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.

  • Progress Article
  • Published:

On-chip quantum simulation with superconducting circuits

Abstract

Using a well-controlled quantum system to simulate complex quantum matter is an idea that has been around for 30 years and put into practice in systems of ultracold atoms for more than a decade. Much recent excitement has focused on a new implementation of quantum simulators using superconducting circuits, where conventional microchip fabrication can be used to take design concepts to experimental reality, quickly and flexibly. Because the quantum ‘particles’ in these simulators are circuit excitations rather than physical particles subject to conservation laws, superconducting simulators provide a complement to ultracold atoms by naturally accessing non-equilibrium physics. Here, we review the recent wealth of theoretical explorations and experimental prospects of realizing these new devices.

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

Figure 1: Elementary circuit-QED building block for a quantum simulator.
Figure 2: Cavity lattice for quantum simulation.
Figure 3: Superfluid-to-Mott-insulator transition in the Jaynes–Cummings lattice.

Similar content being viewed by others

References

  1. Feynman, R. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982).

    Article  MathSciNet  Google Scholar 

  2. Fisher, M. P. A., Weichman, P. B., Grinstein, G. & Fisher, D. S. Boson localization and the superfluid–insulator transition. Phys. Rev. B 40, 546–570 (1989).

    ADS  Google Scholar 

  3. Aspuru-Guzik, A., Dutoi, A. D., Love, P. J. & Head-Gordon, M. Simulated quantum computation of molecular energies. Science 309, 1704–1707 (2005).

    ADS  Google Scholar 

  4. Lanyon, B. P. et al. Towards quantum chemistry on a quantum computer. Nature Chem. 2, 106–111 (2010).

    ADS  Google Scholar 

  5. Buluta, I. & Nori, F. Quantum simulators. Science 326, 108–111 (2009).

    ADS  Google Scholar 

  6. Lewenstein, M. et al. Ultracold atomic gases in optical lattices: Mimicking condensed matter physics and beyond. Adv. Phys. 56, 243–379 (2007).

    ADS  Google Scholar 

  7. Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008).

    ADS  Google Scholar 

  8. Bloch, I., Dalibard, J. & Nascimbène, S. Quantum simulations with ultracold quantum gases. Nature Phys. 8, 267–276 (2012).

    ADS  Google Scholar 

  9. Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001).

    Article  ADS  Google Scholar 

  10. Aspuru-Guzik, A. & Walther, P. Photonic quantum simulators. Nature Phys. 8, 285–291 (2012).

    ADS  Google Scholar 

  11. Gerritsma, R. et al. Quantum simulation of the Dirac equation. Nature 463, 68–71 (2010).

    ADS  Google Scholar 

  12. Blatt, R. & Roos, C. F. Quantum simulations with trapped ions. Nature Phys. 8, 277–284 (2012).

    ADS  Google Scholar 

  13. Mooij, J. E. & Schön, G. in Coherence in Superconducting Networks Vol. 152 (eds Mooij, J. E. & Schön, G.) (NATO Proceedings, North-Holland, 1988).

    Google Scholar 

  14. Fazio, R. & van der Zant, H. Quantum phase transitions and vortex dynamics in superconducting networks. Phys. Rep. 355, 235–334 (2001).

    ADS  MATH  Google Scholar 

  15. Bruder, C., Fazio, R. & Schön, G. The Bose–Hubbard model: From Josephson junction arrays to optical lattices. Ann. Phys. (Leipzig) 14, 566–577 (2005).

    ADS  MATH  Google Scholar 

  16. Manousakis, E. A quantum-dot array as model for copper-oxide superconductors: A dedicated quantum simulator for the many-fermion problem. J. Low Temp. Phys. 126, 1501–1513 (2002).

    ADS  Google Scholar 

  17. Platzman, P. M. Quantum computing with electrons floating on liquid helium. Science 284, 1967–1969 (1999).

    Google Scholar 

  18. Makhlin, Y., Schön, G. & Shnirman, A. Quantum-state engineering with Josephson-junction devices. Rev. Mod. Phys. 73, 357–400 (2001).

