Complex quantum networks: From universal breakdown to optimal transport

Mülken, Oliver; Dolgushev, Maxim; Galiceanu, Mircea

doi:10.1103/physreve.93.022304

Cited by 30 publications

(36 citation statements)

References 24 publications

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“…The dual patterns are realized based on sequentially connected rings whose size follows a scale-free degree distribution [13]. Hence the topology of these networks varies with the power-law exponent γ of the scale-free distribution.…”

Section: Discussionmentioning

confidence: 99%

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Dynamics of Dual Scale-Free Polymer Networks

Galiceanu¹,

Carvalho²,

Mülken³

et al. 2017

Preprint

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Abstract:We focus on macromolecules which are modeled as sequentially growing dual scale-free networks. The dual networks are built by replacing star-like units of the primal treelike scale-free networks through rings, which are then transformed in a small-world manner up to the complete graphs. In this respect, the parameter γ describing the degree distribution in the primal treelike scale-free networks regulates the size of the dual units. The transition towards the networks of complete graphs is controlled by the probability p of adding link between non-neighboring nodes of the same initial ring. The relaxation dynamics of the polymer networks is studied in the framework of generalized Gaussian structures by using the full eigenvalue spectrum of the Laplacian matrix. The dynamical quantities on which we focus here are the averaged monomer displacement and the mechanical relaxation moduli. For several intermediate values of the parameter's set (γ, p) we encounter for these dynamical properties regions of constant in-between slope.

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Section: Discussionmentioning

confidence: 99%

“…[13]. Being the dual structures [14] of treelike scale-free networks, which have a power-law distribution for their degrees [4,9,15,16], our networks contain dual units with their sizes following the same power-law decay.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Dual Scale-Free Polymer Networks

Galiceanu¹,

Carvalho²,

Mülken³

et al. 2017

Preprint

Self Cite

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“…The computational advantages of quantum versus stochastic random walk based algorithms has attracted wide interest with typical focus being on general graphs which consequently do not exhibit complex features. However, many works have compared properties of stochastic [68,69] and quantum random walks [63][64][65] on complex networks [70].…”

Section: Quantum Network Based On Physical Connectivitymentioning

confidence: 99%

Complex networks from classical to quantum

2019

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NETWORKS IN QUANTUM PHYSICS VS COMPLEXITYNetwork and graph theory fundamentally arises in nearly all aspects of quantum information and computation. As is the case with traditional network science, not arXiv:1702.08459v4 [quant-ph] 16 Apr 2019Box 1 Cross-pollination between the fields of complex networks and quantum information science.In recent years, seminal work has been carried out at the intersection of quantum information and computation and complex network theory. We attempt to catalog the scope of this work in Fig. 1. complex networks and quantum physics (current status) quantum algorithms for network analysis algorithms and descriptors quantum transport on complex networks quantum communication networks graphity and emergent models of space-time related types of quantum networks quantum inspired network tools network analysis adapted to quantum physical resources tools for understanding network information theory quantum centrality measures random network models detecting community structure in quantum systems random quantum circuits random tensor networks and geometry quantum generalizations of random graph models entanglement percolation on complex networks quantum inspired network measures polynomial and superpolynomial reductions for certain network problems such as flow and effective resistance polynomial and superpolynomial reductions for certain machine learning and data analysis problems quantum walks solving graph recognition and search engine ranking problems walk models of exciton transport in photosynthetic complexes

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“…Examples include the element distinctness problem [13], the spatial search problem [14], and the hitting problem [15,16]. Consequently, CTQW and excitonmediated quantum walk have been studied in a large variety of networks such as binary and glued trees [16,17], Apollonian networks [18,19], fractal networks [20,21], sequentially growing networks [22] and star graphs [23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

The excitonic qubit coupled with a phonon bath on a star graph: anomalous decoherence and coherence revivals

Yalouz

Falvo

Pouthier

2017

Quantum Inf Process

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Based on the operatorial formulation of perturbation theory, the dynamical properties of a Frenkel exciton coupled with a thermal phonon bath on a star graph are studied. Within this method, the dynamics is governed by an effective Hamiltonian which accounts for exciton-phonon entanglement. The exciton is dressed by a virtual phonon cloud, whereas the phonons are dressed by virtual excitonic transitions. Special attention is paid to the description of the coherence of a qubit state initially located on the central node of the graph. Within the nonadiabatic weak coupling limit, it is shown that several timescales govern the coherence dynamics. In the short time limit, the coherence behaves as if the exciton was insensitive to the phonon bath. Then, quantum decoherence takes place, this decoherence being enhanced by the size of the graph and by temperature. However, the coherence does not vanish in the long time limit. Instead, it exhibits incomplete revivals that occur periodically at specific revival times and it shows almost exact recurrences that take place at particular super-revival times, a singular behavior that has been corroborated by performing exact quantum calculations.

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Complex quantum networks: From universal breakdown to optimal transport

Cited by 30 publications

References 24 publications

Dynamics of Dual Scale-Free Polymer Networks

Dynamics of Dual Scale-Free Polymer Networks

Complex networks from classical to quantum

The excitonic qubit coupled with a phonon bath on a star graph: anomalous decoherence and coherence revivals

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