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.

  • Review Article
  • Published:

Hybrid quantum systems with circuit quantum electrodynamics

Abstract

The rise of quantum information science has provided new perspectives on quantum mechanics, as well as a common language for quantum engineering. The focus on platforms for the manipulation and processing of quantum information bridges between different research areas in physics as well as other disciplines. Such a crossover between borders is well embodied by the development of hybrid quantum systems, where heterogeneous physical systems are combined to leverage their individual strengths for the implementation of novel functionalities. In the microwave domain, the hybridization of various quantum degrees of freedom has been tremendously helped by superconducting quantum circuits, owing to their large zero-point field fluctuations, small dissipation, strong nonlinearity and design flexibility. These efforts take place by expanding the framework of circuit quantum electrodynamics. Here, we review recent research on the creation of hybrid quantum systems based on circuit quantum electrodynamics, encompassing mechanical oscillators, quantum acoustodynamics with surface acoustic waves, quantum magnonics and coupling between superconducting circuits and ensembles or single spins.

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

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Hybrid quantum systems with circuit QED.
Fig. 2: Electromechanics.
Fig. 3: Quantum acoustics devices.
Fig. 4: Quantum magnonics.
Fig. 5: Quantum magnetic resonance.
Fig. 6: Strong spin–photon coupling.

Similar content being viewed by others

References

  1. Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999).

    ADS  Google Scholar 

  2. Martinis, J. M., Devoret, M. H. & Clarke, J. Quantum Josephson junctions and the dawn of artificial atoms. Nat. Phys. https://doi.org/10.1038/s41567-020-0829-5 (2020).

  3. Haroche, S. & Raimond, J.-M. Exploring the Quantum (Oxford Univ. Press, 2006).

  4. Blais, A., Huang, R.-S., Wallraff, A., Girvin, S. M. & Schoelkopf, R. J. Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation. Phys. Rev. A 69, 062320 (2004).

    ADS  Google Scholar 

  5. Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004).

    ADS  Google Scholar 

  6. Haroche, S., Brune, M. & Raimond, J. M. From cavity to circuit quantum electrodynamics. Nat. Phys. https://doi.org/10.1038/s41567-020-0812-1 (2020).

  7. Clerk, A. A., Girvin, S. M., Marquardt, F. & Schoelkopf, R. J. Introduction to quantum noise, measurement, and amplification. Rev. Mod. Phys. 82, 1155–1208 (2010).

    ADS  MathSciNet  MATH  Google Scholar 

  8. Poot, M. & van der Zant, H. S. Mechanical systems in the quantum regime. Phys. Rep. 511, 273–335 (2012).

    ADS  Google Scholar 

  9. Xiang, Z.-L., Ashhab, S., You, J. Q. & Nori, F. Hybrid quantum circuits: superconducting circuits interacting with other quantum systems. Rev. Mod. Phys. 85, 623–653 (2013).

    ADS  Google Scholar 

  10. Aspelmeyer, M., Kippenberg, T. J. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391–1452 (2014).

    ADS  Google Scholar 

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

    Google Scholar 

  12. Kurizki, G. et al. Quantum technologies with hybrid systems. Proc. Natl Acad. Sci. USA 112, 3866–3873 (2015).

    ADS  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

  14. Morton, J. J. L. & Bertet, P. Storing quantum information in spins and high-sensitivity ESR. J. Magn. Reson. 287, 128–139 (2018).

    ADS  Google Scholar 

  15. Lambert, N. J., Rueda, A., Sedlmeir, F. & Schwefel, H. G. L. Coherent conversion between microwave and optical photons — an overview of physical implementations. Preprint at https://arxiv.org/abs/1906.10255 (2019).

  16. Safavi-Naeini, A. H., Thourhout, D. V., Baets, R. & Laer, R. V. Controlling phonons and photons at the wavelength scale: integrated photonics meets integrated phononics. Optica 6, 213–232 (2019).

    ADS  Google Scholar 

  17. Lachance-Quirion, D., Tabuchi, Y., Gloppe, A., Usami, K. & Nakamura, Y. Hybrid quantum systems based on magnonics. Appl. Phys. Express 12, 070101 (2019).

    ADS  Google Scholar 

  18. Blais, A., Girvin, S. M. & Oliver, W. D. Quantum information processing and quantum optics with circuit quantum electrodynamics. Nat. Phys. https://doi.org/10.1038/s41567-020-0806-z (2020).

  19. Filip, R. Quantum interface to a noisy system through a single kind of arbitrary Gaussian coupling with limited interaction strength. Phys. Rev. A 80, 022304 (2009).

