Universality of the fully connected vertex in Laplacian continuous-time quantum walk problems

Razzoli, Luca; Bordone, Paolo; Paris, Matteo G. A.

doi:10.1088/1751-8121/ac72d5

Cited by 6 publications

(3 citation statements)

References 34 publications

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“…Moreover, it is possible to show numerically that the QC-distance for the complete graph is equivalent to that of a larger class of N -nodes graphs, namely those obtained from an N -dimensional complete graph by removing edges that are not connected to the central node |1 . This holds true for the noiseless scenario [36] as well as for the dynamics induced by intrinsic decoherence. If, instead, the initial state is localized on any of the external nodes, we obtain a different distance, that we call D QC (t, e) (see the inset of Fig 1(c)).…”

Section: Star Graphmentioning

confidence: 59%

Decoherence and classicalization of continuous-time quantum walks on graphs

Gabriele

Benedetti

Paris

2022

Quantum Inf Process

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We address decoherence and classicalization of continuous-time quantum walks (CTQWs) on graphs. In particular, we investigate three different models of decoherence and employ the quantum-classical (QC) dynamical distance as a figure of merit to assess whether, and to which extent, decoherence classicalizes the CTQW, i.e. turns it into the analogue classical process. We show that the dynamics arising from intrinsic decoherence, i.e. dephasing in the energy basis, do not fully classicalize the walker and partially preserves quantum features. On the other hand, dephasing in the position basis, as described by the Haken–Strobl master equation or by the quantum stochastic walk (QSW) model, asymptotically destroys the quantumness of the walker, making it equivalent to a classical random walk. We also investigate how fast is the classicalization process and observe a larger rate of convergence of the QC-distance to its asymptotic value for intrinsic decoherence and the QSW models, whereas in the Haken–Strobl scenario, larger values of the decoherence rate induce localization of the walker.

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Section: Star Graphmentioning

confidence: 59%

Decoherence and classicalization of continuous-time quantum walks on graphs

Gabriele

Benedetti

Paris

2022

Quantum Inf Process

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“…The performance of spatial search has been recently investigated in Erdős-Rényi networks [99] as well as networks characterized by a finite spectral dimension [100]. Steps towards necessary and sufficient conditions for a graph to provide optimal spatial search were taken in [101,174,175] where the spectral properties of the network and a dimensionality reduction method were leveraged to reach the main conclusions, respectively. Taken together, the results suggest that spatial search and similar algorithms originally proposed for completely connected networks or lattices may continue to work well also in complex networks.…”

Section: Walkers and Search Algorithmsmentioning

confidence: 99%

Complex quantum networks: a topical review

Nokkala,

Piilo,

Bianconi

2024

J. Phys. A: Math. Theor.

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These are exciting times for quantum physics as new quantum technologies are expected to soon transform computing at an unprecedented level. Simultaneously network science is ﬂourishing proving an ideal mathematical and computational framework to capture the complexity of large interacting systems. Here we provide a comprehensive and timely review of the rising ﬁeld of complex quantum networks. On one side, this subject is key to harness the potential of complex networks in order to provide design principles to boost and enhance quantum algorithms and quantum technologies. On the other side this subject can provide a new generation of quantum algorithms to infer signiﬁcant complex network properties. The ﬁeld features fundamental research questions as diverse as designing networks to shape Hamiltonians and their corresponding phase diagram, taming the complexity of many-body quantum systems with network theory, revealing how quantum physics and quantum algorithms can predict novel network properties and phase transitions, and studying the interplay between architecture, topology and performance in quantum communication networks. Our review covers all of these multifaceted aspects in a self-contained presentation aimed both at network-curious quantum physicists and at quantum-curious network theorists. We provide a framework that uniﬁes the ﬁeld of quantum complex networks along four main research lines: network-generalized, quantum-applied, quantum-generalized and quantum-enhanced. Finally we draw attention to the connections between these research lines, which can lead to new opportunities and new discoveries at the interface between quantum physics and network science.

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“…Making the central vertex the trap preserves such a symmetry and the resulting transport Hamiltonian (4) is invariant under the permutation of all the outer vertices. Since the trap is a fully connected vertex, the subspace (7) for the transport Hamiltonian (4) is the same as that of the complete 024118-8 graph and is spanned by the states (11) [64]. Therefore, the transport efficiency for an initial localized state is (12) and that for an initial superposition of two vertex states is (13).…”

Section: Star Graph: Central Trapmentioning

confidence: 99%

Perturbed graphs achieve unit transport efficiency without environmental noise

et al. 2022

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Coherent transport of an excitation through a network corresponds to continuous-time quantum walk on a graph, and the transport properties of the system may be radically different depending on the graph and on the initial state. The transport efficiency, i.e., the integrated probability of trapping at a certain vertex, is a measure of the success rate of the transfer process. Purely coherent quantum transport is known to be less efficient than the observed excitation transport, e.g., in biological systems, and there is evidence that environmental noise is indeed crucial for excitation transport. At variance with this picture, we here address purely coherent transport on highly symmetric graphs, and show analytically that it is possible to enhance the transport efficiency without environmental noise, i.e., using only a minimal perturbation of the graph. In particular, we show that adding an extra weight to one or two edges, depending on whether the initial state is localized or in a superposition of two vertex states, breaks the inherent symmetries of the graph and may be sufficient to achieve unit transport efficiency. We also briefly discuss the conditions to obtain a null transport efficiency, i.e., to avoid trapping.

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Universality of the fully connected vertex in Laplacian continuous-time quantum walk problems

Cited by 6 publications

References 34 publications

Decoherence and classicalization of continuous-time quantum walks on graphs

Decoherence and classicalization of continuous-time quantum walks on graphs

Complex quantum networks: a topical review

Perturbed graphs achieve unit transport efficiency without environmental noise

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