29
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Quantum percolation and transition point of a directed discrete-time quantum walk

      research-article
      a , 1 , 1
      Scientific Reports
      Nature Publishing Group

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          Quantum percolation describes the problem of a quantum particle moving through a disordered system. While certain similarities to classical percolation exist, the quantum case has additional complexity due to the possibility of Anderson localisation. Here, we consider a directed discrete-time quantum walk as a model to study quantum percolation of a two-state particle on a two-dimensional lattice. Using numerical analysis we determine the fraction of connected edges required (transition point) in the lattice for the two-state particle to percolate with finite (non-zero) probability for three fundamental lattice geometries, finite square lattice, honeycomb lattice, and nanotube structure and show that it tends towards unity for increasing lattice sizes. To support the numerical results we also use a continuum approximation to analytically derive the expression for the percolation probability for the case of the square lattice and show that it agrees with the numerically obtained results for the discrete case. Beyond the fundamental interest to understand the dynamics of a two-state particle on a lattice (network) with disconnected vertices, our study has the potential to shed light on the transport dynamics in various quantum condensed matter systems and the construction of quantum information processing and communication protocols.

          Related collections

          Most cited references11

          • Record: found
          • Abstract: found
          • Article: found
          Is Open Access

          Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer

          Energy transfer within photosynthetic systems can display quantum effects such as delocalized excitonic transport. Recently, direct evidence of long-lived coherence has been experimentally demonstrated for the dynamics of the Fenna-Matthews-Olson (FMO) protein complex [Engel et al., Nature 446, 782 (2007)]. However, the relevance of quantum dynamical processes to the exciton transfer efficiency is to a large extent unknown. Here, we develop a theoretical framework for studying the role of quantum interference effects in energy transfer dynamics of molecular arrays interacting with a thermal bath within the Lindblad formalism. To this end, we generalize continuous-time quantum walks to non-unitary and temperature-dependent dynamics in Liouville space derived from a microscopic Hamiltonian. Different physical effects of coherence and decoherence processes are explored via a universal measure for the energy transfer efficiency and its susceptibility. In particular, we demonstrate that for the FMO complex an effective interplay between free Hamiltonian and thermal fluctuations in the environment leads to a substantial increase in energy transfer efficiency from about 70% to 99%.
            Bookmark
            • Record: found
            • Abstract: found
            • Article: found
            Is Open Access

            Quantum Walk in Position Space with Single Optically Trapped Atoms

            The quantum walk is the quantum analogue of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to extensive applications in quantum information science. In our experiment, we implemented a quantum walk on the line with single neutral atoms by deterministically delocalizing them over the sites of a one-dimensional spin-dependent optical lattice. With the use of site-resolved fluorescence imaging, the final wave function is characterized by local quantum state tomography, and its spatial coherence is demonstrated. Our system allows the observation of the quantum-to-classical transition and paves the way for applications, such as quantum cellular automata.
              Bookmark
              • Record: found
              • Abstract: found
              • Article: not found

              Realization of quantum walks with negligible decoherence in waveguide lattices.

              Quantum random walks are the quantum counterpart of classical random walks, and were recently studied in the context of quantum computation. Physical implementations of quantum walks have only been made in very small scale systems severely limited by decoherence. Here we show that the propagation of photons in waveguide lattices, which have been studied extensively in recent years, are essentially an implementation of quantum walks. Since waveguide lattices are easily constructed at large scales and display negligible decoherence, they can serve as an ideal and versatile experimental playground for the study of quantum walks and quantum algorithms. We experimentally observe quantum walks in large systems ( approximately 100 sites) and confirm quantum walks effects which were studied theoretically, including ballistic propagation, disorder, and boundary related effects.
                Bookmark

                Author and article information

                Journal
                Sci Rep
                Sci Rep
                Scientific Reports
                Nature Publishing Group
                2045-2322
                10 October 2014
                2014
                : 4
                : 6583
                Affiliations
                [1 ]Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University , Okinawa, Japan
                Author notes
                Article
                srep06583
                10.1038/srep06583
                4192638
                25301394
                6fff70d5-5442-472a-8a22-18505a0be058
                Copyright © 2014, Macmillan Publishers Limited. All rights reserved

                This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder in order to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/4.0/

                History
                : 03 April 2014
                : 17 September 2014
                Categories
                Article

                Uncategorized
                Uncategorized

                Comments

                Comment on this article