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Large spin-shuttling oscillations enabling high-fidelity single-qubit gates

Akshay Menon Pazhedath1,2,*, Alessandro David1, Max Oberländer3, Matthias M. Müller1, Tommaso Calarco1,2,4, Hendrik Bluhm3,5, and Felix Motzoi1,2,†

  • *Contact author: a.pazhedath@fz-juelich.de
  • †Contact author: f.motzoi@fz-juelich.de

Phys. Rev. Applied 24, 034029 – Published 11 September, 2025

DOI: https://doi.org/10.1103/4lky-413f

Abstract

There have been impressive breakthroughs in semiconductor quantum dots in recent years, with single- and two-qubit gate fidelities matching other leading platforms and scalability still remaining a relative strength; however, due to qubit wiring considerations, mobile electron architectures have been proposed to facilitate upward scaling, and this opens the possibility of enlarging the motional amplitude for electric-dipole spin resonance (EDSR)-based qubit manipulation. In this work, we examine and demonstrate the possibility of significantly outperforming static-EDSR-type single-qubit pulsing by taking advantage of greater spatial mobility to achieve higher Rabi frequencies and reduce the effect of charge noise. Our theoretical results indicate that fidelities are ultimately bottlenecked by spin-valley physics, which can be suppressed through the use of quantum optimal control. We demonstrate that, across different potential regimes and competing physical models, shuttling-based single-qubit gates retain significant advantages over existing alternatives.

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References (56)

