Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Semiconductor qubits in practice

Abstract

In the past decade, semiconducting qubits have made great strides in overcoming decoherence, improving the prospects for scalability and have become one of the leading contenders for the development of large-scale quantum circuits. In this Review, we describe the current state of the art in semiconductor charge and spin qubits based on gate-controlled semiconductor quantum dots, shallow dopants and colour centres in wide-bandgap materials. We frame the relative strengths of the different semiconductor qubit implementations in the context of applications such as quantum simulation, computing, sensing and networks. By highlighting the status and future perspectives of the basic types of semiconductor qubits, this Review aims to serve as a technical introduction for non-specialists and a forward-looking reference for scientists intending to work in this field.

Key points

  • Semiconductor qubits span an entire ecosystem and are extremely versatile in terms of quantum applications, particularly viewed through the lenses of quantum simulation, sensing, computation and communication.

  • Controlling the charge degree of freedom in gated quantum dots is important for sensing of quantum objects, readout and light–matter coupling.

  • Gate-controlled spin qubits have demonstrated long coherence times, fast two-qubit gates and fault-tolerant operation, with promising prospects for quantum computation.

  • Shallow dopants have shown some of the longest coherence times in the solid state and high sensitivity to magnetic fields, relevant for quantum memories and sensing.

  • Optically active defects have shown great promise as in situ sensors, and their natural ability to serve as spin–photon interfaces makes them suitable for long-distance quantum communication.

  • Looking beyond a fault-tolerant quantum computer, semiconductor qubits will find diverse applications such as light–matter networks, scanning sensors, quantum memories, global cryptographic networks and small-scale designer simulation arrays.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: Semiconductor qubits and their potential applications.
Fig. 2: Material systems hosting semiconductor qubits.
Fig. 3: Readout techniques for semiconductor qubits.
Fig. 4: Manipulation methods for semiconducting qubits.
Fig. 5: Future outlook for semiconductor qubits.

References

  1. DiVincenzo, D. The physical implementation of quantum computation. Fortschr. Phys. 48, 771–783 (2008).

    MATH  Article  Google Scholar 

  2. Hensen, B. et al. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature 526, 682–686 (2015).

    ADS  Article  Google Scholar 

  3. Aslam, N. et al. Nanoscale nuclear magnetic resonance with chemical resolution. Science 357, 67–71 (2017).

    ADS  Article  Google Scholar 

  4. Boss, J. M., Cujia, K. S., Zopes, J. & Degen, C. L. Quantum sensing with arbitrary frequency resolution. Science 356, 837–840 (2017).

    ADS  Article  Google Scholar 

  5. Michler, P. Quantum Dots for Quantum Information Technologies (Springer, 2017).

  6. Kjaergaard, M. et al. Superconducting qubits: Current state of play. Annu. Rev. Condens. Matter Phys. 11, 369–395 (2020).

    Article  Google Scholar 

  7. Lutchyn, R. M. et al. Majorana zero modes in superconductor–semiconductor heterostructures. Nat. Rev. Mater. 3, 52–68 (2018).

    ADS  Article  Google Scholar 

  8. Reed, M. et al. Observation of discrete electronic states in a zero-dimensional semiconductor nanostructure. Phys. Rev. Lett. 60, 535–537 (1988).

    ADS  Article  Google Scholar 

  9. Elzerman, J. M. et al. Few-electron quantum dot circuit with integrated charge read out. Phys. Rev. B 67, 161308 (2003).

    ADS  Article  Google Scholar 

  10. 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).

    ADS  Article  Google Scholar 

  11. 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).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  13. Schoenfield, J. S., Freeman, B. M. & Jiang, H. Coherent manipulation of valley states at multiple charge configurations of a silicon quantum dot device. Nat. Commun. 8, 64 (2017).

    ADS  Article  Google Scholar 

  14. 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).

    ADS  Article  Google Scholar 

  15. 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 (2017).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  20. Burkard, G., Gullans, M. J., Mi, X. & Petta, J. R. Superconductor–semiconductor hybrid-circuit quantum electrodynamics. Nat. Rev. Phys. 2, 129–140 (2020).

    Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    Google Scholar 

  25. 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).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  27. 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).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  30. 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).

    ADS  Article  Google Scholar 

  31. 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).

    ADS  Article  Google Scholar 

  32. Mehl, S. & DiVincenzo, D. P. Noise-protected gate for six-electron double-dot qubit. Phys. Rev. B 88, 161408 (2013).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  35. Levy, J. Universal quantum computation with spin-1/2 pairs and heisenberg exchange. Phys. Rev. Lett. 89, 147902 (2002).

    ADS  MathSciNet  MATH  Article  Google Scholar 

  36. Benjamin, S. C. Simple pulses for universal quantum computation with a Heisenberg ABAB chain. Phys. Rev. A 64, 054303 (2001).

    ADS  Article  Google Scholar 

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

    Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  MathSciNet  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  41. Kornich, V., Kloeffel, C. & Loss, D. Phonon-mediated decay of singlet-triplet qubits in double quantum dots. Phys. Rev. B 89, 085410 (2014).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  44. DiVincenzo, D., Bacon, C., Kempe, J., Burkard, G. & Whaley, K. Universal quantum computation with the exchange interaction. Nature 408, 339–342 (2000).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  46. Russ, M. & Burkard, G. Three-electron spin qubits. J. Phys. Condens. Matter 29, 393001 (2017).

    Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  48. Russ, M., Petta, J. R. & Burkard, G. Quadrupolar exchange-only spin qubit. Phys. Rev. Lett. 121, 177701 (2018).

    ADS  Article  Google Scholar 

  49. Sala, A., Qvist, J. H. & Danon, J. Highly tunable exchange-only singlet-only qubit in a GaAs triple quantum dot. Phys. Rev. Res. 2, 012062 (2020).

