Photonic quantum simulators

Journal name:
Nature Physics
Volume:
8,
Pages:
285–291
Year published:
DOI:
doi:10.1038/nphys2253
Received
Accepted
Published online

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.

At a glance

Figures

  1. First quantum chemistry experiment on a quantum information processor.
    Figure 1: First quantum chemistry experiment on a quantum information processor.

    a, Quantum optics experiment for simulating the energy of the hydrogen molecule in the minimal basis set. A pair of entangled photons generated via the spontaneous parametric down-conversion (SPDC) process implements an iterative phase-estimation scheme where one of the photons represents two 2×2 blocks of the 6×6 full configuration interaction matrix of H2 in the minimal quantum chemistry basis set20. The photons are coupled into free space optical modes C (control) and R (register) and manipulated by using half-wave plates (λ/2) and quarter-wave plates (λ/4) to implement single-qubit rotations around the Bloch axes, Ry and Rz, as well as Hadamard (H) and Pauli X gate (X) operations. Coincident detection events between single photon counting modules (SPCMs) D1 and D3 (D2 and D3) herald a successful run of the circuit. Panel reproduced from ref. 20. b, Plot of the molecular energies of the different electronic states as a function of interatomic distance obtained with the device to 20 bits of precision using an iterative phase-estimation procedure (IPEA) and a majority-voting scheme as a simple error correction protocol.

  2. Schematic of the photonic quantum simulation of delocalized chemical bonds.
    Figure 2: Schematic of the photonic quantum simulation of delocalized chemical bonds.

    a, Two entangled photon pairs are generated through the process of parametric down-conversion. Superimposing one single photon from each pair at a tunable beam splitter results in quantum interference, such that the measured four-photon coincidences correspond to the ground state, for example of a Heisenberg-interacting spin tetramer. Dependent on the reflectivity of the beam splitter, frustration in valence-bond states or so-called spin-liquid states can be investigated23. b, Future experiments using more entangled photon pairs may allow the study of the ground-state properties of molecular ground states, such as the delocalized bonds in benzene.

  3. Photonic quantum circuits for the simulation of quantum and quantum stochastic walks.
    Figure 3: Photonic quantum circuits for the simulation of quantum and quantum stochastic walks.

    a, The bulk-optics set-up employed to simulate a quantum-stochastic-walk transition between a pure quantum walk and a classical walk21. b, Continuously coupled waveguide arrays were also used to realize correlated-photon quantum walks22. The optical micrograph of a 21-waveguide array shows the three input waveguides on the bottom, bending into the 700-μm-long coupling region, and exiting at the top towards the output ports, where the signal is detected. The output pattern (upper inset) and a simulation of the intensity of laser light propagating in the array (lower inset) are also shown. Panel reproduced with permission from ref. 22, © 2010 AAAS.

