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:

Photonic quantum simulators

Abstract

Quantum simulators are controllable quantum systems that can be used to mimic other quantum systems. They have the potential to enable the tackling of problems that are intractable on conventional computers. The photonic quantum technology available today is reaching the stage where significant advantages arise for the simulation of interesting problems in quantum chemistry, quantum biology and solid-state physics. In addition, photonic quantum systems also offer the unique benefit of being mobile over free space and in waveguide structures, which opens new perspectives to the field by enabling the natural investigation of quantum transport phenomena. Here, we review recent progress in the field of photonic quantum simulation, which should break the ground towards the realization of versatile quantum simulators.

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

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

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

Figure 1: First quantum chemistry experiment on a quantum information processor.
Figure 2: Schematic of the photonic quantum simulation of delocalized chemical bonds.
Figure 3: Photonic quantum circuits for the simulation of quantum and quantum stochastic walks.

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. Bakr, W. S., Gillen, J. I., Peng, A., Folling, S. & Greiner, M. A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice. Nature 462, 74–77 (2009).

    Article  ADS  Google Scholar 

  3. Trotzky, S. et al. Suppression of the critical temperature for superfluidity near the Mott transition. Nature Phys. 6, 996–1004 (2010).

    ADS  Google Scholar 

  4. Weitenberg, C. et al. Single-spin addressing in an atomic Mott insulator. Nature 471, 319–324 (2011).

    Article  ADS  Google Scholar 

  5. 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 

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

    ADS  Google Scholar 

  7. Friedenauer, A., Schmitz, H., Glueckert, J. T., Porras, D. & Schaetz, T. Simulating a quantum magnet with trapped ions. Nature Phys. 4, 757–761 (2008).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  9. Barreiro, J. T. et al. An open-system quantum simulator with trapped ions. Nature 470, 486–491 (2011).

    ADS  Google Scholar 

  10. Islam, R. et al. Onset of a quantum phase transition with a trapped ion quantum simulator. Nature Commun. 2, 377 (2011).

    Google Scholar 

  11. Lanyon, B. P. et al. Universal digital quantum simulation with trapped ions. Science 334, 57–61 (2011).

    ADS  Google Scholar 

  12. Kim, K. et al. Quantum simulation of frustrated Ising spins with trapped ions. Nature 465, 590–593 (2010).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  14. Peng, X., Zhang, J., Du, J. & Suter, D. Quantum simulation of a system with competing two- and three-body interactions. Phys. Rev. Lett. 103, 140501 (2009).

    ADS  Google Scholar 

  15. Du, J. et al. NMR implementation of a molecular hydrogen quantum simulation with adiabatic state preparation. Phys. Rev. Lett. 104, 030502 (2010).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  17. Houck, A. A., Türeci, H. E. & Koch, J. On-chip quantum simulation with superconducting circuits. Nature Phys. 8, 292–299 (2012).

    ADS  Google Scholar 

  18. Lu, C-Y. et al. Demonstrating anyonic fractional statistics with a six-qubit quantum simulator. Phys. Rev. Lett. 102, 030502 (2009).

    ADS  Google Scholar 

  19. Pachos, J. K. et al. Revealing anyonic features in a toric code quantum simulation. New J. Phys. 11, 083010 (2009).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  21. Broome, M. A. et al. Discrete single-photon quantum walks with tunable decoherence. Phys. Rev. Lett. 104, 153602 (2010).

    ADS  Google Scholar 

  22. Peruzzo, A. et al. Quantum walks of correlated photons. Science 329, 1500–1503 (2010).

    ADS  Google Scholar 

  23. Ma, X., Dakic, B., Naylor, W., Zeilinger, A. & Walther, P. Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems. Nature Phys. 7, 399–405 (2011).

    ADS  Google Scholar 

  24. Matthews, J. C. F. et al. Simulating quantum statistics with entangled photons: A continuous transition from bosons to fermions. Preprint at http://arxiv.org/abs/1106.1166 (2011).

  25. Sansoni, L. et al. Two-particle bosonic–fermionic quantum walk via 3D integrated photonics. Phys. Rev. Lett. 108, 010502 (2012).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  27. Kitagawa, T. et al. Observation of topologically protected bound states in a one-dimensional photonic system. Preprint at http://arxiv.org/abs/1105.5334 (2011).

  28. National Energy Research Supercomputing Center Annual Report (US Department of Energy, 2010).

  29. Head-Gordon, M. & Artacho, E. Chemistry on the computer. Phys. Today 61, 58–63 (April 2008).

    Google Scholar 

  30. Sokolov, A. N. et al. From computational discovery to experimental characterization of a high hole mobility organic crystal. Nature Commun. 2, 437 (2011).