    ADS  Google Scholar 

  20. Zhang, M., Zou, C.-L. & Jiang, L. Quantum transduction with adaptive control. Phys. Rev. Lett. 120, 020502 (2018).

    ADS  Google Scholar 

  21. Lau, H.-K. & Clerk, A. A. High-fidelity bosonic quantum state transfer using imperfect transducers and interference. npj Quantum Inf. 5, 31 (2019).

    ADS  Google Scholar 

  22. Lau, H.-K. & Clerk, A. A. Ground state cooling and high-fidelity quantum transduction via parametrically-driven bad-cavity optomechanics. Preprint at https://arxiv.org/abs/1904.12984 (2019).

  23. Xiang, Z.-L., Zhang, M., Jiang, L. & Rabl, P. Intracity quantum communication via thermal microwave networks. Phys. Rev. X 7, 011035 (2017).

    Google Scholar 

  24. Caves, C. M., Thorne, K. S., Drever, R. W. P., Sandberg, V. D. & Zimmermann, M. On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. I. Issues of principle. Rev. Mod. Phys. 52, 341–392 (1980).

    ADS  Google Scholar 

  25. Marshall, W., Simon, C., Penrose, R. & Bouwmeester, D. Towards quantum superpositions of a mirror. Phys. Rev. Lett. 91, 130401 (2003).

    ADS  MathSciNet  Google Scholar 

  26. O’Connell, A. D. et al. Quantum ground state and single-phonon control of a mechanical resonator. Nature 464, 697–703 (2010).

    ADS  Google Scholar 

  27. Regal, C. A., Teufel, J. D. & Lehnert, K. W. Measuring nanomechanical motion with a microwave cavity interferometer. Nat. Phys. 4, 555–560 (2008).

    Google Scholar 

  28. Teufel, J. D., Harlow, J. W., Regal, C. A. & Lehnert, K. W. Dynamical backaction of microwave fields on a nanomechanical oscillator. Phys. Rev. Lett. 101, 197203 (2008).

    ADS  Google Scholar 

  29. Teufel, J. D., Donner, T., Castellanos-Beltran, M. A., Harlow, J. W. & Lehnert, K. W. Nanomechanical motion measured with an imprecision below that at the standard quantum limit. Nat. Nanotechnol. 4, 820–823 (2009). This paper demonstrated efficient readout of a circuit QED system enabled by a Josephson parametric amplifier.

    ADS  Google Scholar 

  30. Teufel, J. D. et al. Circuit cavity electromechanics in the strong-coupling regime. Nature 471, 204–208 (2011).

    ADS  Google Scholar 

  31. Teufel, J. D. et al. Sideband cooling of micromechanical motion to the quantum ground state. Nature 475, 359–363 (2011). This paper showed that the radiation pressure force could cool a macroscopic mechanical oscillator to its motional ground state.

    ADS  Google Scholar 

  32. Teufel, J., Lecocq, F. & Simmonds, R. Overwhelming thermomechanical motion with microwave radiation pressure shot noise. Phys. Rev. Lett. 116, 013602 (2016).

    ADS  Google Scholar 

  33. Palomaki, T. A., Teufel, J. D., Simmonds, R. W. & Lehnert, K. W. Entangling mechanical motion with microwave fields. Science 342, 710–713 (2013).

    ADS  Google Scholar 

  34. Wollman, E. E. et al. Quantum squeezing of motion in a mechanical resonator. Science 349, 952–955 (2015).

    ADS  MathSciNet  MATH  Google Scholar 

  35. Pirkkalainen, J. et al. Hybrid circuit cavity quantum electrodynamics with a micromechanical resonator. Nature 494, 211–215 (2013).

    ADS  Google Scholar 

  36. Lecocq, F., Teufel, J. D., Aumentado, J. & Simmonds, R. W. Resolving the vacuum fluctuations of an optomechanical system using an artificial atom. Nat. Phys. 11, 635–639 (2015).

    Google Scholar 

  37. Viennot, J. J., Ma, X. & Lehnert, K. W. Phonon-number-sensitive electromechanics. Phys. Rev. Lett. 121, 183601 (2018).

    ADS  Google Scholar 

  38. Andrews, R. W. et al. Bidirectional and efficient conversion between microwave and optical light. Nat. Phys. 10, 321–326 (2014).

    Google Scholar 

  39. Goryachev, M. et al. Extremely low-loss acoustic phonons in a quartz bulk acoustic wave resonator at millikelvin temperature. Appl. Phys. Lett. 100, 243504 (2012).