    Article  Google Scholar 

  50. Vukušić, L., Kukučka, J., Watzinger, H. & Katsaros, G. Fast hole tunneling times in germanium hut wires probed by single-shot reflectometry. Nano Lett. 17, 5706 (2017).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  52. 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).

    ADS  Article  Google Scholar 

  53. Scappucci, G. et al. The germanium quantum information route. Nat. Rev. Mater. https://doi.org/10.1038/s41578-020-00262-z (2020).

    Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  61. Ono, K., Austing, D. G., Tokura, Y. & Tarucha, S. Current rectification by Pauli exclusion in a weakly coupled double quantum dot system. Science 297, 156–158 (2002).

    Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    Article  Google Scholar 

  65. 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 

  66. Pla, J. J. et al. High-fidelity readout and control of a nuclear spin qubit in silicon. Nature 496, 334–338 (2013).

    ADS  Article  Google Scholar 

  67. 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).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  69. Nadj-Perge, S., Frolov, S., Bakkers, E. & Kouwenhoven, L. Spin–orbit qubit in a semiconductor nanowire. Nature 468, 1084–1087 (2010).

    ADS  Article  Google Scholar 

  70. 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).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  72. Golovach, V. N., Borhani, M. & Loss, D. Electric-dipole-induced spin resonance in quantum dots. Phys. Rev. B 74, 165319 (2006).

    ADS  Article  Google Scholar 

  73. Pioro-Ladriere, M. et al. Electrically driven single-electron spin resonance in a slanting Zeeman field. Nat. Phys. 4, 776–779 (2008).

    Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  MathSciNet  MATH  Article  Google Scholar 

  76. Malinowski, F. et al. Notch filtering the nuclear environment of a spin qubit. Nat. Nanotechnol. 12, 16–20 (2017).

    ADS  Article  Google Scholar 

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

    Google Scholar 

  78. Mortemousque, P. et al. Coherent control of individual electron spins in a two dimensional array of quantum dots. Nat. Nanotechnol. https://doi.org/10.1038/s41565-020-00816-w (2020).

    Article  Google Scholar 

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

    Google Scholar 

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

    ADS  Article  Google Scholar 

  81. Dehollain, J. P. et al. Nagaoka ferromagnetism observed in a quantum dot plaquette. Nature 579, 528–533 (2020).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  84. Ansaloni, F. et al. Single-electron control in a foundry-fabricated two-dimensional qubit array. Nat Commun. 11, 6399 (2020).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  86. Itoh, K. M. & Watanabe, H. Isotope engineering of silicon and diamond for quantum computing and sensing applications. MRS Commun. 4, 143–157 (2014).

    Article  Google Scholar 

  87. Zwanenburg, F. A. et al. Silicon quantum electronics. Rev. Mod. Phys. 85, 961 (2013).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  90. Tahan, C. Democratizing spin qubits. Preprint at arXiv 2001.08251 (2020).

  91. Hoffman, S., Schrade, C., Klinovaja, J. & Loss, D. Universal quantum computation with hybrid spin-Majorana qubits. Phys. Rev. B 94, 045316 (2016).

    ADS  Article  Google Scholar 

  92. Hensgens, T. et al. Quantum simulation of a Fermi–Hubbard model using a semiconductor quantum dot array. Nature 548, 70–73 (2017).

    ADS  Article  Google Scholar 

  93. Veldhorst, M., Eenink, H., Yang, C. & Dzurak, A. Silicon CMOS architecture for a spin-based quantum computer. Nat. Commun. 8, 1766 (2017).

    ADS  Article  Google Scholar 

  94. Vandersypen, L. et al. Interfacing spin qubits in quantum dots and donors—hot, dense, and coherent. Npj Quantum Inf. 3, 34 (2017).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  98. Trif, M., Golovach, V. N. & Loss, D. Spin dynamics in InAs nanowire quantum dots coupled to a transmission line. Phys. Rev. B 77, 045434 (2008).

    ADS  Article  Google Scholar 

  99. 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 (2020).

    ADS  Article  Google Scholar 

  100. Kohn, W. & Luttinger, J. Theory of donor states in silicon. Phys. Rev. 98, 915 (1955).

    ADS  MATH  Article  Google Scholar 

  101. Feher, G. & Gere, E. Electron spin resonance experiments on donors in silicon. II. Electron spin relaxation effects. Phys. Rev. 114, 1245 (1959).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  103. Tyryshkin, A. et al. Coherence of spin qubits in silicon. J. Phys. Condens. Matter 18, S783 (2006).

    Article  Google Scholar 

  104. Tyryshkin, A. M. et al. Electron spin coherence exceeding seconds in high-purity silicon. Nat. Mater. 11, 143–147 (2012).

    ADS  Article  Google Scholar 

  105. Morse, K. J. et al. Zero-field optical magnetic resonance study of phosphorus donors in 28-silicon. Phys. Rev. B 97, 115205 (2018).

    ADS  Article  Google Scholar 

  106. Ma, W.-L., Wolfowicz, G., Li, S.-S., Morton, J. J. L. & Liu, R.-B. Classical nature of nuclear spin noise near clock transitions of bi donors in silicon. Phys. Rev. B 92, 161403 (2015).

    ADS  Article  Google Scholar 

  107. Witzel, W., Hu, X. & Sarma, S. D. Decoherence induced by anisotropic hyperfine interaction in Si spin qubits. Phys. Rev. B 76, 035212 (2007).

    ADS  Article  Google Scholar 

  108. Morton, J. J. et al. Solid-state quantum memory using the 31P nuclear spin. Nature 455, 1085–1088 (2008).

    ADS  Article  Google Scholar 

  109. Simmons, S. et al. Entanglement in a solid-state spin ensemble. Nature 470, 69–72 (2011).

    ADS  Article  Google Scholar 

  110. Steger, M. et al. Quantum information storage for over 180 s using donor spins in a 28Si “semiconductor vacuum”. Science 336, 1280–1283 (2012).