    Google Scholar 

  31. Schuch, N. & Verstraete, F. Computational complexity of interacting electrons and fundamental limitations of density functional theory. Nature Phys. 5, 732–735 (2009).

    ADS  Google Scholar 

  32. Aaronson, S. & Arkhipov, A. The computational complexity of linear optics. Preprint at http://arxiv.org/abs/quant-ph/1011.3245v1 (2010).

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

    ADS  Google Scholar 

  34. Kassal, I., Whitfield, J. D., Perdomo-Ortiz, A., Yung, M-H. & Aspuru-Guzik, A. Simulating chemistry using quantum computers. Annu. Rev. Phys. Chem. 62, 185–207 (2011).

    ADS  Google Scholar 

  35. Whitfield, J. D., Biamonte, J. & Aspuru-Guzik, A. Simulation of electronic structure Hamiltonians using quantum computers. Mol. Phys. 109, 735–750 (2011).

    ADS  Google Scholar 

  36. Abrams, D. & Lloyd, S. Simulation of many-body Fermi systems on a universal quantum computer. Phys. Rev. Lett. 79, 2586–2589 (1997).

    ADS  Google Scholar 

  37. Abrams, D. & Lloyd, S. Quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors. Phys. Rev. Lett. 83, 5162–5165 (1999).

    ADS  Google Scholar 

  38. Lanyon, B. P. et al. Simplifying quantum logic using higher-dimensional Hilbert spaces. Nature Phys. 5, 134–140 (2009).

    ADS  Google Scholar 

  39. Reck, M., Zeilinger, A., Bernstein, H. J. & Bertani, P. Experimental realization of any discrete unitary operator. Phys. Rev. Lett. 73, 58–61 (1994).

    ADS  Google Scholar 

  40. Politi, A., Cryan, M. J., Rarity, J. G., Yu, S. & O’Brien, J. L. Silica-on-silicon waveguide quantum circuits. Science 320, 646–649 (2008).

    ADS  Google Scholar 

  41. Sansoni, L. et al. Polarization entangled state measurement on a chip. Phys. Rev. Lett. 105, 200503 (2010).

    ADS  Google Scholar 

  42. Peruzzo, A., Laing, A., Politi, A., Rudolph, T. & O’Brien, J. L. Multimode quantum interference of photons in multiport integrated devices. Nature Commun. 2, 224 (2011).

    ADS  Google Scholar 

  43. Politi, A., Matthews, J. C. F. & O’Brien, J. L. Shor’s quantum factoring algorithm on a photonic chip. Science 325, 1221 (2009).

    ADS  MathSciNet  MATH  Google Scholar 

  44. Matthews, J., Politi, A., Stefanov, A. & O’Brien, J. Manipulation of multiphoton entanglement in waveguide quantum circuits. Nature Photon. 3, 346–350 (2009).

    ADS  Google Scholar 

  45. Shadbolt, P. J. et al. Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit. Nature Photon. 6, 45–49 (2012).

    ADS  Google Scholar 

  46. Laing, A. et al. High-fidelity operation of quantum photonic circuits. Appl. Phys. Lett. 97, 211109 (2010).

    ADS  Google Scholar 

  47. Marshall, G. D. et al. Laser written waveguide photonic quantum circuits. Opt. Express 17, 12546–12554 (2009).

    ADS  Google Scholar 

  48. Owens, J. O. et al. Two-photon quantum walks in an elliptical direct-write waveguide array. New J. Phys. 13, 075003 (2011).

    ADS  Google Scholar 

  49. Longhi, S. et al. Semiclassical motion of a multiband Bloch particle in a time-dependent field: Optical visualization. Phys. Rev. B 74, 155116 (2006).

    ADS  Google Scholar 

  50. Longhi, S. et al. Observation of dynamic localization in periodically curved waveguide arrays. Phys. Rev. Lett. 96, 243901 (2006).

    ADS  Google Scholar 

  51. Dreisow, F. et al. Classical simulation of relativistic Zitterbewegung in photonic lattices. Phys. Rev. Lett. 105, 143902 (2010).

    ADS  Google Scholar 

  52. Longhi, S. Photonic analog of Zitterbewegung in binary waveguide arrays. Opt. Lett. 35, 235–237 (2010).

    ADS  Google Scholar 

  53. Plotnik, Y. et al. Experimental observation of optical bound states in the continuum. Phys. Rev. Lett. 107, 183901 (2011).

    ADS  Google Scholar 

  54. Perets, H. B. et al. Realization of quantum walks with negligible decoherence in waveguide lattices. Phys. Rev. Lett. 100, 170506 (2008).

    ADS  Google Scholar 

  55. Farhi, E. & Gutmann, S. Quantum computation and decision trees. Phys. Rev. A 58, 915–928 (1998).

    ADS  MathSciNet  Google Scholar 

  56. Whitfield, J. D., Rodrı´guez-Rosario, C. A. & Aspuru-Guzik, A. Quantum stochastic walks: A generalization of classical random walks and quantum walks. Phys. Rev. A 81, 022323 (2010).