    ADS  Google Scholar 

  40. Manenti, R. et al. Surface acoustic wave resonators in the quantum regime. Phys. Rev. B 93, 041411 (2016).

    ADS  Google Scholar 

  41. Gustafsson, M. V. et al. Propagating phonons coupled to an artificial atom. Science 346, 207–211 (2014). This work pioneered the studies on the quantum regime of surface acoustic waves.

    ADS  Google Scholar 

  42. Schuetz, M. J. A. Universal quantum transducers based on surface acoustic waves. Phys. Rev. X 5, 031031 (2015).

    Google Scholar 

  43. Manenti, R. et al. Circuit quantum acoustodynamics with surface acoustic waves. Nat. Commun. 8, 975 (2017).

    ADS  Google Scholar 

  44. Noguchi, A., Yamazaki, R., Tabuchi, Y. & Nakamura, Y. Qubit-assisted transduction for a detection of surface acoustic waves near the quantum limit. Phys. Rev. Lett. 119, 180505 (2017).

    ADS  Google Scholar 

  45. Bolgar, A. N. et al. Quantum regime of a two-dimensional phonon cavity. Phys. Rev. Lett. 120, 223603 (2018).

    ADS  Google Scholar 

  46. Moores, B. A., Sletten, L. R., Viennot, J. J. & Lehnert, K. W. Cavity quantum acoustic device in the multimode strong coupling regime. Phys. Rev. Lett. 120, 227701 (2018).

    ADS  Google Scholar 

  47. Satzinger, K. J. et al. Quantum control of surface acoustic wave phonons. Nature 563, 661–665 (2018).

    ADS  Google Scholar 

  48. Chu, Y. et al. Creation and control of multi-phonon Fock states in a bulk acoustic wave resonator. Nature 563, 666–670 (2018).

    ADS  Google Scholar 

  49. Bienfait, A. et al. Phonon-mediated quantum state transfer and remote qubit entanglement. Science 364, 368–371 (2019).

    ADS  Google Scholar 

  50. Arrangoiz-Arriola, P. et al. Resolving the energy levels of a nanomechanical oscillator. Nature 571, 537–540 (2019). This paper demonstrated phonon-number resolving measurement of a nanomechanical oscillator interacting with a superconducting qubit in the strong dispersive regime.

    ADS  Google Scholar 

  51. Sletten, L. R., Moores, B. A., Viennot, J. J. & Lehnert, K. W. Resolving phonon Fock states in a multimode cavity with a double-slit qubit. Phys. Rev. X 9, 021056 (2019).

    Google Scholar 

  52. Rueda, A. et al. Efficient microwave to optical photon conversion: an electro-optical realization. Optica 3, 597–604 (2016).

    ADS  Google Scholar 

  53. Fan, L. et al. Superconducting cavity electro-optics: a platform for coherent photon conversion between superconducting and photonic circuits. Sci. Adv. 17, eaar4994 (2018).

    ADS  Google Scholar 

  54. Huebl, H. et al. High cooperativity in coupled microwave resonator ferrimagnetic insulator hybrids. Phys. Rev. Lett. 111, 127003 (2013).

    ADS  Google Scholar 

  55. Tabuchi, Y. et al. Hybridizing ferromagnetic magnons and microwave photons in the quantum limit. Phys. Rev. Lett. 113, 083603 (2014).

    ADS  Google Scholar 

  56. Zhang, X., Zou, C.-L., Jiang, L. & Tang, H. X. Strongly coupled magnons and cavity microwave photons. Phys. Rev. Lett. 113, 156401 (2014).

    ADS  Google Scholar 

  57. Goryachev, M. et al. High-cooperativity cavity QED with magnons at microwave frequencies. Phys. Rev. Appl. 2, 054002 (2014).

    ADS  Google Scholar 

  58. Tabuchi, Y. et al. Coherent coupling between a ferromagnetic magnon and a superconducting qubit. Science 349, 405–408 (2015). This paper describes the demonstration of strong coupling between a magnon and a superconducting qubit.

    ADS  MathSciNet  MATH  Google Scholar 

  59. Lachance-Quirion, D. et al. Resolving quanta of collective spin excitations in a millimeter-sized ferromagnet. Sci. Adv. 3, e1603150 (2017). Demonstration of strong dispersive coupling between magnons and a qubit as well as magnon-number resolving measurement.

    ADS  Google Scholar 

  60. Gambetta, J. et al. Qubit-photon interactions in a cavity: measurement-induced dephasing and number splitting. Phys. Rev. A 74, 042318 (2006).