References

  1. Feynman, R. Simulating physics with computers. Int. J. Theor. Phys. 21, 467488 (1982).
  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, 7477 (2009).
  3. Trotzky, S. et al. Suppression of the critical temperature for superfluidity near the Mott transition. Nature Phys. 6, 9961004 (2010).
  4. Weitenberg, C. et al. Single-spin addressing in an atomic Mott insulator. Nature 471, 319324 (2011).
  5. Lewenstein, M. et al. Ultracold atomic gases in optical lattices: Mimicking condensed matter physics and beyond. Adv. Phys. 56, 243379 (2007).
  6. Bloch, I., Dalibard, J. & Nascimbène, S. Quantum simulations with ultracold quantum gases. Nature Phys. 8, 267276 (2012).
  7. Friedenauer, A., Schmitz, H., Glueckert, J. T., Porras, D. & Schaetz, T. Simulating a quantum magnet with trapped ions. Nature Phys. 4, 757761 (2008).
  8. Gerritsma, R. et al. Quantum simulation of the Dirac equation. Nature 463, 6871 (2010).
  9. Barreiro, J. T. et al. An open-system quantum simulator with trapped ions. Nature 470, 486491 (2011).
  10. Islam, R. et al. Onset of a quantum phase transition with a trapped ion quantum simulator. Nature Commun. 2, 377 (2011).
  11. Lanyon, B. P. et al. Universal digital quantum simulation with trapped ions. Science 334, 5761 (2011).
  12. Kim, K. et al. Quantum simulation of frustrated Ising spins with trapped ions. Nature 465, 590593 (2010).
  13. Blatt, R. & Roos, C. F. Quantum simulations with trapped ions. Nature Phys. 8, 277284 (2012).
  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).
  15. Du, J. et al. NMR implementation of a molecular hydrogen quantum simulation with adiabatic state preparation. Phys. Rev. Lett. 104, 030502 (2010).
  16. Neeley, M. et al. Emulation of a quantum spin with a superconducting phase qudit. Science 325, 722725 (2009).
  17. Houck, A. A., Türeci, H. E. & Koch, J. On-chip quantum simulation with superconducting circuits. Nature Phys. 8, 292299 (2012).
  18. Lu, C-Y. et al. Demonstrating anyonic fractional statistics with a six-qubit quantum simulator. Phys. Rev. Lett. 102, 030502 (2009).
  19. Pachos, J. K. et al. Revealing anyonic features in a toric code quantum simulation. New J. Phys. 11, 083010 (2009).
  20. Lanyon, B. P. et al. Towards quantum chemistry on a quantum computer. Nature Chem. 2, 106111 (2010).
  21. Broome, M. A. et al. Discrete single-photon quantum walks with tunable decoherence. Phys. Rev. Lett. 104, 153602 (2010).
  22. Peruzzo, A. et al. Quantum walks of correlated photons. Science 329, 15001503 (2010).
  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, 399405 (2011).
  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).
  26. Buluta, I. & Nori, F. Quantum simulators. Science 326, 108111 (2009).
  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, 5863 (April 2008).
  30. Sokolov, A. N. et al. From computational discovery to experimental characterization of a high hole mobility organic crystal. Nature Commun. 2, 437 (2011).
  31. Schuch, N. & Verstraete, F. Computational complexity of interacting electrons and fundamental limitations of density functional theory. Nature Phys. 5, 732735 (2009).
  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, 17041707 (2005).
  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, 185207 (2011).
  35. Whitfield, J. D., Biamonte, J. & Aspuru-Guzik, A. Simulation of electronic structure Hamiltonians using quantum computers. Mol. Phys. 109, 735750 (2011).
  36. Abrams, D. & Lloyd, S. Simulation of many-body Fermi systems on a universal quantum computer. Phys. Rev. Lett. 79, 25862589 (1997).
  37. Abrams, D. & Lloyd, S. Quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors. Phys. Rev. Lett. 83, 51625165 (1999).
  38. Lanyon, B. P. et al. Simplifying quantum logic using higher-dimensional Hilbert spaces. Nature Phys. 5, 134140 (2009).
  39. Reck, M., Zeilinger, A., Bernstein, H. J. & Bertani, P. Experimental realization of any discrete unitary operator. Phys. Rev. Lett. 73, 5861 (1994).
  40. Politi, A., Cryan, M. J., Rarity, J. G., Yu, S. & O’Brien, J. L. Silica-on-silicon waveguide quantum circuits. Science 320, 646649 (2008).
  41. Sansoni, L. et al. Polarization entangled state measurement on a chip. Phys. Rev. Lett. 105, 200503 (2010).
  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).
  43. Politi, A., Matthews, J. C. F. & O’Brien, J. L. Shor’s quantum factoring algorithm on a photonic chip. Science 325, 1221 (2009).
  44. Matthews, J., Politi, A., Stefanov, A. & O’Brien, J. Manipulation of multiphoton entanglement in waveguide quantum circuits. Nature Photon. 3, 346350 (2009).
  45. Shadbolt, P. J. et al. Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit. Nature Photon. 6, 4549 (2012).
  46. Laing, A. et al. High-fidelity operation of quantum photonic circuits. Appl. Phys. Lett. 97, 211109 (2010).
  47. Marshall, G. D. et al. Laser written waveguide photonic quantum circuits. Opt. Express 17, 1254612554 (2009).
  48. Owens, J. O. et al. Two-photon quantum walks in an elliptical direct-write waveguide array. New J. Phys. 13, 075003 (2011).
  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).
  50. Longhi, S. et al. Observation of dynamic localization in periodically curved waveguide arrays. Phys. Rev. Lett. 96, 243901 (2006).
  51. Dreisow, F. et al. Classical simulation of relativistic Zitterbewegung in photonic lattices. Phys. Rev. Lett. 105, 143902 (2010).
  52. Longhi, S. Photonic analog of Zitterbewegung in binary waveguide arrays. Opt. Lett. 35, 235237 (2010).
