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  • Technical Review
  • Published:

Review of performance metrics of spin qubits in gated semiconducting nanostructures

Nature Reviews Physics volume 4, pages 672–688 (2022)Cite this article

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Abstract

This Technical Review collects values of selected performance characteristics of semiconductor spin qubits defined in electrically controlled nanostructures. The characteristics are envisaged to serve as a community source for the values of figures of merit with agreed definitions allowing the comparison of different spin-qubit platforms. We include characteristics on the qubit coherence, speed, fidelity and qubit size of multi-qubit devices. The focus is on collecting and curating the values of these characteristics as reported in the literature, rather than on their motivation or significance.

Key points

  • Spin qubits hosted in semiconducting nanostructures controlled and probed electrically are among platforms pursued to serve as quantum computing hardware.

  • Their prospect for scalability stems from their versatility and compatibility with modern silicon industrial fabrication.

  • To serve as quantum hardware, qubits have to fulfil a number of stringent criteria concerning their operation, stability and interactions.

  • The overview of experimentally achieved values on coherence, speed, fidelity and multi-qubit array size quantifies the progress of semiconducting spin qubits over the past two decades.

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Fig. 1: Typical decay-curve envelopes.
Fig. 2: Spin coherence and relaxation times.
Fig. 3: Spin coherence times.
Fig. 4: Charge coherence.
Fig. 5: Operation times and fidelities.
Fig. 6: Probabilities describing a two-outcome qubit measurement.
Fig. 7: Quality factors and size of the qubit arrays.

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Code availability

The GitHub project https://github.com/PeterStano/ReviewOfSpinQubits gives the data that are plotted in figures as text files (more precisely, it contains the LaTeX source of the data tables as given in the Supplementary Information). The GitHub project also contains information on how to provide feedback to authors on the review content efficiently, and how to produce customized tables and figures. In addition to some of the references cited up to this point, the data were taken from Refs.77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325.

References

  1. Oosterkamp, T., Van der Wiel, W., DeFrancheschi, S., Harmans, C. & Kouwenhoven, L. Photon assisted tunneling in quantum dots. Preprint at https://arxiv.org/abs/cond-mat/9904359 (1999).

  2. Van der Wiel, W. G. et al. Electron transport through double quantum dots. Rev. Mod. Phys. 75, 1 (2002).

    Article  ADS  Google Scholar 

  3. Schliemann, J., Khaetskii, A. & Loss, D. Electron spin dynamics in quantum dots and related nanostructures due to hyperfine interaction with nuclei. J. Phys. Condens. Matter 15, R1809–R1833 (2003).

    Article  ADS  Google Scholar 

  4. Hanson, R., Kouwenhoven, L. P., Petta, J. R., Tarucha, S. & Vandersypen, L. M. K. Spins in few-electron quantum dots. Rev. Mod. Phys. 79, 1217–1265 (2007).

    Article  ADS  Google Scholar 

  5. Kloeffel, C. & Loss, D. Prospects for spin-based quantum computing in quantum dots. Annu. Rev. Condens. Matter Phys. 4, 51–81 (2013).

    Article  ADS  Google Scholar 

  6. Schreiber, L. R. & Bluhm, H. Silicon comes back. Nat. Nanotechnol. 9, 966 (2014).

    Article  ADS  Google Scholar 

  7. Tahan, C. Opinion: Democratizing spin qubits. Quantum, 5, 584 (2021).

    Article  Google Scholar 

  8. Chatterjee, A. et al. Semiconductor qubits in practice. Nat. Rev. Phys. 3, 157–177 (2021).

    Article  Google Scholar 

  9. Gonzalez-Zalba, M. F. et al. Scaling silicon-based quantum computing using CMOS technology. Nat. Electron. 4, 872–884 (2021).

    Article  Google Scholar 

  10. Scappucci, G. et al. The germanium quantum information route. Nat. Rev. Mater. 6, 926–943 (2021).

    Article  ADS  Google Scholar 

  11. Oiwa, A. et al. Conversion from single photon to single electron spin using electrically controllable quantum dots. J. Phys. Soc. Japan 86, 011008 (2017).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  13. Kuemmeth, F. & Bluhm, H. Roadmap for gallium arsenide spin qubits. Preprint at https://arxiv.org/abs/2011.13907 (2020).

  14. Burkard, G., Ladd, T. D., Nichol, J. M., Pan, A. & Petta, J. R. Semiconductor spin qubits. Preprint at https://arxiv.org/abs/2112.08863 (2021).

  15. Watzinger, H. et al. Heavy-Hole states in germanium hut wires. Nano Lett. 16, 6879–6885 (2016).

    Article  ADS  Google Scholar 

  16. Voisin, B. et al. Electrical control of g-factor in a few-hole silicon nanowire MOSFET. Nano Lett. 16, 88–92 (2016).

    Article  ADS  Google Scholar 

  17. Khaetskii, A. V., Loss, D. & Glazman, L. Electron spin decoherence in quantum dots due to interaction with nuclei. Phys. Rev. Lett. https://doi.org/10.1103/PhysRevLett.88.186802 (2002).

  18. Merkulov, I. A., Efros, A. L. & Rosen, M. Electron spin relaxation by nuclei in semiconductor quantum dots. Phys. Rev. B 65, 205309 (2002).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  20. Slichter, C. P. Principles of Magnetic Resonance 3rd enlarged and updated edn (Springer, 1996).

  21. Hahn, E. L. Spin echoes. Phys. Rev. 80, 580–594 (1950).

    Article  ADS  MATH  Google Scholar 

  22. Álvarez, G. A., Ajoy, A., Peng, X. & Suter, D. Performance comparison of dynamical decoupling sequences for a qubit in a rapidly fluctuating spin bath. Phys. Rev. A 82, 042306 (2010).

    Article  ADS  Google Scholar 

  23. Malinowski, F. K. et al. Notch filtering the nuclear environment of a spin qubit. Nat. Nanotechnol. 12, 16–20 (2016).

    Article  ADS  Google Scholar 

  24. Redfield, A. G. Nuclear magnetic resonance saturation and rotary saturation in solids. Phys. Rev. 98, 1787–1809 (1955).

    Article  ADS  Google Scholar 

  25. Laucht, A. et al. A dressed spin qubit in silicon. Nat. Nanotechnol. 12, 61–66 (2016).

    Article  ADS  Google Scholar 

  26. Bloch, F. Nuclear induction. Phys. Rev. 70, 460–474 (1946).

    Article  ADS  Google Scholar 

  27. Ezzouch, R. et al. Dispersively probed microwave spectroscopy of a silicon hole double quantum dot. Phys. Rev. Appl. 16, 034031 (2021).

    Article  ADS  Google Scholar 

  28. Cottet, A. et al. Cavity QED with hybrid nanocircuits: from atomic-like physics to condensed matter phenomena. J. Phys. Condens. Matter 29, 433002 (2017).

    Article  Google Scholar 

  29. Scarlino, P. et al. All-microwave control and dispersive readout of gate-defined quantum dot qubits in circuit quantum electrodynamics. Phys. Rev. Lett. https://doi.org/10.1103/PhysRevLett.122.206802 (2019).

  30. Ithier, G. et al. Decoherence in a superconducting quantum bit circuit. Phys. Rev. B https://doi.org/10.1103/PhysRevB.72.134519 (2005).

  31. Fischer, J. & Loss, D. Dealing with decoherence. Science 324, 1277–1278 (2009).

    Article  Google Scholar 

  32. Cywiński, Ł., Lutchyn, R. M., Nave, C. P. & Das Sarma, S. How to enhance dephasing time in superconducting qubits. Phys. Rev. B 77, 174509 (2008).

    Article  ADS  Google Scholar 

  33. Medford, J. et al. Scaling of dynamical decoupling for spin qubits. Phys. Rev. Lett. https://doi.org/10.1103/PhysRevLett.108.086802 (2012).

