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Omnidirectional Shuttling to Avoid Valley Excitations in Si/SiGe Quantum Wells

Róbert Németh1,2, Vatsal K. Bandaru2,*, Pedro Alves2,*, Emma Brann2, Owen M. Eskandari2, Hudaiba Soomro2, Avani Vivrekar2, M.A. Eriksson2, Merritt P. Losert2 et al.

Mark Friesen2,†

  • *These authors contributed equally.
  • †Contact author: friesen@physics.wisc.edu
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PRX Quantum 7, 010336 – Published 20 February, 2026

DOI: https://doi.org/10.1103/615j-xjyh

Abstract

Conveyor-mode shuttling is a key approach for implementing intermediate-range coupling between electron-spin qubits in quantum dots. Initial implementations are encouraging; however, long shuttling trajectories are guaranteed to encounter regions of low conduction-band valley-energy splittings, due to the presence of random-alloy disorder in Si/SiGe quantum wells. Here, we theoretically explore two schemes for avoiding valley-state excitations at these valley-splitting minima, by allowing the electrons to detour around them. A multichannel shuttling scheme allows electrons to tunnel between parallel channels, while a two-dimensional (2D) shuttler provides full omnidirectional control. Using simulations, we estimate shuttling fidelities in these two schemes, obtaining a clear preference for the 2D shuttler. Based on such encouraging results, we propose a modular qubit architecture based on 2D shuttling, which enables all-to-all connectivity within qubit plaquettes and high-fidelity communication between different plaquettes.

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Popular Summary

Direct communication between quantum-dot spin qubits in silicon is limited by the extremely short range of the fundamental coupling mechanism between electron spins: the exchange interaction. Conveyor-mode shuttling has emerged as a leading scheme to enable spin-based information transfer over length scales of 1–10 μm. However, alloy disorder in the Si/SiGe quantum well leads to unavoidable excitations of the electrons during the shuttling process, ultimately limiting the transfer fidelity. Here, we investigate shuttling schemes beyond the conventional one-dimensional (1D) approach, which allow electrons to detour around the danger zones. We show that fully 2D operation enables huge improvements for the shuttling fidelity. Moreover, 2D shuttling architectures provide a potential solution to the connectivity problem, which is a key bottleneck for large-scale, fault-tolerant quantum computing applications based on inherently short-range interactions.

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References (56)