    ADS  MATH  Google Scholar 

  19. Devoret, M. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Quantum Inf. Process. 3, 163–203 (2004).

    MATH  Google Scholar 

  20. Clarke, J. & Wilhelm, F. Superconducting quantum bits. Nature 453, 1031–1042 (2008).

    ADS  Google Scholar 

  21. Schoelkopf, R. J. & Girvin, S. M. Wiring up quantum systems. Nature 451, 664–669 (2008).

    ADS  Google Scholar 

  22. Bouchiat, V., Vion, D., Joyez, P., Esteve, D. & Devoret, M. Quantum coherence with a single Cooper pair. Phys. Scr. T76, 165–170 (1998).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  24. Vion, D. et al. Manipulating the quantum state of an electrical circuit. Science 296, 886–889 (2002).

    ADS  Google Scholar 

  25. Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007).

    ADS  Google Scholar 

  26. Schreier, J. et al. Suppressing charge noise decoherence in superconducting charge qubits. Phys. Rev. B 77, 180502 (2008).

    ADS  Google Scholar 

  27. Mooij, J. E. et al. Josephson persistent-current qubit. Science 285, 1036–1039 (1999).

    Google Scholar 

  28. Friedman, J. R., Patel, V., Chen, W., Tolpygo, S. K. & Lukens, J. E. Quantum superposition of distinct macroscopic states. Nature 406, 43–46 (2000).

    ADS  Google Scholar 

  29. Van der Wal, C. H. et al. Quantum superposition of macroscopic persistent-current states. Science 290, 773–777 (2000).

    ADS  Google Scholar 

  30. Martinis, J. M., Nam, S., Aumentado, J. & Urbina, C. Rabi oscillations in a large Josephson-junction qubit. Phys. Rev. Lett. 89, 117901 (2002).

    ADS  Google Scholar 

  31. Houck, A. A., Koch, J., Devoret, M., Girvin, S. M. & Schoelkopf, R. J. Life after charge noise: Recent results with transmon qubits. Quantum Inf. Process. 8, 105–115 (2009).

    Google Scholar 

  32. Pashkin, Y. A. et al. Quantum oscillations in two coupled charge qubits. Nature 421, 823–826 (2003).

    ADS  Google Scholar 

  33. McDermott, R. et al. Simultaneous state measurement of coupled Josephson phase qubits. Science 307, 1299–1302 (2005).

    ADS  Google Scholar 

  34. Majer, J., Paauw, F., ter Haar, A., Harmans, C. & Mooij, J. Spectroscopy on two coupled superconducting flux qubits. Phys. Rev. Lett. 94, 090501 (2005).

    ADS  Google Scholar 

  35. Hime, T. et al. Solid-state qubits with current-controlled coupling. Science 314, 1427–1429 (2006).

    ADS  Google Scholar 

  36. Niskanen, A. O. et al. Quantum coherent tunable coupling of superconducting qubits. Science 316, 723–726 (2007).

    ADS  Google Scholar 

  37. Harris, R. et al. Sign- and magnitude-tunable coupler for superconducting flux qubits. Phys. Rev. Lett. 98, 177001 (2007).

    ADS  Google Scholar 

  38. Van der Ploeg, S. et al. Controllable coupling of superconducting flux qubits. Phys. Rev. Lett. 98, 057004 (2007).

    ADS  Google Scholar 

  39. Allman, M. S. et al. rf-SQUID-mediated coherent tunable coupling between a superconducting phase qubit and a lumped-element resonator. Phys. Rev. Lett. 104, 177004 (2010).

    ADS  Google Scholar 

  40. Bialczak, R. et al. Fast tunable coupler for superconducting qubits. Phys. Rev. Lett. 106, 060501 (2011).

    ADS  Google Scholar 

  41. Srinivasan, S., Hoffman, A., Gambetta, J. & Houck, A. Tunable coupling in circuit quantum electrodynamics using a superconducting charge qubit with a V-shaped energy level diagram. Phys. Rev. Lett. 106, 083601 (2011).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  43. Sillanpää, M. A., Park, J. I. & Simmonds, R. W. Coherent quantum state storage and transfer between two phase qubits via a resonant cavity. Nature 449, 438–442 (2007).

