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arXiv:2404.01173 · Linear Algebra and its Applications

Strong quantum state transfer on graphs via loop edges

Gábor Lippner, Yujia Shi

Published Oct 10, 2024• 0 citations
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Abstract

We quantify the effect of weighted loops at the source and target nodes of a graph on the strength of quantum state transfer between these vertices. We give lower bounds on loop weights that guarantee strong transfer fidelity that works for any graph where this protocol is feasible. By considering local spectral symmetry, we show that the required weight size depends only on the maximum degree of the graph and, in some less favorable cases, the distance between vertices. Additionally, we explore the duration for which transfer strength remains above a specified threshold.

DOI
10.1016/j.laa.2024.10.008

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We quantify the effect of weighted loops at the source and target nodes of a graph on the strength of quantum state transfer between these vertices. We give lower bounds on loop weights that guarantee strong transfer fidelity that works for any graph where this protocol is feasible. By considering local spectral symmetry, we show that the required weight size depends only on the maximum degree of the graph and, in some less favorable cases, the distance between vertices. Additionally, we explore the duration for which transfer strength remains above a specified threshold.
This dissertation investigates continuous-time quantum walks and asymptotic state transfer in weighted graphs, with a particular focus on the impact of starting and target node weights on transfer fidelity and readout time. Through analysis of the eigenvectors and eigenvalues of the Hamiltonian, we derive quantitative results applicable to generalized graph structures. Our findings focus on the relationship between a graph's maximum degree and the minimum weights required to achieve specific transfer fidelities. This research advances the understanding of quantum state transfer in spin networks, with potential applications in quantum communication and computing.--Author's abstract
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