Time evolution of continuous-time quantum walks on dynamical percolation graphs

Darázs, Zoltán; Kiss, T.

doi:10.1088/1751-8113/46/37/375305

Cited by 20 publications

(26 citation statements)

References 49 publications

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“…In this paper we analyze the effects of RTN on spatial search on graphs with generic topology. Other models of CTQW subject to dynamical noise have been proposed as well [28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Quantum spatial search on graphs subject to dynamical noise

et al. 2018

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We address quantum spatial search on graphs and its implementation by continuous-time quantum walks in the presence of dynamical noise. In particular, we focus on search on the complete graph and on the star graph of order N, also proving that noiseless spatial search shows optimal quantum speedup in the latter, in the computational limit N 1. The noise is modeled by independent sources of random telegraph noise (RTN), dynamically perturbing the links of the graph. We observe two different behaviors depending on the switching rate of RTN: fast noise only slightly degrades performance, whereas slow noise is more detrimental and, in general, lowers the success probability. In particular, we still find a quadratic speed-up for the average running time of the algorithm, while for the star graph with external target node we observe a transition to classical scaling. We also address how the effects of noise depend on the order of the graphs, and discuss the role of the graph topology. Overall, our results suggest that realizations of quantum spatial search are possible with current technology, and also indicate the star graph as the perfect candidate for the implementation by noisy quantum walks, owing to its simple topology and nearly optimal performance also for just few nodes.

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“…In this paper we analyze the effects of RTN on spatial search on graphs with generic topology. Other models of CTQW subject to dynamical noise have been proposed as well [28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Quantum spatial search on graphs subject to dynamical noise

et al. 2018

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“…The way this general property is manifested still depends largely on the detailed substitutions, as well as on the energy of the eigenstates. Thus, many issues remain open in understanding how the lattice structure [7], disorder [8], and eigenstate energy favors the wave function localization on particular sets of sites, and on the possibility of controlling the wave function localization [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

How the site degree influences quantum probability on inhomogeneous substrates

et al. 2017

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We investigate the effect of the node degree and energy E on the electronic wave function for regular and irregular structures, namely, regular lattices, disordered percolation clusters, and complex networks. We evaluate the dependence of the quantum probability for each site on its degree. For bi-regular structures, we prove analytically that the probability P k (E) of finding the particle on any site with k neighbors is independent of E. For more general structures, the dependency of P k (E) on E is discussed by taking into account exact results on a one-dimensional semi-regular chain: P k (E) is large for small values of E when k is also small, and its maximum values shift towards large values of |E| with increasing k. Numerical evaluations of P k (E) for two different types of percolation clusters and the Apollonian network suggest that this feature might be generally valid.

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“…In the former, the network configuration does not change during propagation, whereas in the latter, connections between sites do alter in time. Both variants have extensively been studied so far in the context of transport and spreading properties for discrete-and continuous-time quantum walks [32][33][34][35][36][37][38][39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

Coherent transport over an explosive percolation lattice

Yalçınkaya

Gedik

2017

J. Phys. A: Math. Theor.

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Abstract. We investigate coherent transport over a finite square lattice in which the growth of bond percolation clusters are subjected to an Achlioptas type selection process, i.e., whether a bond will be placed or not depends on the sizes of clusters it may potentially connect. Different than the standard percolation where the growth of discrete clusters are completely random, clusters in this case grow in correlation with one another. We show that certain values of correlation strength, if chosen in a way to suppress the growth of the largest cluster which actually results in an explosive growth later on, may lead to more efficient transports than in the case of standard percolation, satisfied that certain fraction of total possible bonds are present in the lattice. In this case transport efficiency increases as a power function of bond fraction in the vicinity of where effective transport begins. It turns out that the higher correlation strengths may also reduce the efficiency as well. We also compare our results with those of the incoherent transport and examine the average spreading of eigenstates for different bond fractions. In this way, we demonstrate that structural differences of discrete clusters due to different correlations result in different localization properties.

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Time evolution of continuous-time quantum walks on dynamical percolation graphs

Cited by 20 publications

References 49 publications

Quantum spatial search on graphs subject to dynamical noise

Quantum spatial search on graphs subject to dynamical noise

How the site degree influences quantum probability on inhomogeneous substrates

Coherent transport over an explosive percolation lattice

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