    ADS  Google Scholar 

  44. Majer, J. et al. Coupling superconducting qubits via a cavity bus. Nature 449, 443–447 (2007).

    ADS  Google Scholar 

  45. Koch, J., Houck, A. A., Le Hur, K. & Girvin, S. M. Time-reversal-symmetry breaking in circuit-QED-based photon lattices. Phys. Rev. A 82, 043811 (2010).

    ADS  Google Scholar 

  46. Tsomokos, D., Ashhab, S. & Nori, F. Using superconducting qubit circuits to engineer exotic lattice systems. Phys. Rev. A 82, 052311 (2010).

    ADS  Google Scholar 

  47. Leek, P. J. et al. Observation of Berry’s phase in a solid-state qubit. Science 318, 1889–1892 (2007).

    ADS  MathSciNet  MATH  Google Scholar 

  48. Neeley, M. et al. Emulation of a quantum spin with a superconducting phase qudit. Science 325, 722–725 (2009).

    ADS  Google Scholar 

  49. Johnson, M. W. et al. Quantum annealing with manufactured spins. Nature 473, 194–198 (2011).

    ADS  Google Scholar 

  50. Bishop, L. S. et al. Nonlinear response of the vacuum Rabi resonance. Nature Phys. 5, 105–109 (2008).

    ADS  Google Scholar 

  51. Fink, J. M. et al. Climbing the Jaynes–Cummings ladder and observing its nonlinearity in a cavity QED system. Nature 454, 315–318 (2008).

    ADS  Google Scholar 

  52. Hofheinz, M. et al. Generation of Fock states in a superconducting quantum circuit. Nature 454, 310–314 (2008).

    ADS  Google Scholar 

  53. Lang, C. et al. Observation of resonant photon blockade at microwave frequencies using correlation function measurements. Phys. Rev. Lett. 106, 243601 (2011).

    ADS  Google Scholar 

  54. Hoffman, A. et al. Dispersive photon blockade in a superconducting circuit. Phys. Rev. Lett. 107, 053602 (2011).

    ADS  Google Scholar 

  55. Schmidt, S., Gerace, D., Houck, A. A., Blatter, G. & Türeci, H. E. Nonequilibrium delocalization–localization transition of photons in circuit quantum electrodynamics. Phys. Rev. B 82, 100507 (2010).

    ADS  Google Scholar 

  56. Irish, E. K., Ogden, C. D. & Kim, M. S. Polaritonic characteristics of insulator and superfluid states in a coupled-cavity array. Phys. Rev. A 77, 033801 (2008).

    ADS  Google Scholar 

  57. Hartmann, M., Brandão, F. & Plenio, M. Strongly interacting polaritons in coupled arrays of cavities. Nature Phys. 2, 849–855 (2006).

    ADS  Google Scholar 

  58. Angelakis, D., Santos, M. & Bose, S. Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays. Phys. Rev. A 76, 031805 (2007).

    ADS  Google Scholar 

  59. Hartmann, M., Brandão, F. & Plenio, M. Effective spin systems in coupled microcavities. Phys. Rev. Lett. 99, 160501 (2007).

    ADS  Google Scholar 

  60. Makin, M. I., Cole, J. H., Tahan, C., Hollenberg, L. & Greentree, A. D. Quantum phase transitions in photonic cavities with two-level systems. Phys. Rev. A 77, 053819 (2008).

    ADS  Google Scholar 

  61. Nunnenkamp, A., Koch, J. & Girvin, S. M. Synthetic gauge fields and homodyne transmission in Jaynes–Cummings lattices. New J. Phys. 13, 095008 (2011).

    ADS  Google Scholar 

  62. Carusotto, I. et al. Fermionized photons in an array of driven dissipative nonlinear cavities. Phys. Rev. Lett. 103, 033601 (2009).

    ADS  Google Scholar 

  63. Gerace, D., Türeci, H. E., Imamoglu, A., Giovannetti, V. & Fazio, R. The quantum-optical Josephson interferometer. Nature Phys. 5, 281–284 (2009).

    ADS  Google Scholar 

  64. Leib, M. & Hartmann, M. J. Bose–Hubbard dynamics of polaritons in a chain of circuit quantum electrodynamics cavities. New J. Phys. 12, 093031 (2010).

