One-dimensional lackadaisical quantum walks

Wang, Kun; Wu, Nan; Xu, Ping; Song, Fangmin

doi:10.1088/1751-8121/aa9235

Cited by 10 publications

(11 citation statements)

References 30 publications

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“…On the other hand, when considering evolutionary games on interdependent networks, which typically contain different nodes in each layer, direct strategy exchange across the layers is not allowed. Rather, players in a given layer can obtain information concerning strategy and payoffs in the other layer via dependency links [92,95,96,[134][135][136][137][138]. Indeed, evolutionary games on interdependent network have to date received the most attention in comparison to evolutionary games on other multilayer networks.…”

Section: Interconnected Networkmentioning

confidence: 99%

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Evolutionary games on multilayer networks: a colloquium

et al. 2015

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Networks form the backbone of many complex systems, ranging from the Internet to human societies. Accordingly, not only is the range of our interactions limited and thus best described and modeled by networks, it is also a fact that the networks that are an integral part of such models are often interdependent or even interconnected. Networks of networks or multilayer networks are therefore a more apt description of social systems. This colloquium is devoted to evolutionary games on multilayer networks, and in particular to the evolution of cooperation as one of the main pillars of modern human societies. We first give an overview of the most significant conceptual differences between single-layer and multilayer networks, and we provide basic definitions and a classification of the most commonly used terms. Subsequently, we review fascinating and counterintuitive evolutionary outcomes that emerge due to different types of interdependencies between otherwise independent populations. The focus is on coupling through the utilities of players, through the flow of information, as well as through the popularity of different strategies on different network layers. The colloquium highlights the importance of pattern formation and collective behavior for the promotion of cooperation under adverse conditions, as well as the synergies between network science and evolutionary game theory.

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Section: Interconnected Networkmentioning

confidence: 99%

“…To explore this option, a coevolutionary rule between strategy change and network interdependence has been proposed and studied in [137]. More precisely, it was assumed that a suc- For details see [138].…”

Section: A Coupling Through Utilitiesmentioning

confidence: 99%

Evolutionary games on multilayer networks: a colloquium

et al. 2015

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“…Here, we focus on the lackadaisical quantum walk, where a single, weighted self-loop is added to each vertex [11]. This can cause faster dispersion on the line [11][12][13], and it also speeds up quantum search on the complete graph [10,11] and two-dimensional periodic square lattice (or discrete torus) [14,15].…”

Section: Introductionmentioning

confidence: 99%

Search by lackadaisical quantum walks with nonhomogeneous weights

Rhodes

Wong

2019

Phys. Rev. A

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The lackadaisical quantum walk, which is a quantum walk with a weighted self-loop at each vertex, has been shown to speed up dispersion on the line and improve spatial search on the complete graph and periodic square lattice. In these investigations, each self-loop had the same weight, owing to each graph's vertex-transitivity. In this paper, we propose lackadaisical quantum walks where the self-loops have different weights. We investigate spatial search on the complete bipartite graph, which can be irregular with N1 and N2 vertices in each partite set, and this naturally leads to self-loops in each partite set having different weights l1 and l2, respectively. We analytically prove that for large N1 and N2, if the k marked vertices are confined to, say, the first partite set, then with the typical initial uniform state over the vertices, the success probability is improved from its non-lackadaisical value when l1 = kN2/2N1 and N2 > (3 − 2 √ 2)N1, regardless of l2. When the initial state is stationary under the quantum walk, however, then the success probability is improved when l1 = kN2/2N1, now without a constraint on the ratio of N1 and N2, and again independent of l2. Next, when marked vertices lie in both partite sets, then for either initial state, there are many configurations for which the self-loops yield no improvement in quantum search, no matter what weights they take.

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“…Initially, cooperators and defectors are randomly distributed with the equal probability 0.5. Individuals asynchronously update their strategies in a random sequential order [39][40][41]. Firstly, an individual i is randomly selected who obtains the payoff P i according to the above equations.…”

Section: Modelmentioning

confidence: 99%

Promoting cooperation by punishing minority

Yang

Chen

2018

Applied Mathematics and Computation

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Punishment is an effective way to sustain cooperation among selfish individuals. In most of previous studies, objects of punishment are set to be defectors. In this paper, we propose a mechanism of punishment, in which individuals with the majority strategy will punish those with the minority strategy in a public goods game group. Both theoretical analysis and simulation show that the cooperation level can be greatly enhanced by punishing minority. For no punishment or small values of punishment fine, the fraction of cooperators continuously increases with the multiplication factor. However, for large values of punishment fine, there exists a critical value of multiplication factor, at which the fraction of cooperators suddenly jumps from 0 to 1. The density of different types of groups is also studied.

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One-dimensional lackadaisical quantum walks

Cited by 10 publications

References 30 publications

Evolutionary games on multilayer networks: a colloquium

Evolutionary games on multilayer networks: a colloquium

Search by lackadaisical quantum walks with nonhomogeneous weights

Promoting cooperation by punishing minority

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