    ADS  Article  Google Scholar 

  111. Saeedi, K. et al. Room-temperature quantum bit storage exceeding 39 minutes using ionized donors in silicon-28. Science 342, 830–833 (2013).

    ADS  Article  Google Scholar 

  112. Bienfait, A. et al. Controlling spin relaxation with a cavity. Nature 531, 74–77 (2016).

    ADS  Article  Google Scholar 

  113. Fuechsle, M. et al. A single-atom transistor. Nat. Nanotechnol. 7, 242–246 (2012).

    ADS  Article  Google Scholar 

  114. Jamieson, D. N. et al. Controlled shallow single-ion implantation in silicon using an active substrate for sub-20-keV ions. Appl. Phys. Lett. 86, 202101 (2005).

    ADS  Article  Google Scholar 

  115. 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).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  122. Gumann, P. et al. NMR study of optically hyperpolarized phosphorus donor nuclei in silicon. Phys. Rev. B 98, 180405 (2018).

    ADS  Article  Google Scholar 

  123. Dreher, L., Hoehne, F., Stutzmann, M. & Brandt, M. S. Nuclear spins of ionized phosphorus donors in silicon. Phys. Rev. Lett. 108, 027602 (2012).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  125. Dehollain, J. P. et al. Bell’s inequality violation with spins in silicon. Nat. Nanotechnol. 11, 242–246 (2016).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  128. Wolfowicz, G. et al. Atomic clock transitions in silicon-based spin qubits. Nat. Nanotechnol. 8, 561–564 (2013).

    ADS  Article  Google Scholar 

  129. Asaad, S. et al. Coherent electrical control of a single high-spin nucleus in silicon. Nature 579, 205–209 (2020).

    ADS  Article  Google Scholar 

  130. Kobayashi, T. Engineering long spin coherence times of spin–orbit qubits in silicon. Nat. Mater. 20, 38–42 (2021).

    ADS  Article  Google Scholar 

  131. Morello, A., Pla, J. J., Bertet, P. & Jamieson, D. N. Donor spins in silicon for quantum technologies. Adv. Quantum Technol. 3, 2000005 (2020).

    Article  Google Scholar 

  132. Franke, D. P. et al. Interaction of strain and nuclear spins in silicon: Quadrupolar effects on ionized donors. Phys. Rev. Lett. 115, 057601 (2015).

    ADS  Article  Google Scholar 

  133. Zhang, Q. et al. Single rare-earth ions as atomic-scale probes in ultrascaled transistors. Nano Lett. 19, 5025–5030 (2019).

    ADS  Article  Google Scholar 

  134. Pezzè, L., Smerzi, A., Oberthaler, M. K., Schmied, R. & Treutlein, P. Quantum metrology with nonclassical states of atomic ensembles. Rev. Mod. Phys. 90, 035005 (2018).

    ADS  MathSciNet  Article  Google Scholar 

  135. Matsuzaki, Y., Benjamin, S. C. & Fitzsimons, J. Magnetic field sensing beyond the standard quantum limit under the effect of decoherence. Phys. Rev. A 84, 012103 (2011).

    ADS  Article  Google Scholar 

  136. Wüst, G. et al. Role of the electron spin in determining the coherence of the nuclear spins in a quantum dot. Nat. Nanotechnol. 11, 885–889 (2016).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  139. Salfi, J. et al. Quantum simulation of the Hubbard model with dopant atoms in silicon. Nat. Commun. 7, 11342 (2016).

    ADS  Article  Google Scholar 

  140. Sieberer, L. M. et al. Digital quantum simulation, Trotter errors, and quantum chaos of the kicked top. Npj Quantum Inf. 5, 78 (2019).

    ADS  Article  Google Scholar 

  141. Mourik, V. et al. Exploring quantum chaos with a single nuclear spin. Phys. Rev. E 98, 042206 (2018).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  143. González-Zalba, M. F. et al. An exchange-coupled donor molecule in silicon. Nano Lett. 14, 5672–5676 (2014).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  145. Kalra, R., Laucht, A., Hill, C. D. & Morello, A. Robust two-qubit gates for donors in silicon controlled by hyperfine interactions. Phys. Rev. X 4, 021044 (2014).

    Google Scholar 

  146. 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 

  147. Koiller, B., Hu, X. & Sarma, S. D. Exchange in silicon-based quantum computer architecture. Phys. Rev. Lett. 88, 027903 (2001).

    ADS  Article  Google Scholar 

  148. Srinivasa, V., Xu, H. & Taylor, J. M. Tunable spin-qubit coupling mediated by a multielectron quantum dot. Phys. Rev. Lett. 114, 226803 (2015).

    ADS  Article  Google Scholar 

  149. Mohiyaddin, F. A. et al. Transport of spin qubits with donor chains under realistic experimental conditions. Phys. Rev. B 94, 045314 (2016).

    ADS  Article  Google Scholar 

  150. Trifunovic, L., Pedrocchi, F. L. & Loss, D. Long-distance entanglement of spin qubits via ferromagnet. Phys. Rev. X 3, 041023 (2013).

    Google Scholar 

  151. Salfi, J., Mol, J. A., Culcer, D. & Rogge, S. Charge-insensitive single-atom spin-orbit qubit in silicon. Phys. Revi. Lett. 116, 246801 (2016).

    ADS  Article  Google Scholar 

  152. Calderon, M., Koiller, B., Hu, X. & Sarma, S. D. Quantum control of donor electrons at the Si–SiO2 interface. Phys. Rev. Lett. 96, 096802 (2006).