  34. Shrivastava, K. N. Theory of spin–lattice relaxation. Phys. Stat. Solidi B 117, 437–458 (1983).

    Article  ADS  Google Scholar 

  35. Khaetskii, A. V. & Nazarov, Y. V. Spin-flip transitions between Zeeman sublevels in semiconductor quantum dots. Phys. Rev. B https://doi.org/10.1103/PhysRevB.64.125316 (2001).

  36. 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. https://doi.org/10.1103/PhysRevLett.103.160503 (2009).

  37. Nakajima, T. et al. Robust single-shot spin measurement with 99.5% fidelity in a quantum dot array. Phys. Rev. Lett. 119, 017701 (2017).

    Article  ADS  Google Scholar 

  38. Broome, M. A. et al. High-fidelity single-shot singlet–triplet readout of precision-placed donors in silicon. Phys. Rev. Lett. 119, 046802 (2017).

    Article  ADS  Google Scholar 

  39. Camenzind, L. C. et al. Hyperfine-phonon spin relaxation in a single-electron GaAs quantum dot. Nat. Commun. 9, 3454 (2018).

    Article  ADS  Google Scholar 

  40. Takeda, K., Noiri, A., Nakajima, T., Kobayashi, T. & Tarucha, S. Quantum error correction with silicon spin qubits. Preprint at https://doi.org/10.48550/arXiv.2201.08581 (2022).

  41. Reilly, D. J., Marcus, C. M., Hanson, M. P. & Gossard, A. C. Fast single-charge sensing with a rf quantum point contact. Appl. Phys. Lett. 91, 162101 (2007).

    Article  ADS  Google Scholar 

  42. Wang, L.-J. et al. A graphene quantum dot with a single electron transistor as an integrated charge sensor. Appl. Phys. Lett. 97, 262113 (2010).

    Article  ADS  Google Scholar 

  43. Fringes, S. et al. Charge detection in a bilayer graphene quantum dot. Phys. Stat. Solidi B 248, 2684–2687 (2011).

    Article  ADS  Google Scholar 

  44. Colless, J. I. et al. Dispersive readout of a few-electron double quantum dot with fast rf gate sensors. Phys. Rev. Lett. 110, 046805 (2013).

    Article  ADS  Google Scholar 

  45. Stehlik, J. et al. Fast charge sensing of a cavity-coupled double quantum dot using a Josephson parametric amplifier. Phys. Rev. Applied 4, 014018 (2015).

    Article  ADS  Google Scholar 

  46. Gonzalez-Zalba, M. F., Barraud, S., Ferguson, A. J. & Betz, A. C. Probing the limits of gate-based charge sensing. Nat. Commun. 6, 6084 (2015).

    Article  ADS  Google Scholar 

  47. Zajac, D. M., Hazard, T. M., Mi, X., Nielsen, E. & Petta, J. R. Scalable gate architecture for a one-dimensional array of semiconductor spin qubits. Phys. Rev. Appl. 6, 054013 (2016).

    Article  ADS  Google Scholar 

  48. Zheng, G. et al. Rapid gate-based spin read-out in silicon using an on-chip resonator. Nat. Nanotechnol. 14, 742–746 (2019).

    Article  ADS  Google Scholar 

  49. Chanrion, E. et al. Charge detection in an array of CMOS quantum dots. Phys. Rev. Applied 14, 024066 (2020).

    Article  ADS  Google Scholar 

  50. Schupp, F. J. et al. Sensitive radiofrequency readout of quantum dots using an ultra-low-noise SQUID amplifier. J. Appl. Phys. 127, 244503 (2020).

    Article  ADS  Google Scholar 

  51. Schaal, S. et al. Fast gate-based readout of silicon quantum dots using Josephson parametric amplification. Phys. Rev. Lett. 124, 067701 (2020).

    Article  ADS  Google Scholar 

  52. Keith, D. et al. Single-shot spin readout in semiconductors near the shot-noise sensitivity limit. Phys. Rev. X 9, 041003 (2019).

    Google Scholar 

  53. Hanson, R. et al. Zeeman energy and spin relaxation in a one-electron quantum dot. Phys. Rev. Lett. 91, 196802 (2003).

    Article  ADS  Google Scholar 

  54. Ono, K., Austing, D. G., Tokura, Y. & Tarucha, S. Current rectification by Pauli exclusion in a weakly coupled double quantum dot system. Science 297, 1313–1317 (2002).

    Article  ADS  Google Scholar 

  55. Epstein, J. M., Cross, A. W., Magesan, E. & Gambetta, J. M. Investigating the limits of randomized benchmarking protocols. Phys. Rev. A 89, 062321 (2014).

    Article  ADS  Google Scholar 

  56. Sanders, Y. R., Wallman, J. J. & Sanders, B. C. Bounding quantum gate error rate based on reported average fidelity. New J. Phys. 18, 012002 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  57. Blume-Kohout, R. et al. Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography. Nat. Commun. 8, 14485 (2017).

    Article  Google Scholar 

  58. Heinosaari, T. & Ziman, M. Guide to mathematical concepts of quantum theory. Acta Phys. Slovaca 58, 487–674 (2008).

    Article  ADS  Google Scholar 

  59. Wootters, W. K. Statistical distance and Hilbert space. Phys. Rev. D 23, 357–362 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  60. Gilchrist, A., Langford, N. K. & Nielsen, M. A. Distance measures to compare real and ideal quantum processes. Phys. Rev. A 71, 062310 (2005).

    Article  ADS  Google Scholar 

  61. Gottesman, D. Theory of fault-tolerant quantum computation. Phys. Rev. A 57, 127–137 (1998).

    Article  ADS  Google Scholar 

  62. Magesan, E., Gambetta, J. M. & Emerson, J. Characterizing quantum gates via randomized benchmarking. Phys. Rev. A 85, 042311 (2012).

    Article  ADS  Google Scholar 

  63. Magesan, E. et al. Efficient measurement of quantum gate error by interleaved randomized benchmarking. Phys. Rev. Lett. 109, 080505 (2012).

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  65. Petit, L. et al. Universal quantum logic in hot silicon qubits. Nature 580, 355–359 (2020).

    Article  ADS  Google Scholar 

  66. Xue, X. et al. Benchmarking gate fidelities in a Si/SiGe two-qubit device. Phys. Rev. X 9, 021011 (2019).

    Google Scholar 

  67. Lawrie, W. I. L. et al. Simultaneous driving of semiconductor spin qubits at the fault-tolerant threshold. Preprint at http://arxiv.org/abs/2109.07837 (2021).

  68. Dial, O. E. et al. Charge noise spectroscopy using coherent exchange oscillations in a singlet-triplet qubit. Phys. Rev. Lett. https://doi.org/10.1103/PhysRevLett.110.146804 (2013).

  69. Veldhorst, M. et al. A two-qubit logic gate in silicon. Nature 526, 410–414 (2015).

    Article  ADS  Google Scholar 

  70. Devitt, S. J., Nemoto, K. & Munro, W. J. Quantum error correction for beginners. Rep. Prog. Phys. 76, 076001 (2013).

    Article  ADS  Google Scholar 

  71. van Diepen, C. J. et al. Quantum simulation of antiferromagnetic heisenberg chain with gate-defined quantum dots. Phys. Rev. X 11, 041025 (2021).

    Google Scholar 

  72. Dehollain, J. P. et al. Nagaoka ferromagnetism observed in a quantum dot plaquette. Nature http://www.nature.com/articles/s41586-020-2051-0 (2020).

  73. Zajac, D. M. et al. Resonantly driven CNOT gate for electron spins. Science 359, 439–442 (2018).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  74. Watson, T. F. et al. A programmable two-qubit quantum processor in silicon. Nature 555, 633–637 (2018).

    Article  ADS  Google Scholar 

  75. Takeda, K. et al. Quantum tomography of an entangled three-qubit state in silicon. Nat. Nanotechnol. 16, 965–969 (2021).

