Ekert, A. & Jozsa, R. Quantum computation and Shor’s factoring algorithm. Rev. Mod. Phys. 68, 733–753 (1996).

Kimble, H. J. The quantum internet. Nature 453, 1023–1030 (2008).

Degen, C. L., Reinhard, F. & Cappellaro, P. Quantum sensing. Rev. Mod. Phys. 89, 035002 (2017).

Knill, E. Quantum computing with realistically noisy devices. Nature 434, 39–44 (2005).

Ladd, T. D. et al. Quantum computers. Nature 464, 45–53 (2010).

Loss, D. & DiVincenzo, D. P. Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998).

Kane, B. E. A silicon-based nuclear spin quantum computer. Nature 393, 133–137 (1998).

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).

Chan, K. W. et al. Assessment of a silicon quantum dot spin qubit environment via noise spectroscopy. Phys. Rev. Appl. 10, 044017 (2018).

Muhonen, J. T. et al. Quantifying the quantum gate fidelity of single-atom spin qubits in silicon by randomized benchmarking. J. Phys. Condens. Matter 27, 154205 (2015).

Huang, W. et al. Fidelity benchmarks for two-qubit gates in silicon. Nature 569, 532–536 (2019).

Zajac, D. M., Hazard, T. M., Mi, X., Nielsen, E. & Petta, J. R. Scalable gate architecture for densely packed semiconductor spin qubits. Phys. Rev. Appl. 6, 054013 (2016).

Mortemousque, P.-A. et al. Coherent control of individual electron spins in a two dimensional array of quantum dots. Preprint at https://arxiv.org/abs/1808.06180 (2018).

Mukhopadhyay, U., Dehollain, J. P., Reichl, C., Wegscheider, W. & Vandersypen, L. M. K. A 2 × 2 quantum dot array with controllable inter-dot tunnel couplings. Appl. Phys. Lett. 112, 183505 (2018).

Volk, C. et al. Loading a quantum-dot based “Qubyte” register. npj Quantum Inf. 5, 29 (2019).

Mi, X. et al. A coherent spin–photon interface in silicon. Nature 555, 599–603 (2018).

Samkharadze, N. et al. Strong spin-photon coupling in silicon. Science 359, 1123–1127 (2018).

Landig, A. J. et al. Coherent spin–photon coupling using a resonant exchange qubit. Nature 560, 179–184 (2018).

Mills, A. R. et al. Shuttling a single charge across a one-dimensional array of silicon quantum dots. Nat. Commun. 10, 1063 (2019).

Fujita, T., Baart, T. A., Reichl, C., Wegscheider, W. & Vandersypen, L. M. K. Coherent shuttle of electron-spin states. npj Quantum Inf. 3, 22 (2017).

Flentje, H. et al. Coherent long-distance displacement of individual electron spins. Nat. Commun. 8, 501 (2017).

Nakajima, T. et al. Coherent transfer of electron spin correlations assisted by dephasing noise. Nat. Commun. 9, 2133 (2018).

Baart, T. A. et al. Single-spin CCD. Nat. Nanotechnol. 11, 330–334 (2016).

Greentree, A. D., Cole, J. H., Hamilton, A. R. & Hollenberg, L. C. L. Coherent electronic transfer in quantum dot systems using adiabatic passage. Phys. Rev. B 70, 235317 (2004).

Shilton, J. M. et al. High-frequency single-electron transport in a quasi-one-dimensional GaAs channel induced by surface acoustic waves. J. Phys. Condens. Matter 8, 531–539 (1996).

Bertrand, B. et al. Fast spin information transfer between distant quantum dots using individual electrons. Nat. Nanotechnol. 11, 672–676 (2016).

Baart, T. A., Fujita, T., Reichl, C., Wegscheider, W. & Vandersypen, L. M. K. Coherent spin-exchange via a quantum mediator. Nat. Nanotechnol. 12, 26–30 (2017).

Malinowski, F. K. et al. Fast spin exchange across a multielectron mediator. Nat. Commun. 10, 1196 (2019).

Aharonov, D. & Ben-Or, M. Fault-tolerant quantum computation with constant error. In Proc. Twenty-ninth Annual ACM Symposium on Theory of Computing 176–188 (ACM Press, 1997).

Gottesman, D. Fault-tolerant quantum computation with local gates. J. Mod. Opt. 47, 333–345 (2000).

Fowler, A. G., Hill, C. D. & Hollenberg, L. C. L. Quantum-error correction on linear-nearest-neighbor qubit arrays. Phys. Rev. A 69, 042314 (2004).

Friesen, M., Biswas, A., Hu, X. & Lidar, D. Efficient multiqubit entanglement via a spin bus. Phys. Rev. Lett. 98, 230503 (2007).

Petta, J. R. et al. Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180–2184 (2005).

Angus, S. J., Ferguson, A. J., Dzurak, A. S. & Clark, R. G. Gate-defined quantum dots in intrinsic silicon. Nano Lett. 7, 2051–2055 (2007).

Zajac, D. M., Hazard, T. M., Mi, X., Wang, K. & Petta, J. R. A reconfigurable gate architecture for Si/SiGe quantum dots. Appl. Phys. Lett. 106, 223507 (2015).

Nichol, J. M. et al. Quenching of dynamic nuclear polarization by spin–orbit coupling in GaAs quantum dots. Nat. Commun. 6, 7682 (2015).

Foletti, S., Bluhm, H., Mahalu, D., Umansky, V. & Yacoby, A. Universal quantum control of two-electron spin quantum bits using dynamic nuclear polarization. Nat. Phys. 5, 903–908 (2009).

Taylor, J. M. et al. Relaxation, dephasing, and quantum control of electron spins in double quantum dots. Phys. Rev. B 76, 035315 (2007).

Shulman, M. D. et al. Suppressing qubit dephasing using real-time Hamiltonian estimation. Nat. Commun. 5, 5156 (2014).

Bluhm, H., Foletti, S., Mahalu, D., Umansky, V. & Yacoby, A. Enhancing the coherence of a spin qubit by operating it as a feedback loop that controls its nuclear spin bath. Phys. Rev. Lett. 105, 216803 (2010).

Barthel, C., Reilly, D. J., Marcus, C. M., Hanson, M. P. & Gossard, A. C. Rapid single-shot measurement of a singlet-triplet qubit. Phys. Rev. Lett. 103, 160503 (2009).

Studenikin, S. et al. Enhanced charge detection of spin qubit readout via an intermediate state. Appl. Phys. Lett. 101, 233101 (2012).

Reed, M. D. et al. Reduced sensitivity to charge noise in semiconductor spin qubits via symmetric operation. Phys. Rev. Lett. 116, 110402 (2016).

Martins, F. et al. Noise suppression using symmetric exchange gates in spin qubits. Phys. Rev. Lett. 116, 116801 (2016).

Orona, L. A. et al. Readout of singlet–triplet qubits at large magnetic field gradients. Phys. Rev. B 98, 125404 (2018).

Wang, X. et al. Composite pulses for robust universal control of singlet–triplet qubits. Nat. Commun. 3, 997 (2012).

Nichol, J. M., Orona, L. A., Harvey, S. P., Fallahi, S., Gardner, G. C., Manfra, M. J. & Yacoby, A. High-fidelity entangling gate for double-quantum-dot spin qubits. npj Quantum Inf. 3, 3 (2017).

Sigillito, A. J., Gullans, M. J., Edge, L. F., Borselli, M. & Petta, J. R. Coherent transfer of quantum information in silicon using resonant SWAP gates. Preprint at https://arxiv.org/abs/1906.04512 (2019).