Bravyi, S. et al. High-threshold and low-overhead fault-tolerant quantum memory. Nature 627, 778–782 (2024).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Xu, Q. et al. Constant-overhead fault-tolerant quantum computation with reconfigurable atom arrays. Nat. Phys. 20, 1084–1090 (2024).

Article 
CAS 

Google Scholar
 

Goto, H. Many-hypercube codes: high-rate quantum error-correcting codes for high-performance fault-tolerant quantum computing. Sci. Adv. 10, eadp6388 (2024).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Pino, J. M. et al. Demonstration of the trapped-ion quantum CCD computer architecture. Nature 592, 209–213 (2021).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Sterk, J. D. et al. Closed-loop optimization of fast trapped-ion shuttling with sub-quanta excitation. npj Quantum Inf. 8, 68 (2022).

Article 
ADS 

Google Scholar
 

Bluvstein, D. et al. A quantum processor based on coherent transport of entangled atom arrays. Nature 604, 451–456 (2022).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Bluvstein, D. et al. Logical quantum processor based on reconfigurable atom arrays. Nature 626, 58–65 (2024).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Struck, T. et al. Spin-EPR-pair separation by conveyor-mode single electron shuttling in Si/SiGe. Nat. Commun. 15, 1325 (2024).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

De Smet, M. et al. High-fidelity single-spin shuttling in silicon. Nat. Nanotechnol. 20, 866–872 (2025).

Article 
ADS 
PubMed 
PubMed Central 

Google Scholar
 

Vandersypen, L. M. K. & Eriksson, M. A. Quantum computing with semiconductor spins. Phys. Today 72, 38–45 (2019).

Article 
CAS 

Google Scholar
 

Veldhorst, M. et al. An addressable quantum dot qubit with fault-tolerant control-fidelity. Nat. Nanotechnol. 9, 981–985 (2014).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Yoneda, J. et al. A quantum-dot spin qubit with coherence limited by charge noise and fidelity higher than 99.9%. Nat. Nanotechnol. 13, 102–106 (2018).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Yang, C. H. et al. Silicon qubit fidelities approaching incoherent noise limits via pulse engineering. Nat. Electron. 2, 151–158 (2019).

Article 

Google Scholar
 

Lawrie, W. I. L. et al. Simultaneous single-qubit driving of semiconductor spin qubits at the fault-tolerant threshold. Nat. Commun. 14, 3617 (2023).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Xue, X. et al. Quantum logic with spin qubits crossing the surface code threshold. Nature 601, 343–347 (2022).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Noiri, A. et al. Fast universal quantum gate above the fault-tolerance threshold in silicon. Nature 601, 338–342 (2022).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Mills, A. R. et al. Two-qubit silicon quantum processor with operation fidelity exceeding 99%. Sci. Adv. 8, 5130 (2022).

Article 

Google Scholar
 

Wang, C.-A. et al. Operating semiconductor quantum processors with hopping spins. Science 385, 447–452 (2024).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Tanttu, T. et al. Assessment of the errors of high-fidelity two-qubit gates in silicon quantum dots. Nat. Phys. 20, 1804–1809 (2024).

Article 
CAS 

Google Scholar
 

Steinacker, P. et al. Bell inequality violation in gate-defined quantum dots. Nat. Commun. 16, 3606 (2025).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Maurand, R. et al. A CMOS silicon spin qubit. Nat. Commun. 7, 13575 (2016).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Zwerver, A. M. J. et al. Qubits made by advanced semiconductor manufacturing. Nat. Electron. 5, 184–190 (2022).

Article 

Google Scholar
 

George, H. C. et al. 12-spin-qubit arrays fabricated on a 300 mm semiconductor manufacturing line. Nano Lett. 25, 793–799 (2024).

Article 
ADS 
PubMed 
PubMed Central 

Google Scholar
 

Steinacker, P. et al. Industry-compatible silicon spin-qubit unit cells exceeding 99% fidelity. Nature 646, 81–87 (2025).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Huckemann, T. et al. Industrially fabricated single-electron quantum dots in Si/Si–Ge heterostructures. IEEE Electron Device Lett. 46, 868–871 (2025).

Article 
ADS 
CAS 

Google Scholar
 

Undseth, B. et al. Hotter is easier: unexpected temperature dependence of spin qubit frequencies. Phys. Rev. X 13, 041015 (2023).

CAS 

Google Scholar
 

Huang, J. Y. et al. High-fidelity spin qubit operation and algorithmic initialization above 1 K. Nature 627, 772–777 (2024).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Taylor, J. M. et al. Fault-tolerant architecture for quantum computation using electrically controlled semiconductor spins. Nat. Phys. 1, 177–183 (2005).