    Article  ADS  Google Scholar 

  76. Hendrickx, N. W. et al. A four-qubit germanium quantum processor. Nature 591, 580–585 (2021).

    Article  ADS  Google Scholar 

  77. Fujisawa, T., Austing, D. G., Tokura, Y., Hirayama, Y. & Tarucha, S. Allowed and forbidden transitions in artificial hydrogen and helium atoms. Nature 419, 278–281 (2002).

    Article  ADS  Google Scholar 

  78. Hayashi, T., Fujisawa, T., Cheong, H. D., Jeong, Y. H. & Hirayama, Y. Coherent manipulation of electronic states in a double quantum dot. Phys. Rev. Lett. 91, 226804 (2003).

    Article  ADS  Google Scholar 

  79. Elzerman, J. M. et al. Single-shot read-out of an individual electron spin in a quantum dot. Nature 430, 431–435 (2004).

    Article  ADS  Google Scholar 

  80. Petta, J. R., Johnson, A. C., Marcus, C. M., Hanson, M. P. & Gossard, A. C. Manipulation of a single charge in a double quantum dot. Phys. Rev. Lett. 93, 186802 (2004).

    Article  ADS  Google Scholar 

  81. Johnson, A. C. et al. Triplet–singlet spin relaxation via nuclei in a double quantum dot. Nature 435, 925–928 (2005).

    Article  ADS  Google Scholar 

  82. Koppens, F. H. L. Control and detection of singlet-triplet mixing in a random nuclear field. Science 309, 1346–1350 (2005).

    Article  ADS  Google Scholar 

  83. Laird, E. A. et al. Effect of exchange interaction on spin dephasing in a double quantum dot. Phys. Rev. Lett. 97, 056801 (2006).

    Article  ADS  Google Scholar 

  84. Koppens, F. H. L. et al. Driven coherent oscillations of a single electron spin in a quantum dot. Nature 442, 766–771 (2006).

    Article  ADS  Google Scholar 

  85. Meunier, T. et al. High fidelity measurement of Singlet–Triplet state in a quantum dot. Phys. Status Solidi (b) 243, 3855–3858 (2006).

    Article  ADS  Google Scholar 

  86. Meunier, T. et al. Nondestructive measurement of electron spins in a quantum dot. Phys. Rev. B 74, 195303 (2006).

    Article  ADS  Google Scholar 

  87. Meunier, T. et al. Experimental signature of phonon-mediated spin relaxation in a two-electron quantum dot. Phys. Rev. Lett. 98, 126601 (2007).

    Article  ADS  Google Scholar 

  88. Koppens, F. H. L. et al. Universal phase shift and nonexponential decay of driven single-spin oscillations. Phys. Rev. Lett. 99, 106803 (2007).

    Article  ADS  Google Scholar 

  89. Nowack, K. C., Koppens, F. H. L., Nazarov, Yu. V. & Vandersypen, L. M. K. Coherent control of a single electron spin with electric fields. Science 318, 1430–1433 (2007).

    Article  ADS  Google Scholar 

  90. Laird, E. A. et al. Hyperfine-mediated gate-driven electron spin resonance. Phys. Rev. Lett. 99, 246601 (2007).

    Article  ADS  Google Scholar 

  91. Amasha, S. et al. Electrical control of spin relaxation in a quantum dot. Phys. Rev. Lett. 100, 046803 (2008).

    Article  ADS  Google Scholar 

  92. Koppens, F. H. L., Nowack, K. C. & Vandersypen, L. M. K. Spin echo of a single electron spin in a quantum dot. Phys. Rev. Lett. 100, 236802 (2008).

    Article  ADS  Google Scholar 

  93. Reilly, D. J. et al. Measurement of temporal correlations of the Overhauser field in a double quantum dot. Phys. Rev. Lett. 101, 236803 (2008).

    Article  ADS  Google Scholar 

  94. Churchill, H. O. H. et al. Relaxation and dephasing in a two-electron c 13 nanotube double quantum dot. Phys. Rev. Lett. 102, 166802 (2009).

    Article  ADS  Google Scholar 

  95. Gaudreau, L. et al. A tunable few electron triple quantum dot. Appl. Phys. Lett. 95, 193101 (2009).

    Article  ADS  Google Scholar 

  96. Xiao, M., House, M. G. & Jiang, H. W. Measurement of the spin relaxation time of single electrons in a silicon metal-oxide-semiconductor-based quantum dot. Phys. Rev. Lett. 104, 096801 (2010).

    Article  ADS  Google Scholar 

  97. Barthel, C. et al. Fast sensing of double-dot charge arrangement and spin state with a radio-frequency sensor quantum dot. Phys. Rev. B 81, 161308 (2010).

    Article  ADS  Google Scholar 

  98. Reilly, D. J. et al. Exchange control of nuclear spin diffusion in a double quantum dot. Phys. Rev. Lett. 104, 236802 (2010).

    Article  ADS  Google Scholar 

  99. Petersson, K. D. et al. Charge and spin state readout of a double quantum dot coupled to a resonator. Nano Lett. 10, 2789–2793 (2010).

    Article  ADS  Google Scholar 

  100. Laird, E. A. et al. Coherent spin manipulation in an exchange-only qubit. Phys. Rev. B 82, 075403 (2010).

    Article  ADS  Google Scholar 

  101. Morello, A. et al. Single-shot readout of an electron spin in silicon. Nature 467, 687–691 (2010).

    Article  ADS  Google Scholar 

  102. 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).

    Article  ADS  Google Scholar 

  103. Barthel, C., Medford, J., Marcus, C. M., Hanson, M. P. & Gossard, A. C. Interlaced dynamical decoupling and coherent operation of a singlet-triplet qubit. Phys. Rev. Lett. 105, 266808 (2010).

    Article  ADS  Google Scholar 

  104. Bluhm, H. et al. Dephasing time of GaAs electron-spin qubits coupled to a nuclear bath exceeding 200 ms. Nat. Phys. 7, 109–113 (2010).

    Article  Google Scholar 

  105. Nadj-Perge, S., Frolov, S. M., Bakkers, E. P. A. M. & Kouwenhoven, L. P. Spin–Orbit qubit in a semiconductor nanowire. Nature 468, 1084–1087 (2010).

    Article  ADS  Google Scholar 

  106. Petersson, K. D., Petta, J. R., Lu, H. & Gossard, A. C. Quantum coherence in a one-electron semiconductor charge qubit. Phys. Rev. Lett. 105, 246804 (2010).

    Article  ADS  Google Scholar 

  107. Simmons, C. B. et al. Tunable spin loading and T1 of a silicon spin qubit measured by single-shot readout. Phys. Rev. Lett. 106, 156804 (2011).

    Article  ADS  Google Scholar 

  108. van Weperen, I. et al. Charge-state conditional operation of a spin qubit. Phys. Rev. Lett. 107, 030506 (2011).

    Article  Google Scholar 

  109. Nowack, K. C. et al. Single-shot correlations and two-qubit gate of solid-state spins. Science 333, 1269–1272 (2011).

    Article  ADS  Google Scholar 

  110. Brunner, R. et al. Two-qubit gate of combined single-spin rotation and interdot spin exchange in a double quantum dot. Phys. Rev. Lett. 107, 146801 (2011).

    Article  ADS  Google Scholar 

  111. Dovzhenko, Y. et al. Nonadiabatic quantum control of a semiconductor charge qubit. Phys. Rev. B 84, 161302 (2011).

    Article  ADS  Google Scholar 

  112. Gaudreau, L. et al. Coherent control of three-spin states in a triple quantum dot. Nat. Phys. 8, 54–58 (2011).

    Article  Google Scholar 

  113. Barthel, C. et al. Relaxation and readout visibility of a singlet-triplet qubit in an Overhauser field gradient. Phys. Rev. B 85, 035306 (2012).

    Article  ADS  Google Scholar 

  114. Frey, T. et al. Dipole coupling of a double quantum dot to a microwave resonator. Phys. Rev. Lett. 108, 046807 (2012).

