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


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.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13


  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)

    Article  ADS  Google 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)

    Article  ADS  Google Scholar 

  3. 3.

    Nalbach, P., Eckel, J., Thorwart, M.: Quantum coherent biomolecular energy transfer with spatially correlated fluctuations. New J. Phys. 12, 065043 (2010)

    Article  ADS  Google 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)

    Article  ADS  Google 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)

    Article  ADS  Google Scholar 

  6. 6.

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

    Article  ADS  Google Scholar 

  7. 7.

    Plenio, M., Huelga, S.: Dephasing assisted transport: quantum networks and biomolecules. New J. Phys. 10, 113019 (2008)

    Article  ADS  Google 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)

    Article  ADS  Google 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)

    Article  ADS  Google 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)

    Article  ADS  Google 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)

    Article  ADS  Google 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)

    Article  ADS  Google 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)

    Article  Google 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)

    Article  ADS  Google 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)

    Article  ADS  Google Scholar 

  16. 16.

    Riazanov, G.V.: The Feynman path integral for the Dirac equation. Sov. Phys. JETP 6, 1107–1113 (1958)

    MathSciNet  ADS  Google Scholar 

  17. 17.

    Feynman, R.: Quantum mechanical computers. Found. Phys. 16, 507 (1986)

    MathSciNet  Article  ADS  Google Scholar 

  18. 18.

    Parthasarathy, K.R.: The passage from random walk to diffusion in quantum probability. J. Appl. Probab. 25, 151–166 (1988)

    Article  MATH  MathSciNet  Google 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)

    MathSciNet  MATH  Google Scholar 

  20. 20.

    Aharonov, Y., Davidovich, L., Zagury, N.: Quantum random walk. Phys. Rev. A 48, 1687 (1993)

    Article  ADS  Google Scholar 

  21. 21.

    Meyer, D.A.: From quantum cellular automata to quantum lattice gases. J. Stat. Phys. 85, 551 (1996)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  22. 22.

    Farhi, E., Gutmann, S.: Quantum computation and decision trees. Phys. Rev. A 58, 915 (1998)

    MathSciNet  Article  ADS  Google Scholar 

  23. 23.

    Kempe, J.: Contemp. Quantum random walks-an introductory overview. Contemp. Phys. 44, 307 (2003)

    Article  ADS  Google Scholar 

  24. 24.

    Ambainis, A.: Quantum walk and their algorithmic applications. Int. J. Quantum Inf. 1(4), 507–518 (2003)

    Article  MATH  Google Scholar 

  25. 25.

    Chandrashekar, C.M., Laflamme, R.: Quantum phase transition using quantum walks in an optical lattice. Phys. Rev. A 78, 022314 (2008)

    Article  ADS  Google Scholar 

  26. 26.

    Chandrashekar, C.M.: Disordered-quantum-walk-induced localization of a Bose–Einstein. Phys. Rev. A 83, 022320 (2011)

    Article  ADS  Google Scholar 

  27. 27.

    Kitagawa, T., Rudner, M.S., Berg, E., Demler, E.: Exploring topological phases with quantum walks. Phys. Rev. A 82, 033429 (2010)

    Article  ADS  Google 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)

    Article  ADS  Google Scholar 

  29. 29.

    Kurzyński, P., Wójcik, A.: Discrete time quantum walk approach to state transfer. Phys. Rev. A 83, 062315 (2011)

    Article  ADS  Google 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)

    MathSciNet  Article  ADS  MATH  Google 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)

    MathSciNet  Article  ADS  Google 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)

    MathSciNet  Article  MATH  Google 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)

    Article  Google Scholar 

  35. 35.

    Chandrashekar, C.M., Srikanth, R., Banerjee, S.: Symmetries and noise in quantum walk. Phys. Rev. A 76, 022316 (2007)

    MathSciNet  Article  ADS  Google 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)

    Article  ADS  Google 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)

    MathSciNet  Article  ADS  Google Scholar 

  38. 38.

    Luo, S.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008)

    Article  ADS  Google 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)

    Article  ADS  Google 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)

    Article  ADS  Google 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)

    Article  ADS  Google 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)

    Article  ADS  Google 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)

    Article  ADS  Google 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)

    Article  ADS  Google 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)

    Article  ADS  Google 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)

    Article  ADS  Google 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)

    Article  ADS  Google 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)

    Article  ADS  Google 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)

    Article  ADS  Google 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)

    Article  ADS  Google 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)

    Article  ADS  Google Scholar 

Download references


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.

Author information



Corresponding author

Correspondence to C. M. Chandrashekar.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Chandrashekar, C.M., Busch, T. Noise-enhanced quantum transport on a closed loop using quantum walks. Quantum Inf Process 13, 1313–1329 (2014).

Download citation


  • Initial Position
  • Closed Loop
  • Quantum Correlation
  • Transport Efficiency
  • Quantum Walk