    ADS  Google Scholar 

  57. Knight, P. L., Roldán, E. & Sipe, J. E. Quantum walk on the line as an interference phenomenon. Phys. Rev. A 68, 020301 (2003).

    ADS  Google Scholar 

  58. Schreiber, A. et al. Photons walking the line: A quantum walk with adjustable coin operations. Phys. Rev. Lett. 104, 050502 (2010).

    ADS  Google Scholar 

  59. Schreiber, A. et al. Decoherence and disorder in quantum walks: From ballistic spread to localization. Phys. Rev. Lett. 106, 180403 (2011).

    ADS  Google Scholar 

  60. Engel, G. et al. Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems. Nature 446, 782–786 (2007).

    ADS  Google Scholar 

  61. Collini, E. et al. Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature. Nature 463, 644–647 (2010).

    ADS  Google Scholar 

  62. Panitchayangkoon, G. et al. Long-lived quantum coherence in photosynthetic complexes at physiological temperature. Proc. Natl Acad. Sci. USA 107, 12766–12770 (2010).

    ADS  Google Scholar 

  63. Mohseni, M., Rebentrost, P., Lloyd, S. & Aspuru-Guzik, A. Environment-assisted quantum walks in energy transfer of photosynthetic complexes. J. Chem. Phys. 129, 174106 (2008).

    ADS  Google Scholar 

  64. Rebentrost, P., Mohseni, M., Kassal, I., Lloyd, S. & Aspuru-Guzik, A. Environment-assisted quantum transport. New J. Phys. 11, 033003 (2009).

    ADS  Google Scholar 

  65. Plenio, M. B. & Huelga, S. F. Dephasing assisted transport: Quantum networks and biomolecules. New J. Phys. 10, 113019 (2008).

    ADS  Google Scholar 

  66. Caruso, F., Spagnolo, N., Vitelli, C., Sciarrino, F. & Plenio, M. B. Simulation of noise-assisted transport via optical cavity networks. Phys. Rev. A 83, 013811 (2011).

    ADS  Google Scholar 

  67. Keil, R. et al. Photon correlations in two-dimensional waveguide arrays and their classical estimate. Phys. Rev. A 81, 023834 (2010).

    ADS  Google Scholar 

  68. Marshall, W. Antiferromagnetism. Proc. R. Soc. A 232, 48–68 (1955).

    ADS  MATH  Google Scholar 

  69. Anderson, P. W. The resonating valence bond state in La2CuO4 and superconductivity. Science 235, 1196–1198 (1987).

    ADS  Google Scholar 

  70. Coffman, V., Kundu, J. & Wootters, W. K. Distributed entanglement. Phys. Rev. A 61, 052306 (2000).

    ADS  Google Scholar 

  71. Osborne, T. J. & Verstraete, F. General monogamy inequality for bipartite qubit entanglement. Phys. Rev. Lett. 96, 220503 (2006).

    ADS  Google Scholar 

  72. Mattle, K., Michler, M, Weinfurter, H., Zeilinger, A. & Zukowski, M. Non-classical statistics at multiport beam splitters. Appl. Phys. B 60, 111–117 (1995).

    Google Scholar 

  73. Strekalov, D. V., Pittman, T. B., Sergienko, A. V., Shih, Y. H. & Kwiat, P. G. Postselection-free energy-time entanglement. Phys. Rev. A 54, R1–R4 (1996).

    ADS  Google Scholar 

  74. Hong, C. K., Ou, Z. Y. & Mandel, L. Measurement of subpicosecond time intervals between two photons by interference. Phys. Rev. Lett. 59, 2044–2046 (1987).

    ADS  Google Scholar 

  75. Braunstein, S. L. & Mann, A. Measurement of the Bell operator and quantum teleportation. Phys. Rev. A 51, R1727–R1730 (1995).

    ADS  Google Scholar 

  76. Bouwmeester, D. et al. Experimental quantum teleportation. Nature 390, 575–579 (1997).

    ADS  MATH  Google Scholar 

  77. Semião, F. L. & Paternostro, M. Quantum circuits for spin and flavor degrees of freedom of quarks forming nucleons. Quant. Inf. Proc. 11, 67–75 (2011).

    MATH  Google Scholar 

  78. O’Brien, J. L., Furusawa, A. & Vuckovic, J. Photonic quantum technologies. Nature Photon. 3, 687–695 (2009).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  80. Kok, P. et al. Linear optical quantum computing with photonic qubits. Rev. Mod. Phys. 79, 135–174 (2007).

