Continuous-Time Quantum State Transfer with a Generalized Laplacian
Quantum Physics
2025-10-13 v2 Combinatorics
Abstract
Quantum walks generated by the adjacency matrix or the Laplacian are known to exhibit low transfer fidelity on general graphs. In this paper, we study continuous-time quantum walks governed by the generalized Laplacian operator L_k = A+kD, where A is the adjacency matrix, D is the degree matrix, and k is a real-valued parameter. Recent work of Duda, McLaughlin, and Wong showed that in the single-excitation Heisenberg (XYZ) spin model, one can realize walks generated by this family of operators on signed weighted graphs. Motivated by earlier studies on vertex-weighted graphs, we demonstrate that for certain graphs, tuning the parameter k can significantly enhance the fidelity of state transfer between endpoints.
Keywords
Cite
@article{arxiv.2509.05454,
title = {Continuous-Time Quantum State Transfer with a Generalized Laplacian},
author = {Yujia Shi},
journal= {arXiv preprint arXiv:2509.05454},
year = {2025}
}