Continuous-time quantum walks on planar lattices and the role of the magnetic field

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

doi:10.1103/physreva.101.032336

Cited by 15 publications

(8 citation statements)

References 79 publications

(102 reference statements)

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“…Triangular and square lattices are Bravais lattices, while honeycomb and truncated square lattices are not. This difference is reflected in the spreading of CTQWs, which is ballistic on Bravais lattices and subballistic on non-Bravais lattices [81]. A generic vertex in the triangular lattice has degree 6, in the square lattice has degree 4, and both in the honeycomb and in the truncated square lattice has degree 3.…”

Section: E Latticesmentioning

confidence: 99%

Role of topology in determining the precision of a finite thermometer

et al. 2021

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Temperature fluctuations of a finite system follow the Landau bound δT 2 = T 2 /C(T ) where C(T ) is the heat capacity of the system. In turn, the same bound sets a limit to the precision of temperature estimation when the system itself is used as a thermometer. In this paper, we employ graph theory and the concept of Fisher information to assess the role of topology on the thermometric performance of a given system. We find that low connectivity is a resource to build precise thermometers working at low temperatures, whereas highly connected systems are suitable for higher temperatures. Upon modeling the thermometer as a set of vertices for the quantum walk of an excitation, we compare the precision achievable by position measurement to the optimal one, which itself corresponds to energy measurement.

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Section: E Latticesmentioning

confidence: 99%

Role of topology in determining the precision of a finite thermometer

et al. 2021

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“…Triangular and square lattices are Bravais lattices, while honyecomb and truncated square lattice are not. This difference is reflected in the spreading of CTQWs, which is ballistic on Bravais lattices and subballistic on non-Bravais lattices [76]. A generic vertex in the triangular lattice has degree 6, in the square lattice has degree 4, and both in the honeycomb and in the truncated square lattice has degree 3.…”

Section: E Latticesmentioning

confidence: 99%

Role of topology in determining the precision of a finite thermometer

Candeloro,

Razzoli,

Bordone

et al. 2021

Preprint

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Temperature fluctuations of a finite system follows the Landau bound δT 2 = T 2 /C(T ) where C(T ) is the heat capacity of the system. In turn, the same bound sets a limit to the precision of temperature estimation when the system itself is used as a thermometer. In this paper, we employ graph theory and the concept of Fisher information to assess the role of topology on the thermometric performance of a given system. We find that low connectivity is a resource to build precise thermometers working at low temperatures, whereas highly connected systems are suitable for higher temperatures. Upon modelling the thermometer as a set of vertices for the quantum walk of an excitation, we compare the precision achievable by position measurement to the optimal one, which itself corresponds to energy measurement.

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“…( 18), is cumbersome and we can not find a more manageable form of the FI than its explicit definition in Eq. (59).…”

Section: Cycle Graphmentioning

confidence: 99%

Continuous-time quantum walks in the presence of a quadratic perturbation

Candeloro,

Razzoli,

Cavazzoni

et al. 2020

Preprint

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Motivated by their potential use to describe gravity induced perturbations, or next-nearestneighbor tunnelling, we investigate in details the properties of continuous-time quantum walks (CTQW) with Hamiltonians of the form H = L + λL 2 , being L the Laplacian (Kirchoff) matrix of the underlying graph. In particular, we focus attention to CTQW on cycle, complete, and star graphs, as they describe paradigmatic models with low/high connectivity and/or symmetry. At first, we investigate the dynamics of an initially localized walker, looking at the resulting site distribution, mixing, inverse participation ratio, and coherence. We then devote attention to the characterization of perturbation, i.e. the estimation of the perturbation parameter λ using only a snapshot of the walker dynamics. Our analysis shows that a walker on a cycle graph is spreading ballistically independently of the perturbation, whereas on complete and star graphs one observes perturbation-dependent revivals and strong localization phenomena. Concerning characterization, we determine the walker preparations that maximize the Quantum Fisher Information, and assess the performance of position measurement, which turns out to be optimal, or nearly optimal, in several situations of interest. Our study is based on exact analytic derivations supplemented by numerical results, and besides fundamental interest, it may find applications in the design of enhanced algorithms on graphs.

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Continuous-time quantum walks on planar lattices and the role of the magnetic field

Cited by 15 publications

References 79 publications

Role of topology in determining the precision of a finite thermometer

Role of topology in determining the precision of a finite thermometer

Role of topology in determining the precision of a finite thermometer

Continuous-time quantum walks in the presence of a quadratic perturbation

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