    ADS  Article  Google Scholar 

  153. Tosi, G. et al. Silicon quantum processor with robust long-distance qubit couplings. Nat. Commun. 8, 450 (2017).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  155. Hill, C. D. et al. A surface code quantum computer in silicon. Sci. Adv. 1, e1500707 (2015).

    ADS  Article  Google Scholar 

  156. O’Gorman, J., Nickerson, N. H., Ross, P., Morton, J. J. & Benjamin, S. C. A silicon-based surface code quantum computer. Npj Quantum Inf. 2, 15019 (2016).

    ADS  Article  Google Scholar 

  157. Pica, G., Lovett, B. W., Bhatt, R. N., Schenkel, T. & Lyon, S. A. Surface code architecture for donors and dots in silicon with imprecise and nonuniform qubit couplings. Phys. Rev. B 93, 035306 (2016).

    ADS  Article  Google Scholar 

  158. Wesenberg, J. H. et al. Quantum computing with an electron spin ensemble. Phys. Rev. Lett. 103, 070502 (2009).

    ADS  Article  Google Scholar 

  159. Morse, K. J. et al. A photonic platform for donor spin qubits in silicon. Sci. Adv. 3, e1700930 (2017).

    ADS  Article  Google Scholar 

  160. Yan, X. et al. A quantum computer architecture based on silicon donor qubits coupled by photons. Adv. Quantum Technol. 3, 2000011 (2020).

    Article  Google Scholar 

  161. Yin, C. et al. Optical addressing of an individual erbium ion in silicon. Nature 497, 91–94 (2013).

    ADS  Article  Google Scholar 

  162. Dutt, M. V. G. et al. Quantum register based on individual electronic and nuclear spin qubits in diamond. Science 316, 1312–1316 (2007).

    Article  Google Scholar 

  163. Dolde, F. et al. Room-temperature entanglement between single defect spins in diamond. Nat. Phys. 9, 139–143 (2013).

    Article  Google Scholar 

  164. Neumann, P. et al. Quantum register based on coupled electron spins in a room-temperature solid. Nat. Phys. 6, 249–253 (2010).

    Article  Google Scholar 

  165. Bradley, C. E. et al. A ten-qubit solid-state spin register with quantum memory up to one minute. Phys. Rev. X 9, 031045 (2019).

    Google Scholar 

  166. Maze, J. R. et al. Nanoscale magnetic sensing with an individual electronic spin in diamond. Nature 455, 644–647 (2008).

    ADS  Article  Google Scholar 

  167. Taylor, J. M. et al. High-sensitivity diamond magnetometer with nanoscale resolution. Nat. Phys. 4, 810–816 (2008).

    Article  Google Scholar 

  168. Lovchinsky, I. et al. Nuclear magnetic resonance detection and spectroscopy of single proteins using quantum logic. Science 351, 836–841 (2016).

    ADS  MathSciNet  MATH  Article  Google Scholar 

  169. Schmitt, S. et al. Submillihertz magnetic spectroscopy performed with a nanoscale quantum sensor. Science 356, 832–837 (2017).

    ADS  Article  Google Scholar 

  170. Togan, E. et al. Quantum entanglement between an optical photon and a solid-state spin qubit. Nature 466, 730–734 (2010).

    ADS  Article  Google Scholar 

  171. Warburton, R. J. Single spins in self-assembled quantum dots. Nat. Mater. 12, 483–493 (2013).

    ADS  Article  Google Scholar 

  172. Widmann, M. et al. Coherent control of single spins in silicon carbide at room temperature. Nat. Mater. 14, 164–168 (2015).

    ADS  Article  Google Scholar 

  173. Robledo, L. et al. High-fidelity projective read-out of a solid-state spin quantum register. Nature 477, 574–578 (2011).

    ADS  Article  Google Scholar 

  174. Nagy, R. et al. High-fidelity spin and optical control of single silicon-vacancy centres in silicon carbide. Nat. Commun. 10, 1954 (2019).

    ADS  Article  Google Scholar 

  175. Abobeih, M. H. et al. One-second coherence for a single electron spin coupled to a multi-qubit nuclear-spin environment. Nat. Commun. 9, 2552 (2018).

    ADS  Article  Google Scholar 

  176. Sukachev, D. D. et al. Silicon-vacancy spin qubit in diamond: a quantum memory exceeding 10 ms with single-shot state readout. Phys. Rev. Lett. 119, 223602 (2017).

    ADS  Article  Google Scholar 

  177. Raha, M. et al. Optical quantum nondemolition measurement of a single rare earth ion qubit. Nat. Commun. 11, 1605 (2020).

    Article  Google Scholar 

  178. Hadden, J. P. et al. Strongly enhanced photon collection from diamond defect centers under microfabricated integrated solid immersion lenses. Appl. Phys. Lett. 97, 241901 (2010).

    ADS  Article  Google Scholar 

  179. Dibos, A. M., Raha, M., Phenicie, C. M. & Thompson, J. D. Atomic source of single photons in the telecom band. Phys. Rev. Lett. 120, 243601 (2018).

    ADS  Article  Google Scholar 

  180. Hausmann, B. J. M. et al. Integrated diamond networks for quantum nanophotonics. Nano Lett. 12, 1578–1582 (2012).

    ADS  Article  Google Scholar 

  181. Gould, M. et al. Large-scale GaP-on-diamond integrated photonics platform for NV center-based quantum information. J. Opt. Soc. Am. B 33, B35–B42 (2016).

    ADS  Article  Google Scholar 

  182. Barclay, P. E., Fu, K.-M. C., Santori, C., Faraon, A. & Beausoleil, R. G. Hybrid nanocavity resonant enhancement of color center emission in diamond. Phys. Rev. X 1, 011007 (2011).

