Transport Efficiency of Continuous-Time Quantum Walks on Graphs

Razzoli, Luca; Paris, Matteo G. A.; Bordone, Paolo

doi:10.3390/e23010085

Cited by 17 publications

(17 citation statements)

References 62 publications

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“…This is motivated by the often asked question whether the efficiency of transportand its noise dependence on graphs -are correlated with the network structure described, e.g., by connectivity, regularity and various centrality measures. Studies in the perfect state transfer context indicate that network connectivity measures are not good indicators of the fidelity of state transfer [56][57][58]. However, although we calculated a large number of centrality measures and 3 different clustering coefficients for the networks we study in the current paper, we could not find any statistically significant relation with the efficiency.…”

Section: Classification Of Transport Efficiencycontrasting

confidence: 64%

Quantum transport efficiency in noisy random-removal and small-world networks

Kurt¹,

Rossi²,

Piilo³

2022

Preprint

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We report the results of an in-depth study of the role of graph topology on quantum transport efficiency in random removal and Watts-Strogatz networks. By using four different environmental models -noiseless, driving by classical random telegraph noise (RTN), thermal quantum bath, and bath+RTN -we compare the role of the environment and of the change in network topology in determining the quantum transport efficiency. We find that small and specific changes in network topology is more effective in causing large change in efficiency compared to that achievable by environmental manipulations for both network classes. Furthermore, we have found that noise dependence of transport efficiency in these networks can be categorized into six classes. In general, our results highlight the interplay that network topology and environment models play in quantum transport, and pave the way for transport studies for networks of increasing size and complexity -when going beyond so far often used few-site transport systems.

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Section: Classification Of Transport Efficiencycontrasting

confidence: 64%

Quantum transport efficiency in noisy random-removal and small-world networks

Kurt¹,

Rossi²,

Piilo³

2022

Preprint

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“…Konno [4,5] proved a weak limit theorem for the CTQW on the line and trees, and showed that there is a striking contrast to the central limit theorem of symmetric classical random walks. Mülken and Blumen [6] reviewed applications of CTQWs to transport in various systems, and recently Razzoli et al [7] analytically determined subspaces of states having maximum transport efficiency for many graph topologies. Benedetti et al [8] described CTQW on dynamical percolation graphs with the goal of analyzing the effect of noise produced by randomly adding or removing graph edges.…”

Section: Introductionmentioning

confidence: 99%

Spatial Search on Johnson Graphs by Continuous-Time Quantum Walk

Tanaka,

Sabri,

Portugal

2021

Preprint

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Spatial search on graphs is one of the most important algorithmic applications of quantum walks. To show that a quantum-walk-based search is more efficient than a random-walk-based search is a difficult problem, which has been addressed in several ways. Usually, graph symmetries aid in the calculation of the algorithm's computational complexity, and Johnson graphs are an interesting class regarding symmetries because they are regular, Hamiltonconnected, vertex-and distance-transitive. In this work, we show that spatial search on Johnson graphs by continuous-time quantum walk achieves the Grover lower bound π √ N /2 with success probability 1 asymptotically for every fixed diameter, where N is the number of vertices. The proof is mathematically rigorous and can be used for other graph classes.

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“…For an initially localized state or a superposition of two vertex states evolving under the transport Hamiltonian (4) it is unlikely to achieve a high transport efficiency. In additin, the transport efficiency η usually decreases with the order N of graph [56]. Our starting point is the observation that breaking the symmetries of the graph can actually improve the transport efficiency.…”

Section: Minimal Perturbation Approachmentioning

confidence: 99%

Perturbed graphs achieve unit transport efficiency without environmental noise

Cavazzoni,

Razzoli,

Bordone

et al. 2022

Preprint

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Coherent transport of an excitation through a network corresponds to continuous-time quantum walk on a graph, and the transport properties of the system may be radically different depending on the graph and on the initial state. The transport efficiency, i.e., the integrated probability of trapping at a certain vertex, is a measure of the success rate of the transfer process. Purely coherent quantum transport is known to be less efficient than the observed excitation transport, e.g., in biological systems, and there is evidence that environmental noise is indeed crucial for excitation transport. At variance with this picture, we here address purely coherent transport on highly symmetric graphs, and show analytically that it is possible to enhance the transport efficiency without environmental noise, i.e., using only a minimal perturbation of the graph. In particular, we show that adding an extra weight to one or two edges, depending on whether the initial state is localized or in a superposition of two vertex states, breaks the inherent symmetries of the graph and may be sufficient to achieve unit transport efficiency. We also briefly discuss the conditions to obtain a null transport efficiency, i.e. to avoid trapping.

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Transport Efficiency of Continuous-Time Quantum Walks on Graphs

Cited by 17 publications

References 62 publications

Quantum transport efficiency in noisy random-removal and small-world networks

Quantum transport efficiency in noisy random-removal and small-world networks

Spatial Search on Johnson Graphs by Continuous-Time Quantum Walk

Perturbed graphs achieve unit transport efficiency without environmental noise

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