    Article  ADS  Google Scholar 

  115. Maune, B. M. et al. Coherent singlet-triplet oscillations in a silicon-based double quantum dot. Nature 481, 344–347 (2012).

    Article  ADS  Google Scholar 

  116. Prance, J. R. et al. Single-shot measurement of triplet-singlet relaxation in a Si / SiGe double quantum dot. Phys. Rev. Lett. 108, 046808 (2012).

    Article  ADS  Google Scholar 

  117. Shi, Z. et al. Fast hybrid silicon double-quantum-dot qubit. Phys. Rev. Lett. 108, 140503 (2012).

    Article  ADS  Google Scholar 

  118. Shulman, M. D. et al. Demonstration of entanglement of electrostatically coupled singlet-triplet qubits. Science 336, 202–205 (2012).

    Article  ADS  Google Scholar 

  119. Pla, J. J. et al. A single-atom electron spin qubit in silicon. Nature 489, 541–545 (2012).

    Article  ADS  Google Scholar 

  120. Thalineau, R. et al. A few-electron quadruple quantum dot in a closed loop. Appl. Phys. Lett. 101, 103102 (2012).

    Article  ADS  Google Scholar 

  121. Petersson, K. D. et al. Circuit quantum electrodynamics with a spin qubit. Nature 490, 380–383 (2012).

    Article  ADS  Google Scholar 

  122. Cao, G. et al. Ultrafast universal quantum control of a quantum-dot charge qubit using Landau–Zener–Stückelberg interference. Nat. Commun. 4, 1401 (2013).

    Article  ADS  Google Scholar 

  123. Busl, M. et al. Bipolar spin blockade and coherent state superpositions in a triple quantum dot. Nat. Nanotechnol. 8, 261–265 (2013).

    Article  ADS  Google Scholar 

  124. van den Berg, J. W. G. et al. Fast spin-orbit qubit in an indium antimonide nanowire. Phys. Rev. Lett. 110, 066806 (2013).

    Article  ADS  Google Scholar 

  125. Shafiei, M., Nowack, K. C., Reichl, C., Wegscheider, W. & Vandersypen, L. M. K. Resolving spin-orbit- and hyperfine-mediated electric dipole spin resonance in a quantum dot. Phys. Rev. Lett. 110, 107601 (2013).

    Article  ADS  Google Scholar 

  126. Volk, C. et al. Probing relaxation times in graphene quantum dots. Nat. Commun. 4, 1753 (2013).

    Article  ADS  Google Scholar 

  127. Büch, H., Mahapatra, S., Rahman, R., Morello, A. & Simmons, M. Y. Spin readout and addressability of phosphorus-donor clusters in silicon. Nat. Commun. 4, 2017 (2013).

    Article  ADS  Google Scholar 

  128. Yang, C. H. et al. Spin-valley lifetimes in a silicon quantum dot with tunable valley splitting. Nat. Commun. 4, 2069 (2013).

    Article  ADS  Google Scholar 

  129. Laird, E. A., Pei, F. & Kouwenhoven, L. P. A Valley–Spin qubit in a carbon nanotube. Nat. Nanotechnol. 8, 565–568 (2013).

    Article  ADS  Google Scholar 

  130. Medford, J. et al. Quantum-Dot-based resonant exchange qubit. Phys. Rev. Lett. 111, 050501 (2013).

    Article  ADS  Google Scholar 

  131. Wang, K., Payette, C., Dovzhenko, Y., Deelman, P. W. & Petta, J. R. Charge relaxation in a single-electron Si/SiGe double quantum dot. Phys. Rev. Lett. 111, 046801 (2013).

    Article  ADS  Google Scholar 

  132. Shi, Z. et al. Coherent quantum oscillations and echo measurements of a Si charge qubit. Phys. Rev. B 88, 075416 (2013).

    Article  ADS  Google Scholar 

  133. Basset, J. et al. Single-electron double quantum dot dipole-coupled to a single photonic mode. Phys. Rev. B 88, 125312 (2013).

    Article  ADS  Google Scholar 

  134. Medford, J. et al. Self-consistent measurement and state tomography of an exchange-only spin qubit. Nat. Nanotechnol. 8, 654–659 (2013).

    Article  ADS  Google Scholar 

  135. Higginbotham, A. P., Kuemmeth, F., Hanson, M. P., Gossard, A. C. & Marcus, C. M. Coherent operations and screening in multielectron spin qubits. Phys. Rev. Lett. 112, 026801 (2014).

    Article  ADS  Google Scholar 

  136. Shi, Z. et al. Fast coherent manipulation of three-electron states in a double quantum dot. Nat. Commun. 5, 3020 (2014).

    Article  ADS  Google Scholar 

  137. Takakura, T. et al. Single to quadruple quantum dots with tunable tunnel couplings. Appl. Phys. Lett. 104, 113109 (2014).

    Article  ADS  Google Scholar 

  138. Viennot, J. J., Delbecq, M. R., Dartiailh, M. C., Cottet, A. & Kontos, T. Out-of-equilibrium charge dynamics in a hybrid circuit quantum electrodynamics architecture. Phys. Rev. B 89, 165404 (2014).

    Article  ADS  Google Scholar 

  139. Delbecq, M. R. et al. Full control of quadruple quantum dot circuit charge states in the single electron regime. Appl. Phys. Lett. 104, 183111 (2014).

    Article  ADS  Google Scholar 

  140. Higginbotham, A. P. et al. Hole spin coherence in a Ge/Si heterostructure nanowire. Nano Lett. 14, 3582–3586 (2014).

    Article  ADS  Google Scholar 

  141. Dehollain, J. P. et al. Single-shot readout and relaxation of singlet and triplet states in exchange-coupled P 31 electron spins in silicon. Phys. Rev. Lett. 112, 236801 (2014).

    Article  ADS  Google Scholar 

  142. Kim, D. et al. Quantum control and process tomography of a semiconductor quantum dot hybrid qubit. Nature 511, 70–74 (2014).

    Article  ADS  Google Scholar 

  143. Kawakami, E. et al. Electrical control of a long-lived spin qubit in a Si/SiGe quantum dot. Nat. Nanotechnol. 9, 666–670 (2014).

    Article  ADS  Google Scholar 

  144. Wu, X. et al. Two-axis control of a singlet-triplet qubit with an integrated micromagnet. Proc. Natl. Acad. Sci. 111, 11938–11942 (2014).

    Article  ADS  Google Scholar 

  145. Muhonen, J. T. et al. Storing quantum information for 30 seconds in a nanoelectronic device. Nat. Nanotechnol. 9, 986–991 (2014).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  148. Scarlino, P. et al. Spin-relaxation anisotropy in a GaAs quantum dot. Phys. Rev. Lett. 113, 256802 (2014).

    Article  ADS  Google Scholar 

  149. Yoneda, J. et al. Fast electrical control of single electron spins in quantum dots with vanishing influence from nuclear spins. Phys. Rev. Lett. 113, 267601 (2014).

    Article  ADS  Google Scholar 

  150. Kim, D. et al. Microwave-driven coherent operation of a semiconductor quantum dot charge qubit. Nat. Nanotechnol. 10, 243–247 (2015).

    Article  ADS  Google Scholar 

  151. 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).

    Article  ADS  Google Scholar 

  152. Laucht, A. et al. Electrically controlling single-spin qubits in a continuous microwave field. Sci. Adv. 1, e1500022–e1500022 (2015).

    Article  ADS  Google Scholar 

  153. Eng, K. et al. Isotopically enhanced triple-quantum-dot qubit. Sci. Adv. 1, e1500214 (2015).

    Article  ADS  Google Scholar 

  154. Ranjan, V. et al. Clean carbon nanotubes coupled to superconducting impedance-matching circuits. Nat. Commun. 6, 7165 (2015).

    Article  ADS  Google Scholar 

  155. Li, H.-O. et al. Conditional rotation of two strongly coupled semiconductor charge qubits. Nat. Commun. 6, 7681 (2015).