    Google Scholar 

  183. Steiner, M., Neumann, P., Beck, J., Jelezko, F. & Wrachtrup, J. Universal enhancement of the optical readout fidelity of single electron spins at nitrogen-vacancy centers in diamond. Phys. Rev. B 81, 035205 (2010).

    ADS  Article  Google Scholar 

  184. Shields, B. J., Unterreithmeier, Q. P., De Leon, N. P., Park, H. & Lukin, M. D. Efficient readout of a single spin state in diamond via spin-to-charge conversion. Phys. Rev. Lett. 114, 136402 (2015).

    ADS  Article  Google Scholar 

  185. Jiang, L. et al. Repetitive readout of a single electronic spin via quantum logic with nuclear spin ancillae. Science 326, 267–272 (2009).

    ADS  Article  Google Scholar 

  186. Hopper, D., Shulevitz, H. & Bassett, L. Spin readout techniques of the nitrogen-vacancy center in diamond. Micromachines 9, 437 (2018).

    Article  Google Scholar 

  187. Siyushev, P. et al. Photoelectrical imaging and coherent spin-state readout of single nitrogen-vacancy centers in diamond. Science 363, 728–731 (2019).

    ADS  Article  Google Scholar 

  188. Niethammer, M. et al. Coherent electrical readout of defect spins in silicon carbide by photo-ionization at ambient conditions. Nat. Commun. 10, 5569 (2019).

    ADS  Article  Google Scholar 

  189. Acosta, V. M. et al. Dynamic stabilization of the optical resonances of single nitrogen-vacancy centers in diamond. Phys. Rev. Lett. 108, 206401 (2012).

    ADS  Article  Google Scholar 

  190. Anderson, C. P. et al. Electrical and optical control of single spins integrated in scalable semiconductor devices. Science 366, 1225–1230 (2019).

    ADS  Article  Google Scholar 

  191. Lee, D., Lee, K. W., Cady, J. V., Ovartchaiyapong, P. & Jayich, A. C. B. Topical review: spins and mechanics in diamond. J. Opt. 19, 033001 (2017).

    ADS  Article  Google Scholar 

  192. Macquarrie, E. R., Gosavi, T. A., Jungwirth, N. R., Bhave, S. A. & Fuchs, G. D. Mechanical spin control of nitrogen-vacancy centers in diamond. Phys. Rev. Lett. 111, 227602 (2013).

    ADS  Article  Google Scholar 

  193. Tchebotareva, A. et al. Entanglement between a diamond spin qubit and a photonic time-bin qubit at telecom wavelength. Phys. Rev. Lett. 123, 063601 (2019).

    ADS  Article  Google Scholar 

  194. Heremans, F. J., Yale, C. G. & Awschalom, D. D. Control of spin defects in wide-bandgap semiconductors for quantum technologies. Proc. IEEE 104, 2009–2023 (2016).

    Article  Google Scholar 

  195. Awschalom, D. D., Hanson, R., Wrachtrup, J. & Zhou, B. B. Quantum technologies with optically interfaced solid-state spins. Nat. Photonics 12, 516–527 (2018).

    ADS  Article  Google Scholar 

  196. Atatüre, M., Englund, D., Vamivakas, N., Lee, S.-Y. & Wrachtrup, J. Material platforms for spin-based photonic quantum technologies. Nat. Rev. Mater. 3, 38–51 (2018).

    ADS  Article  Google Scholar 

  197. Weber, J. R. et al. Quantum computing with defects. Proc. Natl Acad. Sci. USA 107, 8513–8518 (2010).

    ADS  Article  Google Scholar 

  198. Bassett, L. C., Alkauskas, A., Exarhos, A. L. & Fu, K.-M. C. Quantum defects by design. Nanophotonics 8, 1867–1888 (2019).

    Article  Google Scholar 

  199. Steinert, S. et al. High sensitivity magnetic imaging using an array of spins in diamond. Rev. Sci. Instrum. 81, 043705 (2010).

    ADS  Article  Google Scholar 

  200. Staudacher, T. et al. Nuclear magnetic resonance spectroscopy on a (5-nanometer) 3 sample volume. Science 339, 561–563 (2013).

    ADS  Article  Google Scholar 

  201. Kucsko, G. et al. Nanometre-scale thermometry in a living cell. Nature 500, 54–58 (2013).

    ADS  Article  Google Scholar 

  202. Chu, Y. et al. Coherent optical transitions in implanted nitrogen vacancy centers. Nano Lett. 14, 1982–1986 (2014).

    ADS  Article  Google Scholar 

  203. Maurer, P. C. et al. Room-temperature quantum bit memory exceeding one second. Science 336, 1283–1286 (2012).

    ADS  Article  Google Scholar 

  204. Evans, R. E., Sipahigil, A., Sukachev, D. D., Zibrov, A. S. & Lukin, M. D. Narrow-linewidth homogeneous optical emitters in diamond nanostructures via silicon ion implantation. Phys. Rev. Appl. 5, 044010 (2016).

    ADS  Article  Google Scholar 

  205. Rogers, L. J. et al. All-optical initialization, readout, and coherent preparation of single silicon-vacancy spins in diamond. Phys. Rev. Lett. 113, 263602 (2014).

    ADS  Article  Google Scholar 

  206. Nguyen, C. T. et al. Quantum network nodes based on diamond qubits with an efficient nanophotonic interface. Phys. Rev. Lett. 123, 183602 (2019).

    ADS  Article  Google Scholar 

  207. Nguyen, C. T. et al. An integrated nanophotonic quantum register based on silicon-vacancy spins in diamond. Phys. Rev. B 100, 165428 (2019).

    ADS  Article  Google Scholar 

  208. Sohn, Y.-I. et al. Controlling the coherence of a diamond spin qubit through its strain environment. Nat. Commun. 9, 2012 (2018).

