- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

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

Numerical simulation of charged-defect-induced decoherence in conveyor-mode spin qubit shuttling in Si/SiGe

Nils Ciroth1, Arnau Sala1, Ran Xue1, Lasse Ermoneit2, Thomas Koprucki2, Markus Kantner2, and Lars R. Schreiber1,3,*

  • *Contact author: lars.schreiber@physik.rwth-aachen.de
PDF

Phys. Rev. B 114, 105305 – Published 19 August, 2026

DOI: https://doi.org/10.1103/styv-ypg9

Abstract

Recent advances in coherent conveyor-mode spin qubit shuttling are paving the way for large-scale quantum computing platforms with qubit connectivity achieved by spin qubit shuttles. We developed a simulation tool to investigate numerically the impact of device imperfections on the spin coherence of conveyor-mode shuttling in Si/SiGe. We simulate the quantum evolution of a mobile electron spin qubit under the influence of sparse and singly charged point defects placed in the Si/SiGe heterostructure in close proximity to the shuttle lane. We consider different locations of a single charge defect with respect to the center of the shuttle lane, multiple orbital states of the electron in the shuttle with g-factor differences between the orbital levels, and orbital relaxation induced by electron-phonon interaction. Our analysis isolates spin decoherence arising from orbital excitations induced by charged defects in close proximity of the shuttled electron. With this simulation framework, we quantify the impact of individual charged defects on qubit coherence and determine the range of defect densities compatible with high-fidelity conveyor-mode spin shuttling.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (57)