    Article  ADS  Google Scholar 

  156. Stockklauser, A. et al. Microwave emission from hybridized states in a semiconductor charge qubit. Phys. Rev. Lett. 115, 046802 (2015).

    Article  ADS  Google Scholar 

  157. Viennot, J. J., Dartiailh, M. C., Cottet, A. & Kontos, T. Coherent coupling of a single spin to microwave cavity photons. Science 349, 408–411 (2015).

    Article  ADS  Google Scholar 

  158. Bertrand, B. et al. Quantum manipulation of two-electron spin states in isolated double quantum dots. Phys. Rev. Lett. 115, 096801 (2015).

    Article  ADS  Google Scholar 

  159. Deng, G.-W. et al. Charge number dependence of the dephasing rates of a graphene double quantum dot in a circuit QED architecture. Phys. Rev. Lett. 115, 126804 (2015).

    Article  ADS  Google Scholar 

  160. Watson, T. F., Weber, B., House, M. G., Büch, H. & Simmons, M. Y. High-fidelity rapid initialization and read-out of an electron spin via the single donor D - charge state. Phys. Rev. Lett. 115, 166806 (2015).

    Article  ADS  Google Scholar 

  161. Veldhorst, M. et al. Spin-orbit coupling and operation of multivalley spin qubits. Phys. Rev. B 92, 201401 (2015).

    Article  ADS  Google Scholar 

  162. Kim, D. et al. High-fidelity resonant gating of a silicon-based quantum dot hybrid qubit. npj Quantum Inf. 1, 15004 (2015).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  164. Delbecq, M. R. et al. Quantum dephasing in a gated gaas triple quantum dot due to nonergodic noise. Phys. Rev. Lett. 116, 046802 (2016).

    Article  ADS  Google Scholar 

  165. Cao, G. et al. Tunable hybrid qubit in a GaAs double quantum dot. Phys. Rev. Lett. 116, 086801 (2016).

    Article  ADS  Google Scholar 

  166. Tracy, L. A. et al. Single shot spin readout using a cryogenic high-electron-mobility transistor amplifier at sub-Kelvin temperatures. Appl. Phys. Lett. 108, 063101 (2016).

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  169. Noiri, A. et al. Coherent electron-spin-resonance manipulation of three individual spins in a triple quantum dot. Appl. Phys. Lett. 108, 153101 (2016).

    Article  ADS  Google Scholar 

  170. Wang, R., Deacon, R. S., Car, D., Bakkers, E. P. A. M. & Ishibashi, K. InSb nanowire double quantum dots coupled to a superconducting microwave cavity. Appl. Phys. Lett. 108, 203502 (2016).

    Article  ADS  Google Scholar 

  171. Baart, T. A., Jovanovic, N., Reichl, C., Wegscheider, W. & Vandersypen, L. M. K. Nanosecond-timescale spin transfer using individual electrons in a quadruple-quantum-dot device. Appl. Phys. Lett. 109, 043101 (2016).

    Article  ADS  Google Scholar 

  172. Otsuka, T. et al. Single-electron spin resonance in a quadruple quantum dot. Sci. Rep. 6, 31820 (2016).

    Article  ADS  Google Scholar 

  173. Takeda, K. et al. A fault-tolerant addressable spin qubit in a natural silicon quantum dot. Sci. Adv. 2, e1600694 (2016).

    Article  ADS  Google Scholar 

  174. 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 (2016).

    Article  ADS  Google Scholar 

  175. Dehollain, J. P. et al. Optimization of a solid-state electron spin qubit using gate set tomography. N. J. Phys. 18, 103018 (2016).

    Article  Google Scholar 

  176. Kawakami, E. et al. Gate fidelity and coherence of an electron spin in an Si/SiGe quantum dot with micromagnet. Proc. Natl Acad. Sci. 113, 11738–11743 (2016).

    Article  ADS  Google Scholar 

  177. Kiyama, H., Nakajima, T., Teraoka, S., Oiwa, A. & Tarucha, S. Single-shot ternary readout of two-electron spin states in a quantum dot using spin filtering by quantum hall edge states. Phys. Rev. Lett. 117, 236802 (2016).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  179. Wang, D. Q. et al. Anisotropic Pauli spin blockade of holes in a GaAs double quantum dot. Nano Lett. 16, 7685–7689 (2016).

    Article  ADS  Google Scholar 

  180. Ito, T. et al. Detection and control of charge states in a quintuple quantum dot. Sci. Rep. 6, 39113 (2016).

    Article  ADS  Google Scholar 

  181. Mi, X., Cady, J. V., Zajac, D. M., Deelman, P. W. & Petta, J. R. Strong coupling of a single electron in silicon to a microwave photon. Science 355, 156–158 (2016).

    Article  ADS  Google Scholar 

  182. Mi, X. et al. Circuit quantum electrodynamics architecture for gate-defined quantum dots in silicon. Appl. Phys. Lett. 110, 043502 (2017).

    Article  ADS  Google Scholar 

  183. Nichol, J. M. et al. High-fidelity entangling gate for double-quantum-dot spin qubits. npj Quantum Inf. 3, 3 (2017).

    Article  ADS  Google Scholar 

  184. Stockklauser, A. et al. Strong coupling cavity QED with gate-defined double quantum dots enabled by a high impedance resonator. Phys. Rev. X 7, 011030 (2017).

    Google Scholar 

  185. Watson, T. F. et al. Atomically engineered electron spin lifetimes of 30 s in silicon. Sci. Adv. 3, e1602811 (2017).

    Article  ADS  Google Scholar 

  186. Malinowski, F. K. et al. Spectrum of the nuclear environment for GaAs spin qubits. Phys. Rev. Lett. 118, 177702 (2017).

    Article  ADS  Google Scholar 

  187. Scarlino, P. et al. Dressed photon-orbital states in a quantum dot: Intervalley spin resonance. Phys. Rev. B 95, 165429 (2017).

    Article  ADS  Google Scholar 

  188. Penfold-Fitch, Z. V., Sfigakis, F. & Buitelaar, M. R. Microwave spectroscopy of a carbon nanotube charge qubit. Phys. Rev. Appl. 7, 054017 (2017).

    Article  ADS  Google Scholar 

  189. Flentje, H. et al. A linear triple quantum dot system in isolated configuration. Appl. Phys. Lett. 110, 233101 (2017).

    Article  ADS  Google Scholar 

  190. 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).

    Article  ADS  Google Scholar 

  191. Malinowski, F. K. et al. Symmetric operation of the resonant exchange qubit. Phys. Rev. B 96, 045443 (2017).

    Article  ADS  Google Scholar 

  192. Thorgrimsson, B. et al. Extending the coherence of a quantum dot hybrid qubit. npj Quantum Inf. 3, 32 (2017).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  194. Harvey-Collard, P. et al. Coherent coupling between a quantum dot and a donor in silicon. Nat. Commun. 8, 1029 (2017).

    Article  ADS  Google Scholar 

  195. Hofmann, A. et al. Anisotropy and suppression of spin-orbit interaction in a GaAs double quantum dot. Phys. Rev. Lett. 119, 176807 (2017).

    Article  ADS  Google Scholar 

  196. Noiri, A. et al. Cotunneling spin blockade observed in a three-terminal triple quantum dot. Phys. Rev. B 96, 155414 (2017).

    Article  ADS  Google Scholar 

  197. 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 (2017).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  199. Corna, A. et al. Electrically driven electron spin resonance mediated by Spin–Valley–Orbit coupling in a silicon quantum dot. npj Quantum Inf. 4, 6 (2018).

    Article  ADS  Google Scholar 

  200. Mi, X. et al. A coherent Spin–Photon interface in silicon. Nature 555, 599–603 (2018).

    Article  ADS  Google Scholar 

  201. Broome, M. A. et al. Two-electron spin correlations in precision placed donors in silicon. Nat. Commun. 9, 980 (2018).