    ADS  Article  Google Scholar 

  209. Iwasaki, T. et al. Tin-vacancy quantum emitters in diamond. Phys. Rev. Lett. 119, 253601 (2017).

    ADS  Article  Google Scholar 

  210. Trusheim, M. E. et al. Lead-related quantum emitters in diamond. Phys. Rev. B 99, 075430 (2019).

    ADS  Article  Google Scholar 

  211. Siyushev, P. et al. Optical and microwave control of germanium-vacancy center spins in diamond. Phys. Rev. B 96, 081201 (2017).

    ADS  Article  Google Scholar 

  212. Trusheim, M. E. et al. Transform-limited photons from a coherent tin-vacancy spin in diamond. Phys. Rev. Lett. 124, 023602 (2020).

    ADS  Article  Google Scholar 

  213. Rose, B. C. et al. Observation of an environmentally insensitive solid-state spin defect in diamond. Science 361, 60–63 (2018).

    ADS  Article  Google Scholar 

  214. Green, B. L. et al. Neutral silicon-vacancy center in diamond: spin polarization and lifetimes. Phys. Rev. Lett. 119, 096402 (2017).

    ADS  Article  Google Scholar 

  215. Rose, B. C. et al. Strongly anisotropic spin relaxation in the neutral silicon vacancy center in diamond. Phys. Rev. B 98, 235140 (2018).

    ADS  Article  Google Scholar 

  216. Li, Q., Davanço, M. & Srinivasan, K. Efficient and low-noise single-photon-level frequency conversion interfaces using silicon nanophotonics. Nat. Photonics 10, 406–414 (2016).

    ADS  Article  Google Scholar 

  217. Lukin, D. M. et al. 4H-silicon-carbide-on-insulator for integrated quantum and nonlinear photonics. Nat. Photonics 14, 330–334 (2020).

    ADS  Article  Google Scholar 

  218. Lohrmann, A., Johnson, B. C., McCallum, J. C. & Castelletto, S. A review on single photon sources in silicon carbide. Rep. Prog. Phys. 80, 034502 (2017).

    ADS  Article  Google Scholar 

  219. Son, N. T. et al. Developing silicon carbide for quantum spintronics. Appl. Phys. Lett. 116, 190501 (2020).

    ADS  Article  Google Scholar 

  220. Christle, D. J. et al. Isolated electron spins in silicon carbide with millisecond coherence times. Nat. Mater. 14, 160–163 (2015).

    ADS  Article  Google Scholar 

  221. Bourassa, A. Entanglement and control of single nuclear spins in isotopically engineered silicon carbide. Nat. Mater. 19, 1319–1325 (2020).

    ADS  Article  Google Scholar 

  222. Zargaleh, S. A. Evidence for near-infrared photoluminescence of nitrogen vacancy centers in 4H-SiC. Phys. Rev. B 94, 060102 (2016).

    ADS  Article  Google Scholar 

  223. Wolfowicz, G. et al. Vanadium spin qubits as telecom quantum emitters in silicon carbide. Sci. Adv. 6, eaaz1192 (2020).

    ADS  Article  Google Scholar 

  224. Crook, A. L. et al. Purcell enhancement of a single silicon carbide color center with coherent spin control. Nano Lett. 20, 3427–3434 (2020).

    ADS  Article  Google Scholar 

  225. Lukin, D. M. et al. Spectrally reconfigurable quantum emitters enabled by optimized fast modulation. Npj Quantum Inf. 6, 80 (2020).

    ADS  Article  Google Scholar 

  226. Thiel, C., Böttger, T. & Cone, R. Rare-earth-doped materials for applications in quantum information storage and signal processing. J. Lumin. 131, 353–361 (2011).

    Article  Google Scholar 

  227. Zhong, T. et al. Nanophotonic rare-earth quantum memory with optically controlled retrieval. Science 357, 1392–1395 (2017).

    ADS  MathSciNet  Article  Google Scholar 

  228. Zhong, T. et al. Optically addressing single rare-earth ions in a nanophotonic cavity. Phys. Rev. Lett. 121, 183603 (2018).

    ADS  Article  Google Scholar 

  229. Kornher, T. et al. Sensing individual nuclear spins with a single rare-earth electron spin. Phys. Rev. Lett. 124, 170402 (2020).

    ADS  Article  Google Scholar 

  230. McAuslan, D. L., Bartholomew, J. G., Sellars, M. J. & Longdell, J. J. Reducing decoherence in optical and spin transitions in rare-earth-metal-ion-doped materials. Phys. Rev. A 85, 032339 (2012).

    ADS  Article  Google Scholar 

  231. Phenicie, C. M. et al. Narrow optical line widths in erbium implanted in TiO2. Nano Lett. 19, 8928–8933 (2019).

    ADS  Article  Google Scholar 

  232. Kornher, T. et al. Production yield of rare-earth ions implanted into an optical crystal. Appl. Phys. Lett. 108, 053108 (2016).

    ADS  Article  Google Scholar 

  233. Ferrenti, A. M., de Leon, N. P., Thompson, J. D. & Cava, R. J. Identifying candidate hosts for quantum defects via data mining. Npj Comput. Mater. 6, 126 (2020).

    ADS  Article  Google Scholar 

  234. Andrich, P. et al. Microscale-resolution thermal mapping using a flexible platform of patterned quantum sensors. Nano Lett. 18, 4684–4690 (2018).

    ADS  Article  Google Scholar 

  235. Knowles, H. S., Kara, D. M. & Atatüre, M. Observing bulk diamond spin coherence in high-purity nanodiamonds. Nat. Mater. 13, 21–25 (2014).