  1. D. P. DiVincenzo, The physical implementation of quantum computation, Fortschr. Phys. 48, 771 (2000).
  2. A. Laucht, F. Hohls, N. Ubbelohde, M. F. Gonzalez-Zalba, D. J. Reilly, S. Stobbe, T. Schröder, P. Scarlino, J. V. Koski, A. Dzurak, C.-H. Yang, J. Yoneda, F. Kuemmeth, H. Bluhm, J. Pla, C. Hill, J. Salfi, A. Oiwa, J. T. Muhonen, E. Verhagen, et al., Roadmap on quantum nanotechnologies, Nanotechnology 32, 162003 (2021).
  3. L. M. K. Vandersypen, H. Bluhm, J. S. Clarke, A. S. Dzurak, R. Ishihara, A. Morello, D. J. Reilly, L. R. Schreiber, and M. Veldhorst, Interfacing spin qubits in quantum dots and donors—hot, dense, and coherent, npj Quantum Inf. 3, 34 (2017).
  4. G. Burkard, T. D. Ladd, A. Pan, J. M. Nichol, and J. R. Petta, Semiconductor spin qubits, Rev. Mod. Phys. 95, 025003 (2023).
  5. J. M. Taylor, H.-A. Engel, W. Dür, A. Yacoby, C. M. Marcus, P. Zoller, and M. D. Lukin, Fault-tolerant architecture for quantum computation using electrically controlled semiconductor spins, Nat. Phys. 1, 177 (2005).
  6. J. M. Boter, J. P. Dehollain, J. P. G. van Dijk, Y. Xu, T. Hensgens, R. Versluis, H. W. L. Naus, J. S. Clarke, M. Veldhorst, F. Sebastiano, and L. M. K. Vandersypen, Spiderweb array: A sparse spin-qubit array, Phys. Rev. Appl. 18, 024053 (2022).
  7. M. Künne, A. Willmes, M. Oberländer, C. Gorjaew, J. D. Teske, H. Bhardwaj, M. Beer, E. Kammerloher, R. Otten, I. Seidler, R. Xue, L. R. Schreiber, and H. Bluhm, The SpinBus architecture for scaling spin qubits with electron shuttling, Nat. Commun. 15, 4977 (2024).
  8. S. B. Bravyi and A. Y. Kitaev, Quantum codes on a lattice with boundary, arXiv:quant-ph/9811052.
  9. R. P. G. McNeil, M. Kataoka, C. J. B. Ford, C. H. W. Barnes, D. Anderson, G. A. C. Jones, I. Farrer, and D. A. Ritchie, On-demand single-electron transfer between distant quantum dots, Nature (London) 477, 439 (2011).
  10. S. Hermelin, S. Takada, M. Yamamoto, S. Tarucha, A. D. Wieck, L. Saminadayar, C. Bäuerle, and T. Meunier, Electrons surfing on a sound wave as a platform for quantum optics with flying electrons, Nature (London) 477, 435 (2011).
  11. B. Jadot, P.-A. Mortemousque, E. Chanrion, V. Thiney, A. Ludwig, A. D. Wieck, M. Urdampilleta, C. Bäuerle, and T. Meunier, Distant spin entanglement via fast and coherent electron shuttling, Nat. Nanotechnol. 16, 570 (2021).
  12. H. Edlbauer, J. Wang, S. Ota, A. Richard, B. Jadot, P.-A. Mortemousque, Y. Okazaki, S. Nakamura, T. Kodera, N.-H. Kaneko, A. Ludwig, A. D. Wieck, M. Urdampilleta, T. Meunier, C. Bäuerle, and S. Takada, In-flight distribution of an electron within a surface acoustic wave, Appl. Phys. Lett. 119, 114004 (2021).
  13. I. Seidler, T. Struck, R. Xue, N. Focke, S. Trellenkamp, H. Bluhm, and L. R. Schreiber, Conveyor-mode single-electron shuttling in Si/SiGe for a scalable quantum computing architecture, npj Quantum Inf. 8, 100 (2022).
  14. V. Langrock, J. A. Krzywda, N. Focke, I. Seidler, L. R. Schreiber, and L. Cywiński, Blueprint of a scalable spin qubit shuttle device for coherent mid-range qubit transfer in disordered Si/SiGe/SiO2, PRX Quantum 4, 020305 (2023).
  15. R. Xue, M. Beer, I. Seidler, S. Humpohl, J.-S. Tu, S. Trellenkamp, T. Struck, H. Bluhm, and L. R. Schreiber, Si/SiGe QuBus for single electron information-processing devices with memory and micron-scale connectivity function, Nat. Commun. 15, 2296 (2024).
  16. M. Beer, R. Xue, L. Deda, S. Trellenkamp, J.-S. Tu, P. Surrey, I. Seidler, H. Bluhm, and L. R. Schreiber, Conveyor mode electron shuttling through a T-junction in Si/SiGe, arXiv:2601.03942.
  17. W. Langheinrich, V. Brackmann, M. Friedrich, M. Wislicenus, P. Muster, S. Pregl, F. Reichmann, N. D. Komerički, D. Bougeard, T. Huckemann, L. R. Schreiber, and H. Bluhm, Fabrication of single-electron shuttling channels in a silicon CMOS fab using high-throughput electron beam lithography, Proc. SPIE 13787, 125 (2025).
  18. T. Struck, M. Volmer, L. Visser, T. Offermann, R. Xue, J.-S. Tu, S. Trellenkamp, L. Cywiński, H. Bluhm, and L. R. Schreiber, Spin-EPR-pair separation by conveyor-mode single electron shuttling in Si/SiGe, Nat. Commun. 15, 1325 (2024).
