Quantum Information Processing

, Volume 13, Issue 6, pp 1313–1329 | Cite as

Noise-enhanced quantum transport on a closed loop using quantum walks

  • C. M. ChandrashekarEmail author
  • Thomas Busch


We study the effect of noise on the transport of a quantum state from a closed loop of \(n\)-sites with one of the sites as a sink. Using a discrete-time quantum walk dynamics, we demonstrate that the transport efficiency can be enhanced with noise when the number of sites in the loop is small and reduced when the number of sites in the loop grows. By using the concept of measurement induced disturbance, we identify the regimes in which genuine quantum effects are responsible for the enhanced transport.


Initial Position Closed Loop Quantum Correlation Transport Efficiency Quantum Walk 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We would like to acknowledge valuable discussions with J. Goold and R. Dorner. This project was supported by Science Foundation Ireland under Project No. 10/IN.1/I2979.


  1. 1.
    Gaab, K.M., Bardeen, C.J.: The effects of connectivity, coherence, and trapping on energy transfer in simple light-harvesting systems studied using the Haken-Strobl model with diagonal disorder. J. Chem. Phys. 121, 7813–7820 (2004)CrossRefADSGoogle Scholar
  2. 2.
    Olaya-Castro, A., Lee, C., Olsen, F., Johnson, N.: Efficiency of energy transfer in a light-harvesting system under quantum coherence. Phys. Rev. B 78, 085115 (2008)CrossRefADSGoogle Scholar
  3. 3.
    Nalbach, P., Eckel, J., Thorwart, M.: Quantum coherent biomolecular energy transfer with spatially correlated fluctuations. New J. Phys. 12, 065043 (2010)CrossRefADSGoogle Scholar
  4. 4.
    Nalbach, P., Braun, D., Thorwart, M.: Exciton transfer dynamics and quantumness of energy transfer in the Fenna–Matthews–Olson complex. Phys. Rev. E 84, 041926 (2011)CrossRefADSGoogle Scholar
  5. 5.
    Scholak, T., Melo, F., Wellens, T., Mintert, F., Buchleitner, A.: Efficient and coherent excitation transfer across disordered molecular networks. Phys. Rev. E 83, 021912 (2011)CrossRefADSGoogle Scholar
  6. 6.
    Rebentrost, P., Mohseni, M., Kassal, I., Lloyd, S., Aspuru-Guzik, A.: Environment-assisted quantum transport. New J. Phys. 11, 033003 (2009)CrossRefADSGoogle Scholar
  7. 7.
    Plenio, M., Huelga, S.: Dephasing assisted transport: quantum networks and biomolecules. New J. Phys. 10, 113019 (2008)CrossRefADSGoogle Scholar
  8. 8.
    Ghosh, P.K., Smirnov, A., Nori, F.: Quantum effects in energy and charge transfer in an artificial photosynthetic complex. J. Chem. Phys. 134, 244103 (2011)CrossRefADSGoogle Scholar
  9. 9.
    Ghosh, P.K., Smirnov, A., Nori, F.: Artificial photosynthetic reaction centers coupled to light-harvesting antennas. Phys. Rev. E 84, 061138 (2011)CrossRefADSGoogle Scholar
  10. 10.
    Engel, G.S., Calhoun, T.R., Read, E.L., Ahn, T., Manal, T., Cheng, Y., Blankenship, R.E., Fleming, G.R.: Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems. Nature 446, 782–786 (2007)CrossRefADSGoogle Scholar
  11. 11.
    Panitchayangkoon, G., Hayes, D., Fransted, K.A., Caram, J.R., Harel, E., Wen, J., Blankenship, R.E., Engel, G.S.: Long-lived quantum coherence in photosynthetic complexes at physiological temperature. Proc. Natl. Acad. Sci. 107, 12766 (2010)CrossRefADSGoogle Scholar
  12. 12.
    Collini, E., Wong, C.Y., Wilk, K.E., Curmi, P.M.G., Brumer, P., Scholes, G.D.: Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature. Nature 463, 644 (2010)CrossRefADSGoogle Scholar
  13. 13.
    Rebentrost, P., Mohseni, M., Aspuru-Guzik, A.: Role of quantum coherence and environmental fluctuations in chromophoric energy transport. J. Phys. Chem. B 113, 9942 (2009)CrossRefGoogle Scholar