    ADS  Article  Google Scholar 

  236. Boudou, J.-P. et al. High yield fabrication of fluorescent nanodiamonds. Nanotechnology 20, 235602 (2009).

    ADS  Article  Google Scholar 

  237. Andrich, P. et al. Engineered micro- and nanoscale diamonds as mobile probes for high-resolution sensing in fluid. Nano Lett. 14, 4959–4964 (2014).

    ADS  Article  Google Scholar 

  238. Beke, D. et al. Room-temperature defect qubits in ultrasmall nanocrystals. J. Phys. Chem. Lett. 11, 1675–1681 (2020).

    Article  Google Scholar 

  239. Trusheim, M. E. et al. Scalable fabrication of high purity diamond nanocrystals with long-spin-coherence nitrogen vacancy centers. Nano Lett. 14, 32–36 (2014).

    ADS  Article  Google Scholar 

  240. Ryan, R. G. et al. Impact of surface functionalization on the quantum coherence of nitrogen-vacancy centers in nanodiamonds. ACS Appl. Mater. Interfaces 10, 13143–13149 (2018).

    Article  Google Scholar 

  241. Tsukahara, R. et al. Removing non-size-dependent electron spin decoherence of nanodiamond quantum sensors by aerobic oxidation. ACS Appl. Nano Mater. 2, 3701–3710 (2019).

    Article  Google Scholar 

  242. Barry, J. F. et al. Sensitivity optimization for NV-diamond magnetometry. Rev. Mod. Phys. 92, 015004 (2020).

    ADS  Article  Google Scholar 

  243. Liu, Y.-X., Ajoy, A. & Cappellaro, P. Nanoscale vector dc magnetometry via ancilla-assisted frequency up-conversion. Phys. Rev. Lett. 122, 100501 (2019).

    ADS  Article  Google Scholar 

  244. Schloss, J. M., Barry, J. F., Turner, M. J. & Walsworth, R. L. Simultaneous broadband vector magnetometry using solid-state spins. Phys. Rev. Appl. 10, 034044 (2018).

    ADS  Article  Google Scholar 

  245. Balasubramanian, G. et al. Ultralong spin coherence time in isotopically engineered diamond. Nat. Mater. 8, 383–387 (2009).

    ADS  MathSciNet  Article  Google Scholar 

  246. Laraoui, A. et al. Imaging thermal conductivity with nanoscale resolution using a scanning spin probe. Nat. Commun. 6, 8954 (2015).

    ADS  Article  Google Scholar 

  247. Pelliccione, M. et al. Scanned probe imaging of nanoscale magnetism at cryogenic temperatures with a single-spin quantum sensor. Nat. Nanotechnol. 11, 700–705 (2016).

    ADS  Article  Google Scholar 

  248. Zhou, T. X., Stöhr, R. J. & Yacoby, A. Scanning diamond NV center probes compatible with conventional AFM technology. Appl. Phys. Lett. 111, 163106 (2017).

    ADS  Article  Google Scholar 

  249. Fukami, M. et al. All-optical cryogenic thermometry based on nitrogen-vacancy centers in nanodiamonds. Phys. Rev. Appl. 12, 014042 (2019).

    ADS  Article  Google Scholar 

  250. Nguyen, C. T. et al. All-optical nanoscale thermometry with silicon-vacancy centers in diamond. Appl. Phys. Lett. 112, 203102 (2018).

    ADS  Article  Google Scholar 

  251. Anisimov, A. N. et al. Optical thermometry based on level anticrossing in silicon carbide. Sci. Rep. 6, 33301 (2016).

    ADS  Article  Google Scholar 

  252. Myers, B. A. et al. Probing surface noise with depth-calibrated spins in diamond. Phys. Rev. Lett. 113, 027602 (2014).

    ADS  Article  Google Scholar 

  253. Fávaro de Oliveira, F. et al. Tailoring spin defects in diamond by lattice charging. Nat. Commun. 8, 15409 (2017).

    ADS  Article  Google Scholar 

  254. Sangtawesin, S. et al. Origins of diamond surface noise probed by correlating single-spin measurements with surface spectroscopy. Phys. Rev. X 9, 031052 (2019).

    Google Scholar 

  255. Yao, N. et al. Scalable architecture for a room temperature solid-state quantum information processor. Nat. Commun. 3, 800 (2012).

    ADS  Article  Google Scholar 

  256. Serbyn, M. et al. Interferometric probes of many-body localization. Phys. Rev. Lett. 113, 147204 (2014).

    ADS  Article  Google Scholar 

  257. Cai, J., Retzker, A., Jelezko, F. & Plenio, M. B. A large-scale quantum simulator on a diamond surface at room temperature. Nat. Phys. 9, 168–173 (2013).

    Article  Google Scholar 

  258. Abobeih, M. H. et al. Atomic-scale imaging of a 27-nuclear-spin cluster using a quantum sensor. Nature 576, 411–415 (2019).

    ADS  Article  Google Scholar 

  259. Choi, S. et al. Observation of discrete time-crystalline order in a disordered dipolar many-body system. Nature 543, 221–225 (2017).

    ADS  Article  Google Scholar 

  260. Zu, C. et al. Experimental realization of universal geometric quantum gates with solid-state spins. Nature 514, 72–75 (2014).

    ADS  Article  Google Scholar 

  261. Bernien, H. et al. Heralded entanglement between solid-state qubits separated by three metres. Nature 497, 86–90 (2013).

    ADS  Article  Google Scholar 

  262. Dréau, A., Tcheborateva, A., Mahdaoui, A. E., Bonato, C. & Hanson, R. Quantum frequency conversion of single photons from a nitrogen-vacancy center in diamond to telecommunication wavelengths. Phys. Rev. Appl. 9, 064031 (2018).

    ADS  Article  Google Scholar 

  263. Sipahigil, A. et al. Indistinguishable photons from separated silicon-vacancy centers in diamond. Phys. Rev. Lett. 113, 113602 (2014).