    ADS  Google Scholar 

  65. Imry, Y. Introduction to Mesoscopic Physics (Oxford Univ. Press, 1997).

    Google Scholar 

  66. Lerner, I. V., Altshuler, B. L. & Gefen, Y. (eds) in Fundamental Problems of Mesoscopic Physics: Interactions and Decoherence (Springer, 2004).

  67. Alhassid, Y. The statistical theory of quantum dots. Rev. Mod. Phys. 72, 895–968 (2000).

    ADS  Google Scholar 

  68. Kurland, I., Aleiner, I. & Altshuler, B. Mesoscopic magnetization fluctuations for metallic grains close to the Stoner instability. Phys. Rev. B 62, 14886 (2000).

    ADS  Google Scholar 

  69. Greentree, A. D., Tahan, C., Cole, J. H. & Hollenberg, L. Quantum phase transitions of light. Nature Phys. 2, 856–861 (2006).

    ADS  Google Scholar 

  70. Illuminati, F. Quantum optics: Light does matter. Nature Phys. 2, 803–804 (2006).

    ADS  Google Scholar 

  71. Hartmann, M., Brandão, F. & Plenio, M. Quantum many-body phenomena in coupled cavity arrays. Laser Photon. Rev. 2, 527–556 (2008).

    ADS  Google Scholar 

  72. Tomadin, A. & Fazio, R. Many-body phenomena in QED-cavity arrays. J. Opt. Soc. B 27, A130 (2010).

    ADS  Google Scholar 

  73. Sachdev, S. Quantum Phase Transitions (Cambridge Univ. Press, 1999).

    MATH  Google Scholar 

  74. Na, N., Utsunomiya, S., Tian, L. & Yamamoto, Y. Strongly correlated polaritons in a two-dimensional array of photonic crystal microcavities. Phys. Rev. A 77, 031803 (2008).

    ADS  Google Scholar 

  75. Koch, J. & Le Hur, K. Superfluid-Mott-insulator transition of light in the Jaynes–Cummings lattice. Phys. Rev. A 80, 023811 (2009).

    ADS  Google Scholar 

  76. Schmidt, S. & Blatter, G. Strong coupling theory for the Jaynes–Cummings–Hubbard model. Phys. Rev. Lett. 103, 086403 (2009).

    ADS  Google Scholar 

  77. Hohenadler, M., Aichhorn, M., Schmidt, S. & Pollet, L. Dynamical critical exponent of the Jaynes–Cummings–Hubbard model. Phys. Rev. A 84, 041608(R) (2011).

    ADS  Google Scholar 

  78. Metzner, W. Linked-cluster expansion around the atomic limit of the Hubbard model. Phys. Rev. B 43, 8549–8563 (1991).

    ADS  Google Scholar 

  79. Zhao, J., Sandvik, A. W. & Ueda, K. Insulator to superfluid transition in coupled photonic cavities in two dimensions. Preprint at http://arxiv.org/abs/0806.3603 (2008).

  80. Aichhorn, M., Hohenadler, M., Tahan, C. & Littlewood, P. Quantum fluctuations, temperature, and detuning effects in solid-light systems. Phys. Rev. Lett. 100, 216401 (2008).

    ADS  Google Scholar 

  81. Rossini, D. & Fazio, R. Mott-insulating and glassy phases of polaritons in 1D arrays of coupled cavities. Phys. Rev. Lett. 99, 186401 (2007).

    ADS  Google Scholar 

  82. Rossini, D., Fazio, R. & Santoro, G. Photon and polariton fluctuations in arrays of QED-cavities. Europhys. Lett. 83, 47011 (2008).

    ADS  Google Scholar 

  83. Knap, M., Arrigoni, E. & von der Linden, W. Variational cluster approach for strongly correlated lattice bosons in the superfluid phase. Phys. Rev. B 83, 134507 (2011).

    ADS  Google Scholar 

  84. Schmidt, S. & Blatter, G. Excitations of strongly correlated lattice polaritons. Phys. Rev. Lett. 104, 216402 (2010).

    ADS  Google Scholar 

  85. Cho, J., Angelakis, D. & Bose, S. Simulation of high-spin Heisenberg models in coupled cavities. Phys. Rev. A 78, 062338 (2008).