    Article  ADS  Google Scholar 

  202. Crippa, A. et al. Electrical spin driving by g -matrix modulation in spin-orbit qubits. Phys. Rev. Lett. 120, 137702 (2018).

    Article  ADS  Google Scholar 

  203. Mukhopadhyay, U., Dehollain, J. P., Reichl, C., Wegscheider, W. & Vandersypen, L. M. K. A 2x2 quantum dot array with controllable inter-dot tunnel couplings. Appl. Phys. Lett. 112, 183505 (2018).

    Article  ADS  Google Scholar 

  204. Bogan, A. et al. Landau-Zener-Stückelberg-Majorana interferometry of a single hole. Phys. Rev. Lett. 120, 207701 (2018).

    Article  ADS  Google Scholar 

  205. Harvey-Collard, P. et al. High-fidelity single-shot readout for a spin qubit via an enhanced latching mechanism. Phys. Rev. X 8, 021046 (2018).

    Google Scholar 

  206. Jock, R. M. et al. A silicon metal-oxide-semiconductor electron spin-orbit qubit. Nat. Commun. 9, 1768 (2018).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  208. Froning, F. N. M. et al. Single, double, and triple quantum dots in Ge/Si nanowires. Appl. Phys. Lett. 113, 073102 (2018).

    Article  ADS  Google Scholar 

  209. Ito, T. et al. Four single-spin Rabi oscillations in a quadruple quantum dot. Appl. Phys. Lett. 113, 093102 (2018).

    Article  ADS  Google Scholar 

  210. Petit, L. et al. Spin lifetime and charge noise in hot silicon quantum dot qubits. Phys. Rev. Lett. 121, 076801 (2018).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  212. Watzinger, H. et al. A germanium hole spin qubit. Nat. Commun. 9, 3902 (2018).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  214. Croot, X. G. et al. Device architecture for coupling spin qubits via an intermediate quantum state. Phys. Rev. Appl. 10, 044058 (2018).

    Article  ADS  Google Scholar 

  215. Fogarty, M. A. et al. Integrated silicon qubit platform with single-spin addressability, exchange control and single-shot singlet-triplet readout. Nat. Commun. 9, 4370 (2018).

    Article  ADS  Google Scholar 

  216. Takeda, K. et al. Optimized electrical control of a Si/SiGe spin qubit in the presence of an induced frequency shift. npj Quantum Inf. 4, 54 (2018).

    Article  ADS  Google Scholar 

  217. van Woerkom, D. J. et al. Microwave photon-mediated interactions between semiconductor qubits. Phys. Rev. X 8, 041018 (2018).

    Google Scholar 

  218. Vukušić, L. et al. Single-shot readout of hole spins in Ge. Nano Lett. 18, 7141–7145 (2018).

    Article  ADS  Google Scholar 

  219. Noiri, A. et al. A fast quantum interface between different spin qubit encodings. Nat. Commun. 9, 5066 (2018).

    Article  ADS  Google Scholar 

  220. Pakkiam, P. et al. Single-shot single-gate rf spin readout in silicon. Phys. Rev. X 8, 041032 (2018).

    Google Scholar 

  221. Weber, B. et al. Spin–Orbit coupling in silicon for electrons bound to donors. npj Quantum Inf. 4, 61 (2018).

    Article  ADS  Google Scholar 

  222. Koch, M. et al. Spin read-out in atomic qubits in an all-epitaxial three-dimensional transistor. Nat. Nanotechnol. 14, 137–140 (2019).

    Article  ADS  Google Scholar 

  223. Bogan, A. et al. Single hole spin relaxation probed by fast single-shot latched charge sensing. Commun. Phys. 2, 17 (2019).

    Article  Google Scholar 

  224. Hardy, W. J. et al. Single and double hole quantum dots in strained Ge/SiGe quantum wells. Nanotechnology 30, 215202 (2019).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  227. West, A. et al. Gate-based single-shot readout of spins in silicon. Nat. Nanotechnol. 14, 437–441 (2019).

    Article  ADS  Google Scholar 

  228. Borjans, F., Zajac, D. M., Hazard, T. M. & Petta, J. R. Single-spin relaxation in a synthetic spin-orbit field. Phys. Rev. Appl. 11, 044063 (2019).

    Article  ADS  Google Scholar 

  229. Nakajima, T. et al. Quantum non-demolition measurement of an electron spin qubit. Nat. Nanotechnol. 14, 555–560 (2019).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  232. Harvey-Collard, P. et al. Spin-orbit interactions for singlet-triplet qubits in silicon. Phys. Rev. Lett. 122, 217702 (2019).

    Article  ADS  Google Scholar 

  233. Landig, A. J. et al. Microwave-cavity-detected spin blockade in a few-electron double quantum dot. Phys. Rev. Lett. 122, 213601 (2019).

    Article  ADS  Google Scholar 

  234. Tanttu, T. et al. Controlling spin-orbit interactions in silicon quantum dots using magnetic field direction. Phys. Rev. X 9, 021028 (2019).

    Google Scholar 

  235. Tenberg, S. B. et al. Electron spin relaxation of single phosphorus donors in metal-oxide-semiconductor nanoscale devices. Phys. Rev. B 99, 205306 (2019).

    Article  ADS  Google Scholar 

  236. Urdampilleta, M. et al. Gate-based high fidelity spin readout in a CMOS device. Nat. Nanotechnol. 14, 737–741 (2019).

    Article  Google Scholar 

  237. Sigillito, A. J. et al. Site-selective quantum control in an isotopically enriched Si 28 / Si 0.7 Ge 0.3 quadruple quantum dot. Phys. Rev. Appl. 11, 061006 (2019).

    Article  ADS  Google Scholar 

  238. Andrews, R. W. et al. Quantifying error and leakage in an encoded Si/SiGe triple-dot qubit. Nat. Nanotechnol. 14, 747–750 (2019).

    Article  Google Scholar 

  239. Crippa, A. et al. Gate-reflectometry dispersive readout and coherent control of a spin qubit in silicon. Nat. Commun. 10, 2776 (2019).

    Article  ADS  Google Scholar 

  240. Cubaynes, T. et al. Highly coherent spin states in carbon nanotubes coupled to cavity photons. npj Quantum Inf. 5, 47 (2019).

    Article  ADS  Google Scholar 

  241. He, Y. et al. A two-qubit gate between phosphorus donor electrons in silicon. Nature 571, 371–375 (2019).

    Article  ADS  Google Scholar 

  242. Jones, A. M. et al. Spin-blockade spectroscopy of Si/Si-Ge quantum dots. Phys. Rev. Appl. 12, 014026 (2019).

    Article  ADS  Google Scholar 

  243. Scarlino, P. et al. Coherent microwave-photon-mediated coupling between a semiconductor and a superconducting qubit. Nat. Commun. 10, 3011 (2019).

    Article  ADS  Google Scholar 

  244. Volk, C., Chatterjee, A., Ansaloni, F., Marcus, C. M. & Kuemmeth, F. Fast charge sensing of Si/SiGe quantum dots via a high-frequency accumulation gate. Nano Lett. 19, 5628–5633 (2019).

    Article  ADS  Google Scholar 

  245. Kandel, Y. P. et al. Coherent spin-state transfer via Heisenberg exchange. Nature 573, 553–557 (2019).

    Article  ADS  Google Scholar 

  246. Landig, A. J. et al. Virtual-photon-mediated Spin-Qubit–Transmon coupling. Nat. Commun. 10, 5037 (2019).

    Article  ADS  Google Scholar 

  247. Penthorn, N. E., Schoenfield, J. S., Rooney, J. D., Edge, L. F. & Jiang, H. Two-axis quantum control of a fast valley qubit in silicon. npj Quantum Inf. 5, 94 (2019).

    Article  ADS  Google Scholar 

  248. Sigillito, A. J., Gullans, M. J., Edge, L. F., Borselli, M. & Petta, J. R. Coherent transfer of quantum information in a silicon double quantum dot using resonant SWAP gates. npj Quantum Inf. 5, 110 (2019).