    ADS  Article  Google Scholar 

  264. Sipahigil, A. et al. An integrated diamond nanophotonics platform for quantum-optical networks. Science 354, 847–850 (2016).

    ADS  Article  Google Scholar 

  265. Evans, R. E. et al. Photon-mediated interactions between quantum emitters in a diamond nanocavity. Science 362, 662–665 (2018).

    ADS  Article  Google Scholar 

  266. Zhang, Z.-H. et al. Optically detected magnetic resonance in neutral silicon vacancy centers in diamond via bound exciton states. Phys. Rev. Lett. 125, 237402 (2020).

    ADS  Article  Google Scholar 

  267. Santori, C. et al. Nanophotonics for quantum optics using nitrogen-vacancy centers in diamond. Nanotechnology 21, 274008 (2010).

    Article  Google Scholar 

  268. Bhaskar, M. K. et al. Experimental demonstration of memory-enhanced quantum communication. Nature 580, 60–64 (2020).

    ADS  Article  Google Scholar 

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

    ADS  MathSciNet  Article  Google Scholar 

  270. Connors, E. J., Nelson, J., Qiao, H., Edge, L. F. & Nichol, J. M. Low-frequency charge noise in Si/SiGe quantum dots. Phys. Rev. B 100, 165305 (2019).

    ADS  Article  Google Scholar 

  271. Mi, X., Kohler, S. & Petta, J. R. Landau-Zener interferometry of valley-orbit states in Si/SiGe double quantum dots. Phys. Rev. B 98, 161404 (2018).

    ADS  Article  Google Scholar 

  272. Dial, O. et al. Charge noise spectroscopy using coherent exchange oscillations in a singlet-triplet qubit. Phys. Rev. Lett. 110, 146804 (2013).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    Article  Google Scholar 

  275. Rong, X. et al. Experimental fault-tolerant universal quantum gates with solid-state spins under ambient conditions. Nat. Commun. 6, 8748 (2015).

    ADS  Article  Google Scholar 

  276. Glenn, D. R. et al. High-resolution magnetic resonance spectroscopy using a solid-state spin sensor. Nature 555, 351–354 (2018).

    ADS  Article  Google Scholar 

  277. Simin, D. et al. Locking of electron spin coherence above 20 ms in natural silicon carbide. Phys. Rev. B 95, 161201 (2017).

    ADS  Article  Google Scholar 

  278. Michl, J. et al. Robust and accurate electric field sensing with solid state spin ensembles. Nano Lett. 19, 4904–4910 (2019).

    ADS  Article  Google Scholar 

  279. 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).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

A.C and F.K. acknowledge support from the European Union’s Horizon 2020 research and innovation programme under grant agreement nos. 688539 and 951852. A.C. acknowledges support from the EPSRC Doctoral Prize Fellowship. S.D.F. acknowledges support from the European Union, through the Horizon 2020 research and innovation programme (grant agreement no. 810504) and from the Agence Nationale de la Recherche, through the CMOSQSPIN project (ANR-17-CE24-0009). A.M. acknowledges funding from the Australian Research Council (projects CE170100012 and DP180100969), the U.S. Army Research Office (grant no. W911NF-17-1-0200) and the Australian Department of Industry, Innovation and Science (grant no. AUSMURI00002). F.K. acknowledges support from the Independent Research Fund Denmark. N.d.L. acknowledges support from the NSF under the EFRI ACQUIRE programme (grant 1640959) and the CAREER programme (grant no. DMR-1752047), the Air Force Office of Scientific Research (award numbers FA9550-17-0158 and FA9550-18-1-0334), the Eric and Wendy Schmidt Transformative Technology Fund and the Princeton Catalysis Initiative.

Author information

Authors and Affiliations

Authors

Contributions

The authors contributed equally to all aspects of the article.

Corresponding author

Correspondence to Ferdinand Kuemmeth.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information

Nature Reviews Physics thanks the anonymous reviewers for their contribution to the peer review of this work.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Glossary

Decoherence-free subspace

A subspace of the qubit’s Hilbert space where it is decoupled from specific environmental noise, leading to an evolution that is close to completely unitary; characterized as passive error correction.

Set of universal quantum gates

A set of quantum gates to which all other quantum operations can be reduced.

Qubit Larmor frequency

Frequency of the spin qubit, rotating via Larmor precession along a static magnetic field in the laboratory frame.

Dynamical decoupling

Applying periodic sequences of short qubit control pulses, with an intended effect of approximately averaging out the unwanted system–environment coupling. Common sequences are the Hahn echo, CPMG and XYXY.

Hahn echo time

Decoherence time obtained via a Hahn echo sequence, a form of dynamical decoupling of the qubit from its environment.

Clifford gate

The Clifford gates are quantum gates from the Clifford group affecting permutations of Pauli operators; examples are the Hadamard gate, the CNOT gate and the X, Y, Z gates.

Spin-squeezed states

Special kinds of entangled states that allow us to go beyond the classical projection noise limit due to the independent nature of single spins; useful for quantum sensing using interferometry.

Kicked-top model

A well-studied model of single-body quantum chaos, the dynamics of the kicked top is described by a time-dependent Hamiltonian combining the top’s spin precession with nonlinear periodic ‘kicks’.

Trotter steps

In digital quantum simulation, the time evolution of a simulation (t) is often decomposed into n Trotter steps of duration t/n, called the ‘kicking period’ for the kicked-top model.

Stark tuning

Electric fields can be used to tune the optical transition frequencies of colour centres, usually by inducing a linear shift in frequency with applied field.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Chatterjee, A., Stevenson, P., De Franceschi, S. et al. Semiconductor qubits in practice. Nat Rev Phys 3, 157–177 (2021). https://doi.org/10.1038/s42254-021-00283-9

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s42254-021-00283-9

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing