Thermodynamic formalism for dissipative quantum walks

Garnerone, Silvano

doi:10.1103/physreva.86.032342

Cited by 23 publications

(26 citation statements)

References 55 publications

(75 reference statements)

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“…From an algorithmic point of view, it is an interesting task to develop a dissipative version of this algorithm and to understand its performance and robustness properties in such scenario. We note that dissipation has already been considered as an element with respect to some aspect of the algorithm6566, but the development of a truly dissipative version in the spirit of dissipative quantum algorithms and computation6768 remains an open question. Furthermore the growing field of complex quantum networks would benefit from a version of the algorithm that is able to rank nodes in the more general case where qubits are located at the nodes of the network.…”

Section: Discussionmentioning

confidence: 99%

Quantum Google in a Complex Network

Paparo

Müller

Comellas

et al. 2013

Sci Rep

137

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We investigate the behaviour of the recently proposed Quantum PageRank algorithm, in large complex networks. We find that the algorithm is able to univocally reveal the underlying topology of the network and to identify and order the most relevant nodes. Furthermore, it is capable to clearly highlight the structure of secondary hubs and to resolve the degeneracy in importance of the low lying part of the list of rankings. The quantum algorithm displays an increased stability with respect to a variation of the damping parameter, present in the Google algorithm, and a more clearly pronounced power-law behaviour in the distribution of importance, as compared to the classical algorithm. We test the performance and confirm the listed features by applying it to real world examples from the WWW. Finally, we raise and partially address whether the increased sensitivity of the quantum algorithm persists under coordinated attacks in scale-free and random networks.

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Section: Discussionmentioning

confidence: 99%

Quantum Google in a Complex Network

Paparo

Müller

Comellas

et al. 2013

Sci Rep

137

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“…Notice that in our system we have decoherence without dissipation, such that the position variance provides a good indicator of the transition. A different approach has been discussed for dissipative systems [79].…”

Section: Dynamics Of Noisy Continuous-time Quantum Walksmentioning

confidence: 99%

Non-Markovian continuous-time quantum walks on lattices with dynamical noise

et al. 2016

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We address the dynamics of continuous-time quantum walks on one-dimensional disordered lattices inducing dynamical noise in the system. Noise is described as time-dependent fluctuations of the tunneling amplitudes between adjacent sites, and attention is focused on non-Gaussian telegraph noise, going beyond the usual assumption of fast Gaussian noise. We observe the emergence of two different dynamical behaviors for the walker, corresponding to two opposite noise regimes: slow noise (i.e. strong coupling with the environment) confines the walker into few lattice nodes, while fast noise (weak coupling) induces a transition between quantum and classical diffusion over the lattice. A phase transition between the two dynamical regimes may be observed by tuning the ratio between the autocorrelation time of the noise and the coupling between the walker and the external environment generating the noise. We also address the non-Markovianity of the quantum map by assessing its memory effects, as well as evaluating the information backflow to the system. Our results suggest that the non-Markovian character of the evolution is linked to the dynamical behavior in the slow noise regime, and that fast noise induces a Markovian dynamics for the walker.

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“…Quantum walks are also of increasing relevance outside physics. As well as being a powerful tool for studying transport in quantum systems [7][8][9][10], e.g., the transport of energy through biological complexes or man-made solar cells, quantum walks have been proposed as a means of analyzing classical sociological networks [11][12][13][14]. To fully understand these phenomena, and others, for networks with non-trivial topologies, requires the merging of the methods of complex networks and quantum mechanics [15].…”

Section: Introductionmentioning

confidence: 99%

Degree Distribution in Quantum Walks on Complex Networks

et al. 2013

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In this theoretical study, we analyze quantum walks on complex networks, which model network-based processes ranging from quantum computing to biology and even sociology. Specifically, we analytically relate the average long time probability distribution for the location of a unitary quantum walker to that of a corresponding classical walker. The distribution of the classical walker is proportional to the distribution of degrees, which measures the connectivity of the network nodes and underlies many methods for analyzing classical networks including website ranking. The quantum distribution becomes exactly equal to the classical distribution when the walk has zero energy and at higher energies the difference, the so-called quantumness, is bounded by the energy of the initial state. We give an example for which the quantumness equals a Renyi entropy of the normalized weighted degrees, guiding us to regimes for which the classical degree-dependent result is recovered and others for which quantum effects dominate.Comment: 8 pages, 4 figures; improved description and new examples; accepted for publication in Phys. Rev.

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Thermodynamic formalism for dissipative quantum walks

Cited by 23 publications

References 55 publications

Quantum Google in a Complex Network

Quantum Google in a Complex Network

Non-Markovian continuous-time quantum walks on lattices with dynamical noise

Degree Distribution in Quantum Walks on Complex Networks

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