  19. M. De Smet, Y. Matsumoto, A.-M. J. Zwerver, L. Tryputen, S. L. de Snoo, S. V. Amitonov, S. R. Katiraee-Far, A. Sammak, N. Samkharadze, Ö. Gül, R. N. M. Wasserman, E. Greplová, M. Rimbach-Russ, G. Scappucci, and L. M. K. Vandersypen, High-fidelity single-spin shuttling in silicon, Nat. Nanotechnol. 20, 866 (2025).
  20. Y. Matsumoto, M. De Smet, L. Tryputen, S. L. d. Snoo, S. V. Amitonov, A. Sammak, M. Rimbach-Russ, G. Scappucci, and L. M. K. Vandersypen, Two-qubit logic and teleportation with mobile spin qubits in silicon, Nature (London) 653, 391 (2026).
  21. F. Ginzel, M. Fellner, C. Ertler, L. R. Schreiber, H. Bluhm, and W. Lechner, Scalable parity architecture with a shuttling-based spin qubit processor, Phys. Rev. B 110, 075302 (2024).
  22. S. M. Patomäki, M. F. Gonzalez-Zalba, M. A. Fogarty, Z. Cai, S. C. Benjamin, and J. J. L. Morton, Pipeline quantum processor architecture for silicon spin qubits, npj Quantum Inf. 10, 31 (2024).
  23. A. Siegel, Z. Cai, H. Jnane, B. Koczor, S. Pexton, A. Strikis, and S. Benjamin, Snakes on a plane: Mobile, low dimensional logical qubits on a 2D surface, PRX Quantum 7, 010339 (2026).
  24. Q.-T. Zhao, Y. Han, H.-C. Han, L. R. Schreiber, T.-E. Lee, H.-L. Chiang, I. Radu, C. Enz, D. Grützmacher, C. Stampfer, S. Takagi, and J. Knoch, Ultra-low-power cryogenic complementary metal oxide semiconductor technology, Nat. Rev. Electr. Eng. 2, 277 (2025).
  25. N. W. Hendrickx, L. Massai, M. Mergenthaler, F. J. Schupp, S. Paredes, S. W. Bedell, G. Salis, and A. Fuhrer, Sweet-spot operation of a germanium hole spin qubit with highly anisotropic noise sensitivity, Nat. Mater. 23, 920 (2024).
  26. I. Seidler, B. Hetényi, L. Sommer, L. Massai, K. Tsoukalas, E. G. Kelly, A. Orekhov, M. Aldeghi, S. W. Bedell, S. Paredes, F. J. Schupp, M. Mergenthaler, G. Salis, A. Fuhrer, and P. Harvey-Collard, Spatial uniformity of g-tensor and spin-orbit interaction in germanium hole spin qubits, arXiv:2510.03125.
  27. J. Rooney, Z. Luo, L. E. A. Stehouwer, G. Scappucci, M. Veldhorst, and H.-W. Jiang, Gate modulation of the hole singlet-triplet qubit frequency in germanium, npj Quantum Inf. 11, 15 (2025).
  28. B. Paquelet Wuetz, M. P. Losert, S. Koelling, L. E. A. Stehouwer, A.-M. J. Zwerver, S. G. J. Philips, M. T. Mądzik, X. Xue, G. Zheng, M. Lodari, S. V. Amitonov, N. Samkharadze, A. Sammak, L. M. K. Vandersypen, R. Rahman, S. N. Coppersmith, O. Moutanabbir, M. Friesen, and G. Scappucci, Atomic fluctuations lifting the energy degeneracy in Si/SiGe quantum dots, Nat. Commun. 13, 7730 (2022).
  29. J. Klos, J. Tröger, J. Keutgen, M. P. Losert, N. V. Abrosimov, J. Knoch, H. Bracht, S. N. Coppersmith, M. Friesen, O. Cojocaru-Mirédin, L. R. Schreiber, and D. Bougeard, Atomistic compositional details and their importance for spin qubits in isotope-purified silicon quantum wells, Adv. Sci. 11, 2407442 (2024).
  30. M. P. Losert, M. A. Eriksson, R. Joynt, R. Rahman, G. Scappucci, S. N. Coppersmith, and M. Friesen, Practical strategies for enhancing the valley splitting in Si/SiGe quantum wells, Phys. Rev. B 108, 125405 (2023).
  31. A. Thayil, L. Ermoneit, and M. Kantner, Theory of valley splitting in Si/SiGe spin-qubits: Interplay of strain, resonances and random alloy disorder, Phys. Rev. B 112, 115303 (2025).
  32. M. Volmer, T. Struck, A. Sala, B. Chen, M. Oberländer, T. Offermann, R. Xue, L. Visser, J.-S. Tu, S. Trellenkamp, Ł . Cywiński, H. Bluhm, and L. R. Schreiber, Mapping of valley splitting by conveyor-mode spin-coherent electron shuttling, npj Quantum Inf. 10, 61 (2024).
  33. M. Volmer, T. Struck, J.-S. Tu, S. Trellenkamp, D. D. Esposti, G. Scappucci, Ł. Cywiński, H. Bluhm, and L. R. Schreiber, Impact of the local valley splitting on the coherence of conveyor-belt spin shuttling in Si28/SiGe, Nat. Commun. 17, 5448 (2026).
  34. M. P. Losert, M. Oberländer, J. D. Teske, M. Volmer, L. R. Schreiber, H. Bluhm, S. N. Coppersmith, and M. Friesen, Strategies for enhancing spin-shuttling fidelities in Si/SiGe quantum wells with random-alloy disorder, PRX Quantum 5, 040322 (2024).
  35. A. David, A. M. Pazhedath, L. R. Schreiber, T. Calarco, H. Bluhm, and F. Motzoi, Long distance spin shuttling enabled by few-parameter velocity optimization, arXiv:2409.07600.
  36. J. Klos, F. Hassler, P. Cerfontaine, H. Bluhm, and L. R. Schreiber, Calculation of tunnel couplings in open gate-defined disordered quantum dot systems, Phys. Rev. B 98, 155320 (2018).