    Article  ADS  Google Scholar 

  249. Borjans, F., Croot, X. G., Mi, X., Gullans, M. J. & Petta, J. R. Resonant microwave-mediated interactions between distant electron spins. Nature 577, 195–198 (2019).

    Article  ADS  Google Scholar 

  250. Zhao, R. et al. Single-spin qubits in isotopically enriched silicon at low magnetic field. Nat. Commun. 10, 5500 (2019).

    Article  ADS  Google Scholar 

  251. Croot, X. et al. Flopping-mode electric dipole spin resonance. Phys. Rev. Res. 2, 012006 (2020).

    Article  Google Scholar 

  252. Hendrickx, N. W., Franke, D. P., Sammak, A., Scappucci, G. & Veldhorst, M. Fast two-qubit logic with holes in germanium. Nature 577, 487–491 (2020).

    Article  ADS  Google Scholar 

  253. Noiri, A. et al. Radio-frequency-detected fast charge sensing in undoped silicon quantum dots. Nano Lett. 20, 947–952 (2020).

    Article  ADS  Google Scholar 

  254. Connors, E. J., Nelson, J. & Nichol, J. M. Rapid high-fidelity spin-state readout in Si / Si - Ge quantum dots via rf reflectometry. Phys. Rev. Appl. 13, 024019 (2020).

    Article  ADS  Google Scholar 

  255. Lawrie, W. I. L. et al. Quantum dot arrays in silicon and germanium. Appl. Phys. Lett. 116, 080501 (2020).

    Article  ADS  Google Scholar 

  256. Leon, R. C. C. et al. Coherent spin control of S-, p-, d- and f-Electrons in a silicon quantum dot. Nat. Commun. 11, 797 (2020).

    Article  ADS  Google Scholar 

  257. Hollmann, A. et al. Large, tunable valley splitting and single-spin relaxation mechanisms in a Si/Si x Ge 1-x quantum dot. Phys. Rev. Appl. 13, 034068 (2020).

    Article  ADS  Google Scholar 

  258. Nakajima, T. et al. Coherence of a driven electron spin qubit actively decoupled from quasistatic noise. Phys. Rev. X 10, 011060 (2020).

    Google Scholar 

  259. Takeda, K., Noiri, A., Yoneda, J., Nakajima, T. & Tarucha, S. Resonantly driven singlet-triplet spin qubit in silicon. Phys. Rev. Lett. 124, 117701 (2020).

    Article  ADS  Google Scholar 

  260. Yoneda, J. et al. Quantum non-demolition readout of an electron spin in silicon. Nat. Commun. 11, 1144 (2020).

    Article  ADS  Google Scholar 

  261. Xue, X. et al. Repetitive quantum nondemolition measurement and soft decoding of a silicon spin qubit. Phys. Rev. X 10, 021006 (2020).

    Google Scholar 

  262. Yang, C. H. et al. Operation of a silicon quantum processor unit cell above one kelvin. Nature 580, 350–354 (2020).

    Article  ADS  Google Scholar 

  263. Koski, J. V. et al. Strong photon coupling to the quadrupole moment of an electron in a solid-state qubit. Nat. Phys. 16, 642–646 (2020).

    Article  Google Scholar 

  264. Struck, T. et al. Low-frequency spin qubit energy splitting noise in highly purified 28Si/SiGe. npj Quantum Inf. 6, 40 (2020).

    Article  ADS  Google Scholar 

  265. Borjans, F. et al. Split-gate cavity coupler for silicon circuit quantum electrodynamics. Appl. Phys. Lett. 116, 234001 (2020).

    Article  ADS  Google Scholar 

  266. Boter, J. M. et al. Spatial noise correlations in a Si/SiGe two-qubit device from Bell state coherences. Phys. Rev. B 101, 235133 (2020).

    Article  ADS  Google Scholar 

  267. Qiao, H. et al. Conditional teleportation of quantum-dot spin states. Nat. Commun. 11, 3022 (2020).

    Article  ADS  Google Scholar 

  268. Zhang, X. et al. Giant anisotropy of spin relaxation and spin-valley mixing in a silicon quantum dot. Phys. Rev. Lett. 124, 257701 (2020).

    Article  ADS  Google Scholar 

  269. Hendrickx, N. W. et al. A single-hole spin qubit. Nat. Commun. 11, 3478 (2020).

    Article  ADS  Google Scholar 

  270. Jang, W. et al. Robust energy-selective tunneling readout of singlet-triplet qubits under large magnetic field gradient. npj Quantum Inf. 6, 64 (2020).

    Article  ADS  Google Scholar 

  271. Kobayashi, T. et al. Engineering long spin coherence times of Spin–Orbit qubits in silicon. Nat. Mater. 20, 38–42 (2020).

    Article  ADS  Google Scholar 

  272. Mądzik, M. T. et al. Controllable freezing of the nuclear spin bath in a single-atom spin qubit. Sci. Adv. 6, eaba3442 (2020).

    Article  ADS  Google Scholar 

  273. Qiao, H. et al. Coherent multispin exchange coupling in a quantum-dot spin chain. Phys. Rev. X 10, 031006 (2020).

    Google Scholar 

  274. Cerfontaine, P. et al. Closed-loop control of a GaAs-based singlet-triplet spin qubit with 99.5% gate fidelity and low leakage. Nat. Commun. 11, 4144 (2020).

    Article  ADS  Google Scholar 

  275. Lawrie, W. I. L. et al. Spin relaxation benchmarks and individual qubit addressability for holes in quantum dots. Nano Lett. 20, 7237–7242 (2020).

    Article  ADS  Google Scholar 

  276. Xu, G. et al. Dipole coupling of a hole double quantum dot in germanium hut wire to a microwave resonator. N. J. Phys. 22, 083068 (2020).

    Article  Google Scholar 

  277. Duan, J. et al. Remote capacitive sensing in two-dimensional quantum-dot arrays. Nano Lett. 20, 7123–7128 (2020).

    Article  ADS  Google Scholar 

  278. MacQuarrie, E. R. et al. Progress toward a capacitively mediated CNOT between two charge qubits in Si/SiGe. npj Quantum Inf. 6, 81 (2020).

    Article  ADS  Google Scholar 

  279. Gilbert, W. et al. Single-electron operation of a silicon-CMOS 2x2 quantum dot array with integrated charge sensing. Nano Lett. 20, 7882–7888 (2020).

    Article  ADS  Google Scholar 

  280. Ansaloni, F. et al. Single-electron operations in a foundry-fabricated array of quantum dots. Nat. Commun. 11, 6399 (2020).

    Article  ADS  Google Scholar 

  281. Bohuslavskyi, H. et al. Reflectometry of charge transitions in a silicon quadruple dot. Preprint at https://arxiv.org/abs/2012.04791 (2020).

  282. Jang, W. et al. Individual two-axis control of three singlet-triplet qubits in a micromagnet integrated quantum dot array. Appl. Phys. Lett. 117, 234001 (2020).

    Article  ADS  Google Scholar 

  283. Mortemousque, P.-A. et al. Coherent control of individual electron spins in a two-dimensional quantum dot array. Nat. Nanotechnol. 16, 296–301 (2020).

    Article  ADS  Google Scholar 

  284. Chan, K. W. et al. Exchange coupling in a linear chain of three quantum-dot spin qubits in silicon. Nano Lett. 21, 1517–1522 (2021).

    Article  ADS  Google Scholar 

  285. Froning, F. N. M. et al. Ultrafast hole spin qubit with gate-tunable Spin–Orbit switch functionality. Nat. Nanotechnol. 16, 308–312 (2021).

    Article  ADS  Google Scholar 

  286. Mądzik, M. T. et al. Conditional quantum operation of two exchange-coupled single-donor spin qubits in a MOS-compatible silicon device. Nat. Commun. 12, 181 (2021).