  53. Plotnik, Y. et al. Experimental observation of optical bound states in the continuum. Phys. Rev. Lett. 107, 183901 (2011).
  54. Perets, H. B. et al. Realization of quantum walks with negligible decoherence in waveguide lattices. Phys. Rev. Lett. 100, 170506 (2008).
  55. Farhi, E. & Gutmann, S. Quantum computation and decision trees. Phys. Rev. A 58, 915928 (1998).
  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).
  57. Knight, P. L., Roldán, E. & Sipe, J. E. Quantum walk on the line as an interference phenomenon. Phys. Rev. A 68, 020301 (2003).
  58. Schreiber, A. et al. Photons walking the line: A quantum walk with adjustable coin operations. Phys. Rev. Lett. 104, 050502 (2010).
  59. Schreiber, A. et al. Decoherence and disorder in quantum walks: From ballistic spread to localization. Phys. Rev. Lett. 106, 180403 (2011).
  60. Engel, G. et al. Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems. Nature 446, 782786 (2007).
  61. Collini, E. et al. Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature. Nature 463, 644647 (2010).
  62. Panitchayangkoon, G. et al. Long-lived quantum coherence in photosynthetic complexes at physiological temperature. Proc. Natl Acad. Sci. USA 107, 1276612770 (2010).
  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).
  64. Rebentrost, P., Mohseni, M., Kassal, I., Lloyd, S. & Aspuru-Guzik, A. Environment-assisted quantum transport. New J. Phys. 11, 033003 (2009).
  65. Plenio, M. B. & Huelga, S. F. Dephasing assisted transport: Quantum networks and biomolecules. New J. Phys. 10, 113019 (2008).
  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).
  67. Keil, R. et al. Photon correlations in two-dimensional waveguide arrays and their classical estimate. Phys. Rev. A 81, 023834 (2010).
  68. Marshall, W. Antiferromagnetism. Proc. R. Soc. A 232, 4868 (1955).
  69. Anderson, P. W. The resonating valence bond state in La2CuO4 and superconductivity. Science 235, 11961198 (1987).
  70. Coffman, V., Kundu, J. & Wootters, W. K. Distributed entanglement. Phys. Rev. A 61, 052306 (2000).
  71. Osborne, T. J. & Verstraete, F. General monogamy inequality for bipartite qubit entanglement. Phys. Rev. Lett. 96, 220503 (2006).
  72. Mattle, K., Michler, M, Weinfurter, H., Zeilinger, A. & Zukowski, M. Non-classical statistics at multiport beam splitters. Appl. Phys. B 60, 111117 (1995).
  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, R1R4 (1996).
  74. Hong, C. K., Ou, Z. Y. & Mandel, L. Measurement of subpicosecond time intervals between two photons by interference. Phys. Rev. Lett. 59, 20442046 (1987).
  75. Braunstein, S. L. & Mann, A. Measurement of the Bell operator and quantum teleportation. Phys. Rev. A 51, R1727R1730 (1995).
  76. Bouwmeester, D. et al. Experimental quantum teleportation. Nature 390, 575579 (1997).
  77. Semião, F. L. & Paternostro, M. Quantum circuits for spin and flavor degrees of freedom of quarks forming nucleons. Quant. Inf. Proc. 11, 6775 (2011).
  78. O’Brien, J. L., Furusawa, A. & Vuckovic, J. Photonic quantum technologies. Nature Photon. 3, 687695 (2009).
  79. Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 4652 (2001).
  80. Kok, P. et al. Linear optical quantum computing with photonic qubits. Rev. Mod. Phys. 79, 135174 (2007).
  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).
  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).
  83. Walther, P. & Zeilinger, A. Experimental realization of a photonic Bell-state analyzer. Phys. Rev. A 72, 010302(R) (2005).
  84. Bao, X-H. et al. Optical nondestructive controlled-NOT gate without using entangled photons. Phys. Rev. Lett. 98, 170502 (2007).
  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, 1006710071 (2011).
  86. Gao, W-B. et al. Teleportation-based realization of an optical quantum two-qubit entangling gate. Proc. Natl Acad. Sci. USA 107, 2086920874 (2010).
  87. Kwiat, P. G. et al. New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett. 75, 43374341 (1995).
  88. Rosfjord, K. M. et al. Nanowire single-photon detector with an integrated optical cavity and anti-reflection coating. Opt. Express 14, 527534 (2006).
  89. Divochiy, A. et al. Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths. Nature Photon. 2, 302306 (2008).
  90. Lita, A. E., Miller, A. J. & Nam, S. W. Counting near-infrared single-photons with 95% efficiency. Opt. Express 16, 30323040 (2008).
  91. Hadfield, R. H. Single-photon detectors for optical quantum information applications. Nature Photon. 3, 696705 (2009).
  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).
  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, 549552 (2010).
  95. Barz, S., Cronenberg, G., Zeilinger, A. & Walther, P. Heralded generation of entangled photon pairs. Nature Photon. 4, 553556 (2010).
  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, 17891793 (2011).
  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, 1868118686 (2008).
  98. Gerrits, T. et al. On-chip, photon-number-resolving, telecom-band detectors for scalable photonic information processing. Phys. Rev. A 84, 060301 (2011).

Download references

Author information

Affiliations

  1. Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA

    • Alán Aspuru-Guzik
  2. Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria

    • Philip Walther

Competing financial interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to:

Author details

Additional data