    ADS  Google Scholar 

  61. Schuster, D. I. et al. Resolving photon number states in a superconducting circuit. Nature 445, 515–518 (2007).

    ADS  Google Scholar 

  62. Crescini, N. et al. Operation of a ferromagnetic axion haloscope at m a = 58μev. Eur. Phys. J. C. 78, 703 (2018).

    ADS  Google Scholar 

  63. Flower, G., Bourhill, J., Goryachev, M. & Tobar, M. E. Broadening frequency range of a ferromagnetic axion haloscope with strongly coupled cavity-magnon polaritons. Phys. Dark Univ. 25, 100306 (2019).

    Google Scholar 

  64. Pfirrmann, M. et al. Magnons at low excitations: observation of incoherent coupling to a bath of two-level-systems. Phys. Rev. Res. 1, 032023(R) (2019).

    Google Scholar 

  65. Kosen, S., van Loo, A. F., Bozhko, D. A., Mihalceanu, L. & Karenowska, A. D. Microwave magnon damping in YIG films at millikelvin temperatures. APL Mater. 7, 101120 (2019).

    ADS  Google Scholar 

  66. Bienfait, A. et al. Controlling spin relaxation with a cavity. Nature 531, 74–77 (2016). Observation of the Purcell effect for spins.

    ADS  Google Scholar 

  67. Sigillito, A. J. et al. Fast, low-power manipulation of spin ensembles in superconducting microresonators. Appl. Phys. Lett. 104, 222407 (2014).

    ADS  Google Scholar 

  68. Eichler, C., Sigillito, A. J., Lyon, S. A. & Petta, J. R. Electron spin resonance at the level of 104 spins using low impedance superconducting resonators. Phys. Rev. Lett. 118, 037701 (2017).

    ADS  Google Scholar 

  69. Probst, S. et al. Inductive-detection electron-spin resonance spectroscopy with 65 spins/ \(\sqrt{\mathrm{Hz}}\) sensitivity. Appl. Phys. Lett. 111, 202604 (2017).

    ADS  Google Scholar 

  70. Budoyo, R. P. et al. Electron paramagnetic resonance spectroscopy of Er3+:Y2SiO5 using a Josephson bifurcation amplifier: observation of hyperfine and quadrupole structures. Phys. Rev. Mater. 2, 011403 (2018).

    Google Scholar 

  71. Angerer, A. et al. Superradiant emission from colour centres in diamond. Nat. Phys. 14, 1168–1172 (2018).

    Google Scholar 

  72. Haikka, P., Kubo, Y., Bienfait, A., Bertet, P. & Moelmer, K. Proposal for detecting a single electron spin in a microwave resonator. Phys. Rev. A 95, 022306 (2017).

    ADS  Google Scholar 

  73. Bienfait, A. et al. Magnetic resonance with squeezed microwaves. Phys. Rev. X 7, 041011 (2017).

    Google Scholar 

  74. Grezes, C. et al. Towards a spin-ensemble quantum memory for superconducting qubits. C. R. Phys. 17, 693–704 (2016). Review of the experimental effort on quantum memories for microwave photons.

    ADS  Google Scholar 

  75. Afzelius, M., Sangouard, N., Johansson, G., Staudt, M. U. & Wilson, C. M. Proposal for a coherent quantum memory for propagating microwave photons. N. J. Phys. 15, 065008 (2013).

    MathSciNet  Google Scholar 

  76. Julsgaard, B., Grezes, C., Bertet, P. & Molmer, K. Quantum memory for microwave photons in an inhomogeneously broadened spin ensemble. Phys. Rev. Lett. 110, 250503 (2013).

    ADS  Google Scholar 

  77. Kubo, Y. et al. Strong coupling of a spin ensemble to a superconducting resonator. Phys. Rev. Lett. 105, 140502 (2010). This paper reports observation of strong coupling of a spin ensemble to a superconducting resonator.

    ADS  Google Scholar 

  78. Schuster, D. I. et al. High-cooperativity coupling of electron-spin ensembles to superconducting cavities. Phys. Rev. Lett. 105, 140501 (2010).

    ADS  Google Scholar 

  79. Amsüss, R. et al. Cavity QED with magnetically coupled collective spin states. Phys. Rev. Lett. 107, 060502 (2011).

    ADS  Google Scholar 

  80. Probst, S. et al. Anisotropic rare-earth spin ensemble strongly coupled to a superconducting resonator. Phys. Rev. Lett. 110, 157001 (2013).

    ADS  Google Scholar 

  81. Zhu, X. et al. Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond. Nature 478, 221–224 (2011).

    ADS  Google Scholar 

  82. Kubo, Y. et al. Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble. Phys. Rev. Lett. 107, 220501 (2011).

    ADS  Google Scholar 

  83. Grezes, C. et al. Multimode storage and retrieval of microwave fields in a spin ensemble. Phys. Rev. X 4, 021049 (2014).

