Continuous-Time Quantum State Transfer with a Generalized Laplacian

2025/09/05 by Shi, Yujia
#05C50 #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2509.05454

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.

Citations

• Quantum Search with a Generalized Laplacian
• Strong quantum state transfer on graphs via loop edges
• Quantifying State Transfer Strength on Graphs with Involution
• State Transfer on Paths with Weighted Loops
• State Transfer on Graphs
• Perfect Transfer of Arbitrary States in Quantum Spin Networks

Related

• Pair State Transfer
• Pretty good state transfer in discrete-time quantum walks
• Quantifying State Transfer Strength on Graphs with Involution
• Continuous Time Quantum Walks on Graphs: Group State Transfer
• Selected Open Problems in Continuous-Time Quantum Walks