Continuous-Time Quantum State Transfer with a Generalized Laplacian

• URL: http://arxiv.org/abs/2509.05454v2
• Date: Thu, 09 Oct 2025 20:09:36 GMT
• Title: Continuous-Time Quantum State Transfer with a Generalized Laplacian
• Authors: Yujia Shi,
• Abstract summary: We study continuous-time quantum walks governed by the Laplacian operator L_k = A+kD.<n>We show that tuning the parameter k can significantly enhance the fidelity of state transfer between endpoints.
• Score: 0.14504054468850663
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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