    Article  Google Scholar 

  287. Qiao, H. et al. Long-distance superexchange between semiconductor quantum-dot electron spins. Phys. Rev. Lett. 126, 017701 (2021).

    Article  ADS  Google Scholar 

  288. Ruffino, A. et al. Integrated multiplexed microwave readout of silicon quantum dots in a cryogenic CMOS chip. Preprint at https://arxiv.org/abs/2101.08295 (2021).

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

    Article  Google Scholar 

  290. van Diepen, C. J. et al. Electron cascade for distant spin readout. Nat. Commun. 12, 77 (2021).

    Article  ADS  Google Scholar 

  291. van Riggelen, F. et al. A two-dimensional array of single-hole quantum dots. Appl. Phys. Lett. 118, 044002 (2021).

    Article  ADS  Google Scholar 

  292. Jadot, B. et al. Distant spin entanglement via fast and coherent electron shuttling. Nat. Nanotechnol. 16, 570–575 (2021).

    Article  ADS  Google Scholar 

  293. Kratochwil, B. et al. Charge qubit in a triple quantum dot with tunable coherence. Phys. Rev. Res. 3, 013171 (2021).

    Article  Google Scholar 

  294. Wang, B. et al. Correlated spectrum of distant semiconductor qubits coupled by microwave photons. Sci. Bull. 66, 332–338 (2021).

    Article  Google Scholar 

  295. Camenzind, L. C. et al. A spin qubit in a fin field-effect transistor. Preprint at https://arxiv.org/abs/2103.07369 (2021).

  296. Ciriano-Tejel, V. N. et al. Spin readout of a CMOS quantum dot by gate reflectometry and spin-dependent tunneling. PRX Quantum 2, 010353 (2021).

    Article  Google Scholar 

  297. Kerckhoff, J. et al. Magnetic gradient fluctuations from quadrupolar 73 Ge in Si/SiGe exchange-only qubits. PRX Quantum 2, 010347 (2021).

    Article  Google Scholar 

  298. Borjans, F., Mi, X. & Petta, J. R. Spin digitizer for high-fidelity readout of a cavity-coupled silicon triple quantum dot. Phys. Rev. Appl. 15, 044052 (2021).

    Article  ADS  Google Scholar 

  299. Borjans, F. et al. Probing the variation of the intervalley tunnel coupling in a silicon triple quantum dot. PRX Quantum 2, 020309 (2021).

    Article  ADS  Google Scholar 

  300. Chen, E. H. et al. Detuning axis pulsed spectroscopy of valley-orbital states in Si/Si-Ge quantum dots. Phys. Rev. Appl. 15, 044033 (2021).

    Article  ADS  Google Scholar 

  301. Kandel, Y. P. et al. Adiabatic quantum state transfer in a semiconductor quantum-dot spin chain. Nat. Commun. 12, 2156 (2021).

    Article  ADS  Google Scholar 

  302. Ibberson, D. J. et al. Large dispersive interaction between a CMOS double quantum dot and microwave photons. PRX Quantum 2, 020315 (2021).

    Article  ADS  Google Scholar 

  303. Kojima, Y. et al. Probabilistic teleportation of a quantum dot spin qubit. npj Quantum Inf. 7, 68 (2021).

    Article  ADS  Google Scholar 

  304. Leon, R. C. C. et al. Bell-state tomography in a silicon many-electron artificial molecule. Nat. Commun. 12, 3228 (2021).

    Article  ADS  Google Scholar 

  305. Xue, X. et al. CMOS-based cryogenic control of silicon quantum circuits. Nature 593, 205–210 (2021).

    Article  ADS  Google Scholar 

  306. Jang, W. et al. Single-shot readout of a driven hybrid qubit in a GaAs double quantum dot. Nano Lett. 21, 4999–5005 (2021).

    Article  ADS  Google Scholar 

  307. Jirovec, D. et al. A singlet-triplet hole spin qubit in planar Ge. Nat. Mater. 20, 1106–1112 (2021).

    Article  ADS  Google Scholar 

  308. Harvey-Collard, P. et al. Circuit quantum electrodynamics with two remote electron spins. Preprint at https://arxiv.org/abs/2108.01206 (2021).

  309. Liu, Y.-Y. et al. Magnetic-gradient-free two-axis control of a valley spin qubit in Si x Ge 1-x. Phys. Rev. Appl. 16, 024029 (2021).

    Article  ADS  Google Scholar 

  310. Mortemousque, P.-A. et al. Enhanced spin coherence while displacing electron in a two-dimensional array of quantum dots. PRX Quantum 2, 030331 (2021).

    Article  ADS  Google Scholar 

  311. Spence, C. et al. Spin-valley coupling anisotropy and noise in CMOS quantum dots. Preprint at http://arxiv.org/abs/2109.13557 (2021).

  312. Fedele, F. et al. Simultaneous Operations in a two-dimensional array of singlet-triplet qubits. PRX Quantum 2, 040306 (2021).

    Article  ADS  Google Scholar 

  313. Johnson, M. A. I. et al. Beating the thermal limit of qubit initialization with a Bayesian ‘Maxwell’s demon’. Preprint at https://arxiv.org/abs/2110.02046 (2021).

  314. Cai, X., Connors, E. J. & Nichol, J. M. Coherent spin-valley oscillations in silicon. Preprint at http://arxiv.org/abs/2111.14847 (2021).

  315. Ha, W. et al. A flexible design platform for Si/SiGe exchange-only qubits with low disorder. Nano Lett. 22, 1443–1448 (2021).

    Article  ADS  Google Scholar 

  316. Mills, A. R. et al. Two-qubit silicon quantum processor with operation fidelity exceeding 99%. Preprint at http://arxiv.org/abs/2111.11937 (2021).

  317. Blumoff, J. Z. et al. Fast and high-fidelity state preparation and measurement in triple-quantum-dot spin qubits. Preprint at http://arxiv.org/abs/2112.09801 (2021).

  318. Gächter, L. M. et al. Single-shot readout in graphene quantum dots. Preprint at http://arxiv.org/abs/2112.12091 (2021).

  319. Mądzik, M. T. et al. Precision tomography of a three-qubit donor quantum processor in silicon. Nature 601, 348–353 (2022).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  321. Wang, K. et al. Ultrafast coherent control of a hole spin qubit in a germanium quantum dot. Nat. Commun. 13, 206 (2022).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  323. Evans, T. J. et al. Fast Bayesian tomography of a two-qubit gate set in silicon. Phys. Rev. Appl. 17, 024068 (2022).

    Article  ADS  Google Scholar 

  324. Jock, R. M. et al. A silicon Singlet–Triplet qubit driven by spin-valley coupling. Nat. Commun. 13, 641 (2022).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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Acknowledgements

We thank T. Nakajima, A. Noiri, K. Takeda and other members of Seigo Tarucha laboratory in RIKEN for discussions that were invaluable for preparing this Technical Review. We also thank L. Camenzind, M. Delbecq, G. Katsaros, B. Kratochwil, F. Kuemmeth, T. Meunier, A. Morello, T. Nakajima, A. Noiri, M. Reed and M. Veldhorst for providing feedback on early versions of the review. We thank A. Morello for pointing out ref.60 to us. Finally, we acknowledge financial support from CREST JST (JPMJCR1675), the Swiss National Science Foundation (SNSF) and NCCR SPIN.

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  1. RIKEN Center for Emergent Matter Science (CEMS), Wako, Japan

    Peter Stano & Daniel Loss

  2. Institute of Physics, Slovak Academy of Sciences, Bratislava, Slovakia

    Peter Stano

  3. RIKEN Center for Quantum Computing (RQC), Wako, Japan

    Daniel Loss

  4. Department of Physics, University of Basel, Basel, Switzerland

    Daniel Loss

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Stano, P., Loss, D. Review of performance metrics of spin qubits in gated semiconducting nanostructures. Nat Rev Phys 4, 672–688 (2022). https://doi.org/10.1038/s42254-022-00484-w

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