  1. 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).
  2. T. Fujita, T. A. Baart, C. Reichl, W. Wegscheider, and L. M. K. Vandersypen, Coherent shuttle of electron-spin states, Npj Quantum Inf. 3, 22 (2017).
  3. A. R. Mills, D. M. Zajac, M. J. Gullans, F. J. Schupp, T. M. Hazard, and J. R. Petta, Shuttling a single charge across a one-dimensional array of silicon quantum dots, Nat. Commun. 10, 1063 (2019).
  4. F. Ginzel, A. R. Mills, J. R. Petta, and G. Burkard, Spin shuttling in a silicon double quantum dot, Phys. Rev. B 102, 195418 (2020).
  5. B. Buonacorsi, B. Shaw, and J. Baugh, Simulated coherent electron shuttling in silicon quantum dots, Phys. Rev. B 102, 125406 (2020).
  6. J. Yoneda, W. Huang, M. Feng, C. H. Yang, K. W. Chan, T. Tanttu, W. Gilbert, R. Leon, F. Hudson, K. Itoh et al., Coherent spin qubit transport in silicon, Nat. Commun. 12, 4114 (2021).
  7. 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).
  8. J. A. Krzywda and L. Cywiński, Interplay of charge noise and coupling to phonons in adiabatic electron transfer between quantum dots, Phys. Rev. B 104, 075439 (2021).
  9. A. Noiri, K. Takeda, T. Nakajima, T. Kobayashi, A. Sammak, G. Scappucci, and S. Tarucha, A shuttling-based two-qubit logic gate for linking distant silicon quantum processors, Nat. Commun. 13, 5740 (2022).
  10. J. M. Boter, J. P. Dehollain, J. P. G. Van Dijk, Y. Xu, T. Hensgens, R. Versluis, Henricus W. L. Naus, J. S. Clarke, M. Veldhorst, F. Sebastiano, and Lieven M. K. Vandersypen, Spiderweb array: A sparse spin-qubit array, Phys. Rev. Appl. 18, 024053 (2022).
  11. 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).
  12. A. M. J. Zwerver, S. V. Amitonov, S. L. de Snoo, M. T. Mądzik, M. Rimbach-Russ, A. Sammak, G. Scappucci, and L. M. K. Vandersypen, Shuttling an electron spin through a silicon quantum dot array, PRX Quantum 4, 030303 (2023).
  13. N. Sato, T. Sekiguchi, T. Utsugi, and H. Mizuno, Generating shuttling procedures for constrained silicon quantum dot array, IEEE Trans. Quantum Eng. 6, 1 (2025).
  14. 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).
  15. J. M. Taylor, H. A. Engel, W. Dur, 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).
  16. 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).
  17. L. Ermoneit, B. Schmidt, T. Koprucki, J. Fuhrmann, T. Breiten, A. Sala, N. Ciroth, R. Xue, L. R. Schreiber, and M. Kantner, Optimal control of conveyor-mode spin-qubit shuttling in a Si/SiGe quantum bus in the presence of charged defects, WIAS Preprint 3082 (2023).
  18. 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).
  19. T. Struck, M. Volmer, L. Visser, T. Offermann, R. Xue, J.-S. Tu, S. Trellenkamp, Ł. 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).
  20. 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).
  21. 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).
  22. A. S. Mokeev, Y.-N. Zhang, and V. V. Dobrovitski, Modeling of decoherence and fidelity enhancement during transport of entangled qubits, arXiv:2409.04404.
  23. 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).
  24. Y. Oda, M. P. Losert, and J. P. Kestner, Suppressing Si valley excitation and valley-induced spin dephasing for long-distance shuttling, Phys. Rev. Lett. 136, 020802 (2026).
  25. M. Friesen, M. A. Eriksson, and S. N. Coppersmith, Magnetic field dependence of valley splitting in realistic Si/SiGe quantum wells, Appl. Phys. Lett. 89, 202106 (2006).
  26. M. Friesen, S. Chutia, C. Tahan, and S. N. Coppersmith, Valley splitting theory of SiGe/Si/SiGe quantum wells, Phys. Rev. B 75, 115318 (2007).
  27. N. Kharche, M. Prada, T. B. Boykin, and G. Klimeck, Valley splitting in strained silicon quantum wells modeled with 2∘ miscuts, step disorder, and alloy disorder, Appl. Phys. Lett. 90, 092109 (2007).
  28. D. Culcer, X. Hu, and S. Das Sarma, Interface roughness, valley-orbit coupling, and valley manipulation in quantum dots, Phys. Rev. B 82, 205315 (2010).
  29. J. K. Gamble, M. A. Eriksson, S. N. Coppersmith, and M. Friesen, Disorder-induced valley-orbit hybrid states in Si quantum dots, Phys. Rev. B 88, 035310 (2013).
  30. P. Boross, G. Széchenyi, D. Culcer, and A. Pályi, Control of valley dynamics in silicon quantum dots in the presence of an interface step, Phys. Rev. B 94, 035438 (2016).
  31. J. C. Abadillo-Uriel, B. Thorgrimsson, D. Kim, L. W. Smith, C. B. Simmons, D. R. Ward, R. H. Foote, J. Corrigan, D. E. Savage, M. G. Lagally, M. J. Calderón, S. N. Coppersmith, M. A. Eriksson, and M. Friesen, Signatures of atomic-scale structure in the energy dispersion and coherence of a Si quantum-dot qubit, Phys. Rev. B 98, 165438 (2018).