    ADS  Google Scholar 

  81. Gasparoni, S., Pan, J-W., Walther, P., Rudolph, T. & Zeilinger, A. Realization of a photonic controlled-NOT gate sufficient for quantum computation. Phys. Rev. Lett. 93, 020504 (2004).

    ADS  Google Scholar 

  82. Zhao, Z. et al. Experimental demonstration of a nondestructive controlled-NOT quantum gate for two independent photon qubits. Phys. Rev. Lett. 94, 030501 (2005).

    ADS  Google Scholar 

  83. Walther, P. & Zeilinger, A. Experimental realization of a photonic Bell-state analyzer. Phys. Rev. A 72, 010302(R) (2005).

    ADS  Google Scholar 

  84. Bao, X-H. et al. Optical nondestructive controlled-NOT gate without using entangled photons. Phys. Rev. Lett. 98, 170502 (2007).

    ADS  Google Scholar 

  85. Okamoto, R., O’Brien, J. L., Hofmann, H. F. & Takeuchi, S. Realization of a Knill–Laflamme–Milburn controlled-NOT photonic quantum circuit combining effective optical nonlinearities. Proc. Natl Acad. Sci. USA 108, 10067–10071 (2011).

    ADS  Google Scholar 

  86. Gao, W-B. et al. Teleportation-based realization of an optical quantum two-qubit entangling gate. Proc. Natl Acad. Sci. USA 107, 20869–20874 (2010).

    ADS  Google Scholar 

  87. Kwiat, P. G. et al. New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett. 75, 4337–4341 (1995).

    ADS  Google Scholar 

  88. Rosfjord, K. M. et al. Nanowire single-photon detector with an integrated optical cavity and anti-reflection coating. Opt. Express 14, 527–534 (2006).

    ADS  Google Scholar 

  89. Divochiy, A. et al. Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths. Nature Photon. 2, 302–306 (2008).

    Google Scholar 

  90. Lita, A. E., Miller, A. J. & Nam, S. W. Counting near-infrared single-photons with 95% efficiency. Opt. Express 16, 3032–3040 (2008).

    ADS  Google Scholar 

  91. Hadfield, R. H. Single-photon detectors for optical quantum information applications. Nature Photon. 3, 696–705 (2009).

    ADS  Google Scholar 

  92. Tanner, M. G. et al. Enhanced telecom wavelength single-photon detection with NbTiN superconducting nanowires on oxidized silicon. Appl. Phys. Lett. 96, 221109 (2010).

    ADS  Google Scholar 

  93. Pernice, W. et al. High speed travelling wave single-photon detectors with near-unity quantum efficiency. Preprint at http://arxiv.org/abs/1108.5299 (2011).

  94. Wagenknecht, C. et al. Experimental demonstration of a heralded entanglement source. Nature Photon. 4, 549–552 (2010).

    ADS  Google Scholar 

  95. Barz, S., Cronenberg, G., Zeilinger, A. & Walther, P. Heralded generation of entangled photon pairs. Nature Photon. 4, 553–556 (2010).

    ADS  Google Scholar 

  96. Ufimtsev, I. S., Luehr, N. & Martinez, T. J. Charge transfer and polarization in solvated proteins from ab initio molecular dynamics. J. Phys. Chem. Lett. 2, 1789–1793 (2011).

    Google Scholar 

  97. Kassal, I., Jordan, S. P., Love, P. J., Mohseni, M. & Aspuru-Guzik, A. Polynomial-time quantum algorithm for the simulation of chemical dynamics. Proc. Natl Acad. Sci. USA 105, 18681–18686 (2008).

    ADS  Google Scholar 

  98. Gerrits, T. et al. On-chip, photon-number-resolving, telecom-band detectors for scalable photonic information processing. Phys. Rev. A 84, 060301 (2011).

    ADS  Google Scholar 

Download references

Acknowledgements

We thank I. Kassal, P. Love, and S. Barz for careful comments on the manuscript and B. Lanyon, A. Fedrizzi and A. White for providing images. M. Tillman, M. Tomandl and L. Kaye prepared the graphics for the manuscript. A.A-G. also acknowledges support from the National Science Foundation under the Center for Chemical Innovation (CCI) programme (CHE-1037992), as well as the Camille and Henry Dreyfus and Sloan Foundations for support. P.W. acknowledges support from the European Commission, QESSENCE (No 248095), the John Templeton Foundation, the Austrian Nano-initiative NAP Platon, the Austrian Science Fund (FWF): [SFB-FOCUS] and [Y585-N20] and the doctoral programme CoQuS, and from the Air Force Office of Scientific Research, Air Force Material Command, USAF, under grant number FA8655-11-1-3004.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Alán Aspuru-Guzik or Philip Walther.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aspuru-Guzik, A., Walther, P. Photonic quantum simulators. Nature Phys 8, 285–291 (2012). https://doi.org/10.1038/nphys2253

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys2253

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