    ADS  Google Scholar 

  86. Kay, A. & Angelakis, D. Reproducing spin lattice models in strongly coupled atom-cavity systems. Europhys. Lett. 84, 20001 (2008).

    ADS  Google Scholar 

  87. Makin, M., Cole, J., Hill, C., Greentree, A. & Hollenberg, L. Time evolution of the one-dimensional Jaynes–Cummings–Hubbard Hamiltonian. Phys. Rev. A 80, 043842 (2009).

    ADS  Google Scholar 

  88. Kiffner, M. & Hartmann, M. Dissipation-induced Tonks–Girardeau gas of polaritons. Phys. Rev. A 81, 021806 (2010).

    ADS  Google Scholar 

  89. Angelakis, D., Huo, M., Kyoseva, E. & Kwek, L. Luttinger liquid of photons and spin-charge separation in hollow-core fibers. Phys. Rev. Lett. 106, 153601 (2011).

    ADS  Google Scholar 

  90. Paredes, B., Zoller, P. & Cirac, J. I. Fractional quantum Hall regime of a gas of ultracold atoms. Solid State Commun. 127, 155–162 (2003).

    ADS  Google Scholar 

  91. Sørensen, A., Demler, E. & Lukin, M. Fractional quantum Hall states of atoms in optical lattices. Phys. Rev. Lett. 94, 086803 (2005).

    ADS  Google Scholar 

  92. Cho, J., Angelakis, D. & Bose, S. Fractional quantum Hall state in coupled cavities. Phys. Rev. Lett. 101, 246809 (2008).

    ADS  Google Scholar 

  93. Kamal, A., Clarke, J. & Devoret, M. H. Noiseless non-reciprocity in a parametric active device. Nature Phys. 7, 311–315 (2011).

    ADS  Google Scholar 

  94. Hartmann, M. Polariton crystallization in driven arrays of lossy nonlinear resonators. Phys. Rev. Lett. 104, 113601 (2010).

    ADS  Google Scholar 

  95. Tomadin, A. et al. Signatures of the superfluid-insulator phase transition in laser-driven dissipative nonlinear cavity arrays. Phys. Rev. A 81, 061801 (2010).

    ADS  Google Scholar 

  96. Astafiev, O. et al. Resonance fluorescence of a single artificial atom. Science 327, 840–843 (2010).

    ADS  Google Scholar 

  97. Shen, J-T. & Fan, S. Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a two-level system. Phys. Rev. Lett. 98, 153003 (2007).

    ADS  Google Scholar 

  98. Longo, P. & Busch, K. Few-photon transport in low-dimensional systems: Interaction-induced radiation trapping. Phys. Rev. Lett. 104, 023602 (2010).

    ADS  Google Scholar 

  99. Le Hur, K. Photonic Kondo resonance and asymptotic freedom from nonlinear optics. Preprint at http://arxiv.org/abs/1104.0708 (2011).

  100. Johnson, B. R. et al. Quantum non-demolition detection of single microwave photons in a circuit. Nature Phys. 6, 663–667 (2010).

    ADS  Google Scholar 

  101. Paik, H. et al. How coherent are Josephson junctions? Phys. Rev. Lett. 107, 240501 (2011).

    ADS  Google Scholar 

  102. Breuer, H-P. & Petruccione, F. The Theory of Open Quantum Systems (Oxford Univ. Press, 2007).

    MATH  Google Scholar 

Download references

Acknowledgements

We thank I. Carusotto, D. Gerace, S. M. Girvin, D. Huse, R. Fazio, A. Imamoglu, J. Keeling, M. Schiro, S. Schmidt and A. Tomadin for valuable and stimulating discussions. This work was supported by the National Science Foundation through grant nos. DMR-0953475 and PHY-1055993, and through the Princeton Center for Complex Materials under grant no. DMR-0819860, by the Army Research Office under contract W911NF-11-1-0086, by the Swiss National Science Foundation through grant no. PP00P2-123519/1, and by the Packard Foundation.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Andrew A. Houck.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Houck, A., Türeci, H. & Koch, J. On-chip quantum simulation with superconducting circuits. Nature Phys 8, 292–299 (2012). https://doi.org/10.1038/nphys2251

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys2251

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