  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. D. Loss and D. P. DiVincenzo, Quantum computation with quantum dots, Phys. Rev. A 57, 120 (1998).
  3. B. Klemt, V. Elhomsy, M. Nurizzo, P. Hamonic, B. Martinez, B. Cardoso Paz, C. Spence, M. C. Dartiailh, B. Jadot, E. Chanrion, V. Thiney, R. Lethiecq, B. Bertrand, H. Niebojewski, C. Bäuerle, M. Vinet, Y.-M. Niquet, T. Meunier, and M. Urdampilleta, Electrical manipulation of a single electron spin in CMOS using a micromagnet and spin-valley coupling, npj Quantum Inf. 9, 1 (2023).
  4. A. M. J. Zwerver, et al., Qubits made by advanced semiconductor manufacturing, Nat. Electron. 5, 184 (2022).
  5. C. B. Simmons, J. R. Prance, B. J. Van Bael, T. S. Koh, Z. Shi, D. E. Savage, M. G. Lagally, R. Joynt, M. Friesen, S. N. Coppersmith, and M. A. Eriksson, Tunable spin loading and T1 of a silicon spin qubit measured by single-shot readout, Phys. Rev. Lett. 106, 156804 (2011).
  6. 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).
  7. R. Neumann and L. R. Schreiber, Simulation of micro-magnet stray-field dynamics for spin qubit manipulation, J. Appl. Phys. 117, 193903 (2015).
  8. 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).
  9. 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).
  10. 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).
  11. 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).
  12. 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, 1 (2017).
  13. J. M. Boter, J. P. Dehollain, J. P. Van Dijk, Y. Xu, T. Hensgens, R. Versluis, H. W. Naus, J. S. Clarke, M. Veldhorst, F. Sebastiano, and L. M. Vandersypen, Spiderweb array: A sparse spin-qubit array, Phys. Rev. Appl. 18, 024053 (2022).
  14. 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).
  15. 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).
  16. Y. Matsumoto, M. D. Smet, L. Tryputen, S. L. de 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, ArXiv:2503.15434.
  17. 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, 1 (2022).
  18. V. Langrock, J. A. Krzywda, N. Focke, I. Seidler, L. R. Schreiber, and Ł. 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).
  19. 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).
  20. 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).
  21. K. C. Nowack, F. H. L. Koppens, Yu. V. Nazarov, and L. M. K. Vandersypen, Coherent control of a single electron spin with electric fields, Science 318, 1430 (2007).
  22. M. Pioro-Ladrière, T. Obata, Y. Tokura, Y.-S. Shin, T. Kubo, K. Yoshida, T. Taniyama, and S. Tarucha, Electrically driven single-electron spin resonance in a slanting Zeeman field, Nat. Phys. 4, 776 (2008).
  23. J. Yoneda, T. Otsuka, T. Nakajima, T. Takakura, T. Obata, M. Pioro-Ladrière, H. Lu, C. J. Palmstrøm, A. C. Gossard, and S. Tarucha, Fast electrical control of single electron spins in quantum dots with vanishing influence from nuclear spins, Phys. Rev. Lett. 113, 267601 (2014).
  24. V. N. Golovach, M. Borhani, and D. Loss, Electric-dipole-induced spin resonance in quantum dots, Phys. Rev. B 74, 165319 (2006).
  25. J. Yoneda, T. Otsuka, T. Takakura, M. Pioro-Ladrière, R. Brunner, H. Lu, T. Nakajima, T. Obata, A. Noiri, C. J. Palmstrøm, A. C. Gossard, and S. Tarucha, Robust micromagnet design for fast electrical manipulations of single spins in quantum dots, Appl. Phys. Express 8, 084401 (2015).
  26. N. I. Dumoulin Stuyck, F. A. Mohiyaddin, R. Li, M. Heyns, B. Govoreanu, and I. P. Radu, Low dephasing and robust micromagnet designs for silicon spin qubits, Appl. Phys. Lett. 119, 094001 (2021).
  27. F. A. Zwanenburg, A. S. Dzurak, A. Morello, M. Y. Simmons, L. C. L. Hollenberg, G. Klimeck, S. Rogge, S. N. Coppersmith, and M. A. Eriksson, Silicon quantum electronics, Rev. Mod. Phys. 85, 961 (2013).
  28. M. Veldhorst, R. Ruskov, C. H. Yang, J. C. C. Hwang, F. E. Hudson, M. E. Flatté, C. Tahan, K. M. Itoh, A. Morello, and A. S. Dzurak, Spin-orbit coupling and operation of multivalley spin qubits, Phys. Rev. B 92, 201401 (2015).
  29. R. Ferdous, E. Kawakami, P. Scarlino, M. P. Nowak, D. R. Ward, D. E. Savage, M. G. Lagally, S. N. Coppersmith, M. Friesen, M. A. Eriksson, L. M. K. Vandersypen, and R. Rahman, Valley dependent anisotropic spin splitting in silicon quantum dots, npj Quantum Inf. 4, 1 (2018).
  30. R. Ruskov, M. Veldhorst, A. S. Dzurak, and C. Tahan, Electron g-factor of valley states in realistic silicon quantum dots, Phys. Rev. B 98, 245424 (2018).
  31. B. P. 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).
  32. M. Friesen, S. Chutia, C. Tahan, and S. N. Coppersmith, Valley splitting theory of {Si}{Ge}/{Si}/{Si}{Ge} quantum wells, Phys. Rev. B 75, 115318 (2007).
  33. M. P. Losert, M. Oberländer, J. D. Teske, M. Volmer, L. R. Schreiber, H. Bluhm, S. Coppersmith, and M. Friesen, Strategies for enhancing spin-shuttling fidelities in Si/SiGe quantum wells with random-alloy disorder, PRX Quantum 5, 040322 (2024).
  34. J. R. F. Lima and G. Burkard, Partial Landau-Zener transitions and applications to qubit shuttling, Phys. Rev. B 111, 235439 (2025).
  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. Y. Oda, M. P. Losert, and J. P. Kestner, Suppressing Si valley excitation and valley-induced spin dephasing for long-distance shuttling, ArXiv:2411.11695.
  37. C. V. Meinersen, D. Fernandez-Fernandez, G. Platero, and M. Rimbach-Russ, Unifying adiabatic state-transfer protocols with (α, β)-hypergeometries, ArXiv:2504.08031.
  38. M. J. Rančić and G. Burkard, Electric dipole spin resonance in systems with a valley-dependent g factor, Phys. Rev. B 93, 205433 (2016).
  39. N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbrüggen, and S. J. Glaser, Optimal control of coupled spin dynamics: Design of NMR pulse sequences by gradient ascent algorithms, J. Magn. Reson. 172, 296 (2005).
  40. J. Bradbury, R. Frostig, P. Hawkins, M. J. Johnson, C. Leary, D. Maclaurin, G. Necula, A. Paszke, J. VanderPlas, S. Wanderman-Milne, and Q. Zhang, JAX: Composable transformations of Python+NumPy programs, 2018, https://github.com/google/jax.
  41. P. Virtanen, et al., SciPy 1.0: Fundamental algorithms for scientific computing in Python, Nat. Methods 17, 261 (2020).
  42. F. Motzoi, J. M. Gambetta, S. T. Merkel, and F. K. Wilhelm, Optimal control methods for rapidly time-varying Hamiltonians, Phys. Rev. A 84, 022307 (2011).
  43. M. A. Nielsen, A simple formula for the average gate fidelity of a quantum dynamical operation, Phys. Lett. A 303, 249 (2002).
  44. S. Sheldon, L. S. Bishop, E. Magesan, S. Filipp, J. M. Chow, and J. M. Gambetta, Characterizing errors on qubit operations via iterative randomized benchmarking, Phys. Rev. A 93, 012301 (2016).
  45. The static dot is examined using the same physical model as that used for the electron shuttler, and the valley splitting is an order of magnitude less (around 50μeV) than the experimental setting (around 140μeV), where 99.9% fidelity gates where demonstrated. The impact of valley phases for the static-dot case might limit the fidelities in the simulation as compared with the experimental result. In any case, the optimized pulses perform close to the experimentally observed fidelity. The observation about shuttling performing better in terms of charge noise remains unaffected.
  46. R. Hanson, L. P. Kouwenhoven, J. R. Petta, S. Tarucha, and L. M. K. Vandersypen, Spins in few-electron quantum dots, Rev. Mod. Phys. 79, 1217 (2007).
  47. S. N. Shevchenko, S. Ashhab, and F. Nori, Landau–Zener–Stückelberg interferometry, Phys. Rep. 492, 1 (2010).
  48. R. Garnett, Bayesian Optimization (Cambridge University Press, Cambridge, UK, 2023).
  49. T. Head, M. Kumar, H. Nahrstaedt, G. Louppe, and I. Shcherbatyi, Scikit-optimize/scikit-optimize, Zenodo, 2021, https://doi.org/10.5281/zenodo.5565057.
  50. 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).
  51. 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).
  52. R. Raussendorf and J. Harrington, Fault-tolerant quantum computation with high threshold in two dimensions, Phys. Rev. Lett. 98, 190504 (2007).
  53. M. Rossignolo, T. Reisser, A. Marshall, P. Rembold, A. Pagano, P. J. Vetter, R. S. Said, M. M. Müller, F. Motzoi, T. Calarco, F. Jelezko, and S. Montangero, QuOCS: The quantum optimal control suite, Comput. Phys. Commun. 291, 108782 (2023).
  54. S. Fauquenot, A. Sarkar, and S. Feld, Open and closed loop approaches for energy efficient quantum optimal control, Adv. Quantum Technol. (2025).
  55. L. Viola and S. Lloyd, Dynamical suppression of decoherence in two-state quantum systems, Phys. Rev. A 58, 2733 (1998).
  56. Data repository: https://doi.org/10.5281/zenodo.16783697.

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