  32. B. Tariq and X. Hu, Effects of interface steps on the valley-orbit coupling in a Si/SiGe quantum dot, Phys. Rev. B 100, 125309 (2019).
  33. A. Hosseinkhani and G. Burkard, Electromagnetic control of valley splitting in ideal and disordered Si quantum dots, Phys. Rev. Res. 2, 043180 (2020).
  34. J. P. Dodson, H. E. Ercan, J. Corrigan, M. P. Losert, N. Holman, T. McJunkin, L. F. Edge, M. Friesen, S. N. Coppersmith, and M. A. Eriksson, How valley-orbit states in silicon quantum dots probe quantum well interfaces, Phys. Rev. Lett. 128, 146802 (2022).
  35. 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).
  36. 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).
  37. J. R. F. Lima and G. Burkard, Interface and electromagnetic effects in the valley splitting of Si quantum dots, Mater. Quantum Technol. 3, 025004 (2023).
  38. L. F. Peña, J. C. Koepke, J. H. Dycus, A. Mounce, A. D. Baczewski, N. T. Jacobson, and E. Bussmann, Modeling Si/SiGe quantum dot variability induced by interface disorder reconstructed from multiperspective microscopy, Npj Quantum Inf. 10, 33 (2024).
  39. 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).
  40. W. Ha, S. D. Ha, M. D. Choi, Y. Tang, A. E. Schmitz, M. P. Levendorf, K. Lee, J. M. Chappell, T. S. Adams, D. R. Hulbert, E. Acuna, R. S. Noah, J. W. Matten, M. P. Jura, J. A. Wright, M. T. Rakher, and M. G. Borselli, A flexible design platform for Si/SiGe exchange-only qubits with low disorder, Nano Lett. 22, 1443 (2022).
  41. E. Acuna, J. D. Broz, K. Shyamsundar, A. B. Mei, C. P. Feeney, V. Smetanka, T. Davis, K. Lee, M. D. Choi, B. Boyd, J. Suh, W. Ha, C. Jennings, A. S. Pan, D. S. Sanchez, M. D. Reed, and J. R. Petta, Coherent control of a triangular exchange-only spin qubit, Phys. Rev. Appl. 22, 044057 (2024).
  42. H. C. George et al., 12-spin-qubit arrays fabricated on a 300 mm semiconductor manufacturing line, Nano Lett. 25, 793 (2025).
  43. J. C. Marcks, E. Eagen, E. C. Brann, M. P. Losert, T. Oh, J. Reily, C. S. Wang, D. Keith, F. A. Mohiyaddin, F. Luthi, M. J. Curry, J. Zhang, F. J. Heremans, M. Friesen, and M. A. Eriksson, Valley splitting correlations across a silicon quantum well containing germanium, Nat. Commun. 16, 11381 (2025).
  44. Y. Ban, X. Chen, E. Y. Sherman, and J. G. Muga, Fast and robust spin manipulation in a quantum dot by electric fields, Phys. Rev. Lett. 109, 206602 (2012).
  45. D. V. Khomitsky, L. V. Gulyaev, and E. Y. Sherman, Spin dynamics in a strongly driven system: Very slow Rabi oscillations, Phys. Rev. B 85, 125312 (2012).
  46. Y. Ban and X. Chen, Counter-diabatic driving for fast spin control in a two-electron double quantum dot, Sci. Rep. 4, 6258 (2014).
  47. D. Degli Esposti, L. E. A. Stehouwer, Ö. Gül, N. Samkharadze, C. Déprez, M. Meyer, I. N. Meijer, L. Tryputen, S. Karwal, M. Botifoll, J. Arbiol, S. V. Amitonov, L. M. K. Vandersypen, A. Sammak, M. Veldhorst, and G. Scappucci, Low disorder and high valley splitting in silicon, Npj Quantum Inf. 10, 32 (2024).
  48. 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).
  49. G. Burkard, T. D. Ladd, A. Pan, J. M. Nichol, and J. R. Petta, Semiconductor spin qubits, Rev. Mod. Phys. 95, 025003 (2023).
  50. S. Bravyi, A. W. Cross, J. M. Gambetta, D. Maslov, P. Rall, and T. J. Yoder, High-threshold and low-overhead fault-tolerant quantum memory, Nature 627, 778 (2024).
  51. R. Németh, V. K. Bandaru, P. Alves, E. Brann, O. M. Eskandari, H. Soomro, A. Vivrekar, M. A. Eriksson, M. P. Losert, and M. Friesen, Figures, codes, and data used in the preparation of the paper, “Omnidirectional shuttling to avoid valley excitations in Si/SiGe quantum wells” (2026), https://doi.org/10.5281/zenodo.18225182, arxiv:2412.09574
  52. S. Neyens, O. Zietz, T. Watson, F. Luthi, A. Nethwewala, H. George, E. Henry, M. Islam, A. Wagner, F. Borjans, E. Connors, J. Corrigan, M. Curry, D. Keith, R. Kotlyar, L. Lampert, M. Mądzik, K. Millard, F. Mohiyaddin, and J. Clarke, Probing single electrons across 300-mm spin qubit wafers, Nature 629, 80 (2024).
  53. J. Johansson, P. Nation, and F. Nori, Qutip: An open-source python framework for the dynamics of open quantum systems, Comput. Phys. Commun. 183, 1760 (2012).
  54. Center for High Throughput Computing (2006), https://doi.org/10.21231/GNT1-HW21.
  55. A. Hosseinkhani and G. Burkard, Relaxation of single-electron spin qubits in silicon in the presence of interface steps, Phys. Rev. B 104, 085309 (2021).
  56. P. Huang and X. Hu, Electron spin relaxation due to charge noise, Phys. Rev. B 89, 195302 (2014).

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PRX Quantum 7, 010336– Published 20 February, 2026
  • Received 11 June 2025
  • Revised 25 October 2025
  • Accepted 2 January 2026
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