  14. 14.
    Caruso, F., Chin, A.W., Datta, A., Huelga, S.F., Plenio, M.B.: Highly efficient energy excitation transfer in light-harvesting complexes: the fundamental role of noise-assisted transport. J. Chem. Phys. 131, 105106 (2009)CrossRefADSGoogle Scholar
  15. 15.
    Mohseni, M., Rebentrost, P., Lloyd, S., Aspuru-Guzik, A.: Environment-assisted quantum walks in photosynthetic energy transfer. J. Chem. Phys. 129, 174106 (2008)CrossRefADSGoogle Scholar
  16. 16.
    Riazanov, G.V.: The Feynman path integral for the Dirac equation. Sov. Phys. JETP 6, 1107–1113 (1958)MathSciNetADSGoogle Scholar
  17. 17.
    Feynman, R.: Quantum mechanical computers. Found. Phys. 16, 507 (1986)MathSciNetCrossRefADSGoogle Scholar
  18. 18.
    Parthasarathy, K.R.: The passage from random walk to diffusion in quantum probability. J. Appl. Probab. 25, 151–166 (1988)CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Lindsay, J.M., Parthasarathy, K.R.: The passage from random walk to diffusion in quantum probability. J. Appl. Probab. Sankhyā Indian J. Stat. Ser. A 50, 151–170 (1988)MathSciNetzbMATHGoogle Scholar
  20. 20.
    Aharonov, Y., Davidovich, L., Zagury, N.: Quantum random walk. Phys. Rev. A 48, 1687 (1993)CrossRefADSGoogle Scholar
  21. 21.
    Meyer, D.A.: From quantum cellular automata to quantum lattice gases. J. Stat. Phys. 85, 551 (1996)CrossRefADSzbMATHMathSciNetGoogle Scholar
  22. 22.
    Farhi, E., Gutmann, S.: Quantum computation and decision trees. Phys. Rev. A 58, 915 (1998)MathSciNetCrossRefADSGoogle Scholar
  23. 23.
    Kempe, J.: Contemp. Quantum random walks-an introductory overview. Contemp. Phys. 44, 307 (2003)CrossRefADSGoogle Scholar
  24. 24.
    Ambainis, A.: Quantum walk and their algorithmic applications. Int. J. Quantum Inf. 1(4), 507–518 (2003)CrossRefzbMATHGoogle Scholar
  25. 25.
    Chandrashekar, C.M., Laflamme, R.: Quantum phase transition using quantum walks in an optical lattice. Phys. Rev. A 78, 022314 (2008)CrossRefADSGoogle Scholar
  26. 26.
    Chandrashekar, C.M.: Disordered-quantum-walk-induced localization of a Bose–Einstein. Phys. Rev. A 83, 022320 (2011)CrossRefADSGoogle Scholar
  27. 27.
    Kitagawa, T., Rudner, M.S., Berg, E., Demler, E.: Exploring topological phases with quantum walks. Phys. Rev. A 82, 033429 (2010)CrossRefADSGoogle Scholar
  28. 28.
    Christandl, M., Datta, N., Ekert, A., Landahl, A.J.: Perfect state transfer in quantum spin networks. Phys. Rev. Lett. 92, 187902 (2004)CrossRefADSGoogle Scholar
  29. 29.
    Kurzyński, P., Wójcik, A.: Discrete time quantum walk approach to state transfer. Phys. Rev. A 83, 062315 (2011)CrossRefADSGoogle Scholar
  30. 30.
    Goyal, S.K., Chandrashekar, C.M.: Spatial entanglement using a quantum walk on a many-body system. J. Phys. A Math. Theor. 43, 235303 (2010)MathSciNetCrossRefADSzbMATHGoogle Scholar
  31. 31.
    Dorner, R., Goold, J., Vedral, V.: Towards quantum simulations of biological information flow. Interface Focus, doi: 10.1098/rsfs.2011.0109 (2012)
  32. 32.
    Muelken, O., Blumen, A.: Continuous-time quantum walks: models for coherent transport on complex networks. Phys. Rep. 502, 37–87 (2011)MathSciNetCrossRefADSGoogle Scholar
  33. 33.
    Bach, E., Coppersmith, S., Goldschen, M.P., Joynt, R., Watrous, J.: One-dimensional quantum walks with absorbing boundaries. J. Comput. Syst. Sci. 69(4), 562–592 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Gönülol, M., Aydiner, E., Shikano, Y., Müstecaplioglu, Ö.E.: Survival probability in a one-dimensional quantum walk on a trapped lattice. New J. Phys. 13, 033037 (2011)CrossRefGoogle Scholar
  35. 35.
    Chandrashekar, C.M., Srikanth, R., Banerjee, S.: Symmetries and noise in quantum walk. Phys. Rev. A 76, 022316 (2007)MathSciNetCrossRefADSGoogle Scholar
