Complex networks from classical to quantum

Biamonte, Jacob; Faccin, Mauro; Domenico, Manlio De

doi:10.1038/s42005-019-0152-6

Cited by 146 publications

(130 citation statements)

References 106 publications

(186 reference statements)

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“…Unlike more traditionally studied networks-for instance, social networks or the World Wide Web-the topology and function of networks describing innately physical systems are generally subject to additional constraints that can arise from physical factors. Such factors include the spatial embedding of network elements [44] and the specific physical laws governing the construction and dynamics of and on the networks [45,46]. Thus, accompanying the ongoing use of network science to investigate physical systems, there exists a growing interest in developing physically-motivated network approaches that more explicitly take these constraints and laws into consideration.…”

Section: Network Approaches For Physical Systemsmentioning

confidence: 99%

Network architecture of energy landscapes in mesoscopic quantum systems

et al. 2019

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Mesoscopic quantum systems exhibit complex many-body quantum phenomena, where interactions between spins and charges give rise to collective modes and topological states. Even simple, noninteracting theories display a rich landscape of energy states-distinct many-particle configurations connected by spin-and energy-dependent transition rates. The ways in which these energy states interact is difficult to characterize or predict, especially in regimes of frustration where many-body effects create a multiply degenerate landscape. Here, we use network science to characterize the complex interconnection patterns of these energy-state transitions. Using an experimentally verified computational model of electronic transport through quantum antidots, we construct networks where nodes represent accessible energy states and edges represent allowed transitions. We find that these networks exhibit Rentian scaling, which is characteristic of efficient transportation systems in computer circuitry, neural circuitry, and human mobility, and can be used to measure the interconnection complexity of a network. We find that the topological complexity of the state transition networks-as measured by Rent's exponent-correlates with the amount of current flowing through the antidot system. Furthermore, networks corresponding to points of frustration (due, for example, to spin-blockade effects) exhibit an enhanced topological complexity relative to non-frustrated networks. Our results demonstrate that network characterizations of the abstract topological structure of energy landscapes capture salient properties of quantum transport. More broadly, our approach motivates future efforts to use network science to understand the dynamics and control of complex quantum systems. mesoscopic system and metallic reservoirs induce transitions between quantum-mechanical states, and these transitions can be detected through currents flowing in the device. Whether tunneling is allowed depends on the many-body configurations of the quantum system together with the spin and energy of electrons in the reservoirs.A quantum antidot exists as a hill in the electrostatic potential landscape of a two-dimensional electron system; see figure 1(A). Antidots exhibit discrete energy spectra due to magnetic confinement of electron orbital states, and they can be treated as 'dots of holes,' analogous to large quantum dots [5][6][7][8]. In devices, quantum antidots can be coupled to extended, propagating edge modes of the integer quantum Hall fluid, where the tunneling to discrete antidot states is controlled by external voltages; see figure 1(B). Whereas antidot transport near zero bias is typically dominated by a small number of energy states, the relevant number of states for nonequilibrium transport grows rapidly with the applied bias. The additional states relevant for non-equilibrium transport include excited states that result from different spin configurations and orbital excitations. The complexity of the interconnection patterns between these excited state...

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Section: Network Approaches For Physical Systemsmentioning

confidence: 99%

Network architecture of energy landscapes in mesoscopic quantum systems

et al. 2019

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“…By character, the combination of network theory and its applications are multidisciplinary and during the recent years a new area applying network theory and complex networks to quantum physical systems has emerged [8,9]. Furthermore, specific features of quantum networks with no classical equivalent have been reported [10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Reconfigurable optical implementation of quantum complex networks

et al. 2018

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Network theory has played a dominant role in understanding the structure of complex systems and their dynamics. Recently, quantum complex networks, i.e.collections of quantum systems arranged in a non-regular topology, have been theoretically explored leading to significant progress in a multitude of diverse contexts including, e.g., quantum transport, open quantum systems, quantum communication, extreme violation of local realism, and quantum gravity theories. Despite important progress in several quantum platforms, the implementation of complex networks with arbitrary topology in quantum experiments is still a demanding task, especially if we require both a significant size of the network and the capability of generating arbitrary topology-from regular to any kind of non-trivial structure-in a single setup. Here we propose an all optical and reconfigurable implementation of quantum complex networks. The experimental proposal is based on optical frequency combs, parametric processes, pulse shaping and multimode measurements allowing the arbitrary control of the number of the nodes (optical modes) and topology of the links (interactions between the modes) within the network. Moreover, we also show how to simulate quantum dynamics within the network combined with the ability to address its individual nodes. To demonstrate the versatility of these features, we discuss the implementation of two recently proposed probing techniques for quantum complex networks and structured environments.

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“…The model can be viewed as a unitary construction of a quantum state associated to a graph by the interaction of a walker with the spins (which physically define the graph connectivity). As such, the system generalizes the simple quantum walk [33,34], used in particular to study topological phases in condensed mater [35,36], and quantum states associated to graphs, used for instance, to investigate the graph structure, or more generally, multipartite quantum states as a computational resource [37][38][39][40][41]. We found that, for rather general graphs and a set of simple rules for the motion and interactions, the particlespins system evolves towards a thermal stationary state well described by the eigenvectors of the unitary operator.…”

Section: Introductionmentioning

confidence: 99%