Article 
CAS 

Google Scholar
 

Seidler, I. et al. Conveyor-mode single-electron shuttling in Si/SiGe for a scalable quantum computing architecture. npj Quantum Inf. 8, 100 (2022).

Article 
ADS 

Google Scholar
 

Xue, R. et al. Si/SiGe QuBus for single electron information-processing devices with memory and micron-scale connectivity function. Nat. Commun. 15, 2296 (2024).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Künne, M. et al. The SpinBus architecture for scaling spin qubits with electron shuttling. Nat. Commun. 15, 4977 (2024).

Article 
ADS 
PubMed 
PubMed Central 

Google Scholar
 

Abadillo-Uriel, J. C., Martinez, B., Filippone, M. & Niquet, Y.-M. Two-body Wigner molecularization in asymmetric quantum dot spin qubits. Phys. Rev. B 104, 195305 (2021).

Article 
ADS 
CAS 

Google Scholar
 

Corrigan, J. et al. Coherent control and spectroscopy of a semiconductor quantum dot Wigner molecule. Phys. Rev. Lett. 127, 127701 (2021).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Jang, W. et al. Wigner-molecularization-enabled dynamic nuclear polarization. Nat. Commun. 14, 2948 (2023).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Degli Esposti, D. et al. Low disorder and high valley splitting in silicon. npj Quantum Inf. 10, 32 (2024).

Article 
ADS 

Google Scholar
 

Obata, T. et al. Coherent manipulation of individual electron spin in a double quantum dot integrated with a micromagnet. Phys. Rev. B 81, 085317 (2010).

Article 
ADS 

Google Scholar
 

Meunier, T., Calado, V. E. & Vandersypen, L. M. K. Efficient controlled-phase gate for single-spin qubits in quantum dots. Phys. Rev. B 83, 121403 (2011).

Article 
ADS 

Google Scholar
 

Mokeev, A. S., Zhang, Y.-N. & Dobrovitski, V. V. Modeling of decoherence and fidelity enhancement during transport of entangled qubits. Preprint at https://arxiv.org/abs/2409.04404 (2023).

Philips, S. G. J. et al. Universal control of a six-qubit quantum processor in silicon. Nature 609, 919–924 (2022).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Bouwmeester, D. et al. Experimental quantum teleportation. Nature 390, 575–579 (1997).

Article 
ADS 
CAS 

Google Scholar
 

Pirandola, S., Eisert, J., Weedbrook, C., Furusawa, A. & Braunstein, S. L. Advances in quantum teleportation. Nat. Photon. 9, 641–652 (2015).

Article 
ADS 
CAS 

Google Scholar
 

D’Ariano, G. M. & Lo Presti, P. Quantum tomography for measuring experimentally the matrix elements of an arbitrary quantum operation. Phys. Rev. Lett. 86, 4195–4198 (2001).

Article 
ADS 
PubMed 

Google Scholar
 

Guţă, M., Kahn, J., Kueng, R. & Tropp, J. A. Fast state tomography with optimal error bounds. J. Phys. A Math. Theor. 53, 204001 (2020).

Article 
ADS 

Google Scholar
 

Surawy-Stepney, T., Kahn, J., Kueng, R. & Guta, M. Projected least-squares quantum process tomography. Quantum 6, 844 (2022).

Article 

Google Scholar
 

Barrett, M. D. et al. Deterministic quantum teleportation of atomic qubits. Nature 429, 737–739 (2004).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Chou, K. S. et al. Deterministic teleportation of a quantum gate between two logical qubits. Nature 561, 368–373 (2018).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Takeda, S., Mizuta, T., Fuwa, M., van Loock, P. & Furusawa, A. Deterministic quantum teleportation of photonic quantum bits by a hybrid technique. Nature 500, 315–318 (2013).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Fernández-Fernández, D., Matsumoto, Y., Vandersypen, L. M. K., Platero, G. & Bosco, S. Spin-orbit-enabled realization of arbitrary two-qubit gates on moving spins. Preprint at https://arxiv.org/abs/2508.08394 (2025).

Boter, J. M. et al. Spiderweb array: a sparse spin-qubit array. Phys. Rev. Appl. 18, 024053 (2022).

Article 
ADS 
CAS 

Google Scholar
 

Seedhouse, A. E. et al. Pauli blockade in silicon quantum dots with spin-orbit control. PRX Quantum 2, 010303 (2021).

Article 

Google Scholar
 

QuTech. Code and dataset for “Two-qubit logic and teleportation with mobile spin qubits in silicon”. Zenodo https://doi.org/10.5281/zenodo.15052065 (2025).