  36. 36.
    Banerjee, S., Srikanth, R., Chandrashekar, C.M., Rungta, P.: Symmetry-noise interplay in a quantum walk on an n-cycle. Phys. Rev. A 78, 052316 (2008)CrossRefADSGoogle Scholar
  37. 37.
    Liu, C., Petulante, N.: Quantum walks on the N-cycle subject to decoherence on the coin degree of freedom. Phys. Rev. E 81, 031113 (2010)MathSciNetCrossRefADSGoogle Scholar
  38. 38.
    Luo, S.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008)CrossRefADSGoogle Scholar
  39. 39.
    Srikanth, R., Banerjee, S., Chandrashekar, C.M.: Quantumness in a decoherent quantum walk using measurement-induced disturbance. Phys. Rev. A 81, 062123 (2010)CrossRefADSGoogle Scholar
  40. 40.
    Du, J., Li, H., Xu, X., Shi, M., Wu, J., Zhou, X., Han, R.: Experimental implementation of the quantum random-walk algorithm. Phys. Rev. A 67, 042316 (2003)CrossRefADSGoogle Scholar
  41. 41.
    Ryan, C.A., Laforest, M., Boileau, J.C., Laflamme, R.: Experimental implementation of a discrete-time quantum random walk on an NMR quantum-information processor. Phys. Rev. A 72, 062317 (2005)CrossRefADSGoogle Scholar
  42. 42.
    Lu, D., Zhu, J., Zou, P., Peng, X., Yu, Y., Zhang, S., Chen, Q., Du, J.: Experimental implementation of a quantum random-walk search algorithm using strongly dipolar coupled spins. Phys. Rev. A 81, 022308 (2010)CrossRefADSGoogle Scholar
  43. 43.
    Schmitz, H., Matjeschk, R., Schneider, C., Glueckert, J., Enderlein, M., Huber, T., Schaetz, T.: Quantum walk of a trapped ion in phase space. Phys. Rev. Lett. 103, 090504 (2009)CrossRefADSGoogle Scholar
  44. 44.
    Zahringer, F., Kirchmair, G., Gerritsma, R., Solano, E., Blatt, R., Roos, C.F.: Realization of a quantum walk with one and two trapped ions. Phys. Rev. Lett. 104, 100503 (2010)CrossRefADSGoogle Scholar
  45. 45.
    Perets, H.B., Lahini, Y., Pozzi, F., Sorel, M., Morandotti, R., Silberberg, Y.: Realization of quantum walks with negligible decoherence in waveguide lattices. Phys. Rev. Lett. 100, 170506 (2008)CrossRefADSGoogle Scholar
  46. 46.
    Schreiber, A., Cassemiro, K.N., Potocek, V., Gabris, A., Mosley, P., Andersson, E., Jex, I., Silberhorn, Ch.: Photons walking the line: a quantum walk with adjustable coin operations. Phys. Rev. Lett. 104, 050502 (2010)CrossRefADSGoogle Scholar
  47. 47.
    Broome, M.A., Fedrizzi, A., Lanyon, B.P., Kassal, I., Aspuru-Guzik, A., White, A.G.: Discrete single-photon quantum walks with tunable decoherence. Phys. Rev. Lett. 104, 153602 (2010)CrossRefADSGoogle Scholar
  48. 48.
    Peruzzo, A., Lobino, M., Matthews, J.C.F., Matsuda, N., Politi, A., Poulios, K., Zhou, X., Lahini, Y., Ismail, N., Wörhoff, K., Bromberg, Y., Silberberg, Y., Thompson, M.G., OBrien, J.L.: Quantum walks of correlated photons. Science 329, 1500 (2010)CrossRefADSGoogle Scholar
  49. 49.
    Schreiber, A., Cassemiro, K.N., Potocek, V., Gabris, A., Jex, I., Silberhorn, Ch.: Decoherence and disorder in quantum walks: from ballistic spread to localization. Phys. Rev. Lett. 106, 180403 (2011)CrossRefADSGoogle Scholar
  50. 50.
    Sansoni, L., Sciarrino, F., Vallone, G., Mataloni, P., Crespi, A., Ramponi, R., Osellame, R.: Two-particle bosonic-fermionic quantum walk via integrated photonics. Phys. Rev. Lett. 108, 010502 (2012)CrossRefADSGoogle Scholar
  51. 51.
    Karski, K., Foster, L., Choi, J.-M., Steffen, A., Alt, W., Meschede, D., Widera, A.: Quantum walk in position space with single optically trapped atoms. Science 325, 174 (2009)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Physics DepartmentUniversity College CorkCorkIreland
  2. 2.Quantum Systems UnitOkinawa Institute of Science and Technology Graduate UniversityOkinawa Japan

Personalised recommendations