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arXiv · 2509.05454

Continuous-Time Quantum State Transfer with a Generalized Laplacian

Yujia Shi
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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.

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Yujia Shi. 2025-09-05. Continuous-Time Quantum State Transfer with a Generalized Laplacian. https://arxiv.org/abs/2509.05454

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