    Google Scholar 

  84. Williamson, L. A., Chen, Y.-H. & Longdell, J. J. Magneto-optic modulator with unit quantum efficiency. Phys. Rev. Lett. 113, 203601 (2014). Proposal for microwave-optical photon conversion based on a spin ensemble.

    ADS  Google Scholar 

  85. Fernandez-Gonzalvo, X., Chen, Y.-H., Yin, C., Rogge, S. & Longdell, J. J. Coherent frequency up-conversion of microwaves to the optical telecommunications band in an Er:YSO crystal. Phys. Rev. A 92, 062313 (2015).

    ADS  Google Scholar 

  86. Mi, X. et al. A coherent spin–photon interface in silicon. Nature 555, 599–603 (2018). This article describes the demonstration of strong single spin–photon coupling and dispersive readout of the electron spin state.

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  89. Cottet, A. & Kontos, T. Spin quantum bit with ferromagnetic contacts for circuit QED. Phys. Rev. Lett. 105, 160502 (2010).

    ADS  Google Scholar 

  90. van der Wiel, W. G. et al. Electron transport through double quantum dots. Rev. Mod. Phys. 75, 1–22 (2002).

    ADS  Google Scholar 

  91. 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). The physics of spins in semiconductor quantum dots is thoroughly reviewed in this article.

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  94. 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).

    ADS  Google Scholar 

  95. 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  Google Scholar 

  96. 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 

  97. Tokura, Y., van der Wiel, W. G., Obata, T. & Tarucha, S. Coherent single electron spin control in a slanting Zeeman field. Phys. Rev. Lett. 96, 047202 (2006). The use of micromagnets for coherent spin control and spin–photon coupling can largely be attributed to this pioneering theoretical paper.

    ADS  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  Google Scholar 

  99. Wallraff, A. et al. Approaching unit visibility for control of a superconducting qubit with dispersive readout. Phys. Rev. Lett. 95, 060501 (2005).

    ADS  Google Scholar 

  100. Heinsoo, J. et al. Rapid high-fidelity multiplexed readout of superconducting qubits. Phys. Rev. Appl. 10, 034040 (2018).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  103. Lyon, S. A. Spin-based quantum computing using electrons on liquid helium. Phys. Rev. 74, 052338 (2006).

    ADS  Google Scholar 

  104. Koolstra, G., Yang, G. & Schuster, D. I. Coupling a single electron on superfluid helium to a superconducting resonator. Nat. Commun. 10, 5323 (2019).

    ADS  Google Scholar 

  105. Schuster, D. I., Fragner, A., Dykman, M. I., Lyon, S. A. & Schoelkopf, R. J. Proposal for manipulating and detecting spin and orbital states of trapped electrons on helium using cavity quantum electrodynamics. Phys. Rev. Lett. 105, 040503 (2010).

    ADS  Google Scholar 

  106. Andrews, R. W., Reed, A. P., Cicak, K., Teufel, J. D. & Lehnert, K. W. Quantum-enabled temporal and spectral mode conversion of microwave signals. Nat. Commun. 6, 10021 (2015).

    ADS  Google Scholar 

  107. Poyatos, J. F., Cirac, J. I. & Zoller, P. Quantum reservoir engineering with laser cooled trapped ions. Phys. Rev. Lett. 77, 4728–4731 (1996).

    ADS  Google Scholar 

Download references

Acknowledgements

P.B. acknowledges support from the European Research Council under grant 615767 (CIRQUSS), and from the Agence Nationale de la Recherche under grants QIPSE and NASNIQ. J.R.P. acknowledges support from Army Research Office grant W911NF-15-1-0149 and the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant GBMF4535. Y.N. acknowledges supports from JST ERATO (no. JPMJER1601) and JSPS KAKENHI (no. 26220601).

Author information

Authors and Affiliations

Authors

Contributions

All authors contributed to the writing, editing and revision of the manuscript.

Corresponding author

Correspondence to Y. Nakamura.

Ethics declarations

Competing interests

J.R.P. and Princeton University have filed a non-provisional patent application related to spin–photon transduction (US patent application no. 16534431).

Additional information

Peer review information Nature Physics thanks Peter Leek and Peter Rabl 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.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Clerk, A.A., Lehnert, K.W., Bertet, P. et al. Hybrid quantum systems with circuit quantum electrodynamics. Nat. Phys. 16, 257–267 (2020). https://doi.org/10.1038/s41567-020-0797-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-020-0797-9

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