Continuous-time quantum walks in the presence of a quadratic
perturbation
- URL: http://arxiv.org/abs/2005.06351v4
- Date: Sun, 11 Oct 2020 16:07:11 GMT
- Title: Continuous-time quantum walks in the presence of a quadratic
perturbation
- Authors: Alessandro Candeloro, Luca Razzoli, Simone Cavazzoni, Paolo Bordone
and Matteo G. A. Paris
- Abstract summary: We address the properties of continuous-time quantum walks with Hamiltonians of the form $mathcalH= L + lambda L2$.
We consider cycle, complete, and star graphs because paradigmatic models with low/high connectivity and/or symmetry.
- Score: 55.41644538483948
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We address the properties of continuous-time quantum walks with Hamiltonians
of the form $\mathcal{H}= L + \lambda L^2$, being $L$ the Laplacian matrix of
the underlying graph and being the perturbation $\lambda L^2$ motivated by its
potential use to introduce next-nearest-neighbor hopping. We consider cycle,
complete, and star graphs because paradigmatic models with low/high
connectivity and/or symmetry. First, we investigate the dynamics of an
initially localized walker. Then, we devote attention to estimating the
perturbation parameter $\lambda$ 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 the estimation of the perturbation, we determine the walker
preparations and the simple graphs that maximize the Quantum Fisher
Information. We also assess the performance of position measurement, which
turns out to be optimal, or nearly optimal, in several situations of interest.
Besides fundamental interest, our study may find applications in designing
enhanced algorithms on graphs.
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