  37. I. Seidler, M. Neul, E. Kammerloher, M. Künne, A. Schmidbauer, L. K. Diebel, A. Ludwig, J. Ritzmann, A. D. Wieck, D. Bougeard, H. Bluhm, and L. R. Schreiber, Tailoring potentials by simulation-aided design of gate layouts for spin-qubit applications, Phys. Rev. Appl. 20, 044058 (2023).
  38. C. Corley-Wiciak, M. H. Zoellner, I. Zaitsev, K. Anand, E. Zatterin, Y. Yamamoto, A. A. Corley-Wiciak, F. Reichmann, W. Langheinrich, L. R. Schreiber, C. L. Manganelli, M. Virgilio, C. Richter, and G. Capellini, Lattice deformation at submicron scale: X-ray nanobeam measurements of elastic strain in electron shuttling devices, Phys. Rev. Appl. 20, 024056 (2023).
  39. Y. Liu, K. P. Gradwohl, C. H. Lu, T. Remmele, Y. Yamamoto, M. H. Zoellner, T. Schroeder, T. Boeck, H. Amari, C. Richter, and M. Albrecht, Role of critical thickness in SiGe/Si/SiGe heterostructure design for qubits, J. Appl. Phys. 132, 085302 (2022).
  40. B. Buonacorsi, B. Shaw, and J. Baugh, Simulated coherent electron shuttling in silicon quantum dots, Phys. Rev. B 102, 125406 (2020).
  41. M. Jeon, S. C. Benjamin, and A. J. Fisher, Robustness of electron charge shuttling: Architectures, pulses, charge defects, and noise thresholds, Phys. Rev. B 111, 195302 (2025).
  42. J. J. Turner, C. W. Binder, G. Burkard, and A. J. Fisher, Modelling the impact of device imperfections on electron shuttling in SiMOS devices, PRX Quantum (2026).
  43. N. E. Penthorn, J. S. Schoenfield, L. F. Edge, and H.W. Jiang, Direct measurement of electron intervalley relaxation in a Si/SiGe quantum dot, Phys. Rev. Appl. 14, 054015 (2020).
  44. F. Schäffler, High-mobility Si and Ge structures, Semicond. Sci. Technol. 12, 1515 (1997).
  45. E. Kawakami, P. Scarlino, D. R. Ward, F. R. Braakman, D. E. Savage, M. G. Lagally, M. Friesen, S. N. Coppersmith, M. A. Eriksson, and L. M. K. Vandersypen, Electrical control of a long-lived spin qubit in a Si/SiGe quantum dot, Nat. Nanotechnol. 9, 666 (2014).
  46. A. Corna, L. Bourdet, R. Maurand, A. Crippa, D. Kotekar-Patil, H. Bohuslavskyi, R. Laviéville, L. Hutin, S. Barraud, X. Jehl, M. Vinet, S. De Franceschi, Y.-M. Niquet, and M. Sanquer, Electrically driven electron spin resonance mediated by spin–valley–orbit coupling in a silicon quantum dot, npj Quantum Inf. 4, 6 (2018).
  47. C. Cohen-Tannoudji, B. Diu, and F. Laloë, Quantum Mechanics, Volume 2: Angular Momentum, Spin, and Approximation Methods (John Wiley & Sons, New York, 1977).
  48. J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics, 3rd ed. (Cambridge University Press, Cambridge, 2020).
  49. A. L. Saraiva, M. J. Calderón, R. B. Capaz, X. Hu, S. Das Sarma, and B. Koiller, Intervalley coupling for interface-bound electrons in silicon: An effective mass study, Phys. Rev. B 84, 155320 (2011).
  50. C. Tahan and R. Joynt, Relaxation of excited spin, orbital, and valley qubit states in ideal silicon quantum dots, Phys. Rev. B 89, 075302 (2014).
  51. M. Raith, P. Stano, and J. Fabian, Theory of single electron spin relaxation in Si/SiGe lateral coupled quantum dots, Phys. Rev. B 83, 195318 (2011).
  52. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002).
  53. I. Rahlff, C. Richter, M. Schmidbauer, M. Oezkent, T. Remmele, M. Hanke, L. R. Schreiber, D. Dütz, S. Umezawa, M. Albrecht, Y.-M. Niquet, T. Salamone, B. M. Diaz, T. Schroeder, J. Martin, and K.-P. Gradwohl, Sharp periodic Ge concentration modulations beyond the conduction band valley wavevector k0 in nuclear spin-free Si quantum wells, arXiv:2605.31358.
  54. N. Ciroth, A. Sala, R. Xue, L. Ermoneit, T. Koprucki, M. Kantner, and L. R. Schreiber, Numerical simulation of coherent spin-shuttling in a qubus with charged defects [Data set], Zenodo, 2025, https://doi.org/10.5281/zenodo.17877238.
  55. T. Inui, Y. Tanabe, and Y. Onodera, Group Theory and Its Applications in Physics (Springer, Berlin, 1990), Vol. 78.
  56. S. Blanes, F. Casas, J. A. Oteo, and J. Ros, The Magnus expansion and some of its applications, Phys. Rep. 470, 151 (2009).
  57. W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math. 7, 649 (1954).

Outline

Information

Phys. Rev. B 114, 105305– Published 19 August, 2026
  • Received 10 December 2025
  • Revised 12 June 2026
  • Accepted 20 July 2026
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