is a valid approach in that Coulomb matrix will converge successfully with increasing M.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation